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IntroductionA band pass filter is an electronic device or circuit that allows signals between two specific frequencies to pass. That is, allowing signals in a specific frequency band to pass while shielding other frequency bands. In other words, a band-pass filter attenuates frequency components in other ranges to an extremely low level, as opposed to the concept of a band-stop filter. For example, the RLC tank is an analog band-pass filter, it is a resistor - inductor - capacitor circuit (RLC circuit). These filtering circuit can also be made by connecting low-pass filters and high-pass filters.How to Design Band Pass Filter CircuitCatalogIntroductionⅠ Band Pass Filter Circuit CharacteristicsⅡ Band Pass Filter Parameters2.1 Center Frequency2.2 Cut-off Frequency2.3 Bandwidth2.4 Quality FactorⅢ Types of Band Pass Filter3.1 Active Band Pass Filter3.2 Passive Band Pass FilterⅣ Band Pass Filter Equation4.1 Cutoff Frequency of Band Pass Filters4.2 General Form of Second-order BPF Transfer Function4.3 Second-order Band Pass Filters4.4 High-Q second-order Band Pass Filters4.5 Dual-operational Amplifier BPF (High-Q)4.6 Second-order Band Pass Filters (Voltage-controlled Type)Ⅴ Band Pass Filter ApplicationsⅠ Band Pass Filter Circuit CharacteristicsAn ideal band pass filter should have a completely flat pass band, no amplification or attenuation. And all frequencies outside the pass band will be completely attenuated. In addition, the conversion outside the pass band is completed in an extremely small frequency range. But in fact, there is no ideal band-pass filter. Because the filter cannot completely attenuate all frequencies outside the desired frequency range, especially there is an attenuated but not isolated frequency range outside the desired pass band. This is usually called the filter roll-off phenomenon, and it is expressed in dB per decade of attenuation amplitude. Generally, the filter design should ensure that the roll-off range is as narrow as possible, so that the performance of the filter is closer to the design requirement. However, as the roll-off range gets smaller and smaller, the pass band becomes no longer flat and causes ripples.The high-pass filter has a low cut-off frequency, and the low-pass filter has a high cut-off frequency. When the high cut-off frequency is lower than the low cut-off frequency, combining the two circuits, and it is possible to design a band pass filter. The gain of the band pass filter is adjusted by the feedback resistor and the current limiting resistor.Figure 1. Band Pass Filter Circuit PartsA band pass filter with a high quality factor refers to a filter with a narrow pass band. In other words, a high-Q factor means that fewer unwanted frequency signals will pass. A low-Q factor means that the pass band is very wide, to allow a wider range of frequencies to pass through.  Ⅱ Band Pass Filter Parameters2.1 Center FrequencyIt usually defined as the midpoint between the two 3dB points of a band pass filter (or a band stop filter), generally expressed by the arithmetic average of the two 3dB points. It is a frequency when the impedance of the entire circuit is a real number.2.2 Cut-off FrequencyIt refers to the frequency point on the right of the low-pass filter and the frequency point on the left of the high pass filter in the pass band. That is, the boundary frequency. It is usually defined as a standard by 1dB or 3dB relative loss point. The band pass filter has two cutoff frequencies, the low cutoff frequency fp1 and the high cutoff frequency fp2. 2.3 BandwidthThe difference between two cut-off frequencies. The bandwidth is defined as B=fp2－fp1.2.4 Quality FactorThe reciprocal of the damping coefficient is called the quality factor, which is an important indicator of the frequency selection characteristics of band pass and band stop filters. In short, it is the ratio of the center frequency to the bandwidth. What’s more, it can be used to describe the shape of the transfer function graph. Ⅲ Types of Band Pass Filter3.1 Active Band Pass FilterFigure 2. Active Band Pass Filter CircuitThe active band pass filter is a cascade of high-pass and low-pass filters and amplifier components. The circuit diagram of the active band pass filter consists of three parts. The first part is the high-pass filter. Then, use the op amp for amplification. The last part of the circuit is the low-pass filter.3.2 Passive Band Pass FilterFigure 3. Passive Band Pass Filter CircuitPassive band pass filters are a combination of passive high-pass and low-pass filters. Passive filters use only passive components, such as resistors, capacitors, and inductors. Therefore, passive band pass filters are also used as passive components and do not use op amps for amplification. Ⅳ Band Pass Filter Equation4.1 Cutoff Frequency of Band Pass FiltersThe characteristic of the band pass filter is that the output signal amplitude in the pass band is independent from the frequency. When f<fp1 or f>fp2, the output signals attenuate quickly. The amplitude-frequency characteristics are shown in the figure:Figure 4. BPF Bandwidth(The broken line is the ideal BPF frequency characteristic, and the solid line is the actual BPF frequency characteristic)The resonance frequency is between fp1 and fp2, where the gain of the filter is the largest, and the bandwidth of the filter is the difference between fp2 and fp1.It can be seen from the frequency characteristics of BPF that it can be composed of LPF and HPF in series, as long as the fpL of LPF (ie, fp2 of BPF) is greater than fpH of HPF (ie, fp1 of BPF).4.2 General Form of Second-order BPF Transfer FunctionFrequency CharacteristicsWhere Aup is the pass-band magnification, center frequency , Q factor Normalized frequency characteristicsNormalized amplitude - frequency characteristicsFigure 5. Amplitude - frequency CharacteristicsFigure 6. Frequency CharacteristicsIt can be seen that the frequency characteristic of the band pass filter is completely determined by the center frequency ωo and the quality factor Q.When f>fo, as the frequency f increases, the amplitude increases. According to the definition of cutoff frequency, the denominator of amplitude-frequency characteristic , that is (since f>fo, take a positive value)1) Upper cutoff frequency（take a positive value）When f<fo, as the frequency f decreases, the output signal amplitude will decrease. According to the definition of cutoff frequency, the denominator of amplitude-frequency characteristic , that is (since f<fo, take a negative value)2) Lower cutoff frequency（take a negative), get the bandwidth When the center frequency fo and bandwidth B (or Q) are known, the upper and lower cutoff frequencies fp1 and fp2 can be calculated. On the contrary, when the upper and lower cutoff frequencies fp1 and fp2 are known, the center frequency fo and bandwidth B (or Q) can be calculated. (where ),  4.3 Second-order Band Pass FiltersA simple second-order band pass filter circuit is shown in the figure below, where R1 and C1 constitute a low-pass filter circuit, and C2 and R3 constitute a high-pass filter circuit.Figure 7. Second-order Band Pass Filter Circuit(1) Transfer FunctionIn order to reduce the amount of parameters matching, generally take C1=C2=CTake , , that is The transfer function can be obtained by using the node current method.(2) Frequency Characteristicswhere band-pass amplification (The negative sign means that the input and output are inverted. Because the filter circuit is an inverting filter.)Center frequency (C1=C2=C), Q factor When Aup, Q, and ωo are known, the resistance of each resistor is (R3 can be calculated with ωo/Q), (Aup<2Q2)When the pass band amplification factor Aup is small, Q should not be too large (that is, the simple second-order BPF has poor selectivity), otherwise R2 will become very small (R2 is generally greater than 1K), which will attenuate the input signal seriously. In order to make the system stable, Aup is generally between 1 and 10, and Q can be between 1 and 20.(3) Design StepsExample: It is known that Aup=5, center frequency fo=450Hz, bandwidth B=200Hz (). Try to calculate the parameters of the band-pass filter and verify.First, according to the center frequency fo, check the parameter table and determine C1, C2, and operational amplifier parameters according to the nominal value.fo=450Hz, take C1=C2=0.01uF(103 capacitor). Since the center frequency is not high, the requirement can be met by using LM358 operational amplifier.Second, calculate the resistance of each resistor. Among them, the range of R1 and R3 should be between 10K ~510K, and R2 should be between 1K ~100K, otherwise the capacitor C needs to be reselected.Substituting the relevant parameters into the above formula, the result is R1=15.9K, R2=15.5K, R3=159K.Third, use simulation software to verify on the computer, and try to take the nominal value of each relevant resistance. The simulation schematic diagram and simulation results are shown in the figure below. The result values obtained from the AC small signal analysis and transmission characteristic analysis basically meet the requirements.Figure 8. Filtering Circuit with LM358Figure 9. Simulation Schematic DiagramFigure 10. Voltage - Time Simulation (ui)Figure 11. Voltage - Time Simulation (ui, uo)The circuit requires a small number of components, and it can work with dual power supplies or with a single power supply (the non-inverting termination is connected to a 1/2Vcc bias potential). In fact, it is widely used in single power supply systems. Because the quality factor Q cannot be too high. Almost all band pass filter circuits with a larger bandwidth B (with a smaller Q value) adopt this circuit form. 4.4 High-Q second-order Band Pass FiltersThe high-Q second-order band pass filter circuit is shown in the following figure. This circuit can work with dual power supplies or single power supplies, which is convenient to use in a single power supply system. Since the Q value can be made larger, it is particularly suitable as a band pass filter.Figure 12. Bandpass Filter Circuit(1) Transfer FunctionIn order to reduce the amount of parameters matching, generally take C1=C2=CWhere , , that is , , getting The transfer function can be obtained by using the node current method.(2) Frequency Characteristics, where band-pass amplification Center frequency , Q factor In order to make the system stable, Aup and Q must be greater than 0, that is, 2RfR4-RFR3>0, which must be guaranteed . Adjusting can control Aup and Q. is more closer to 2, the greater the Aup and Q values. Adjust the capacitor C to select the center frequency ωo. When the values of Aup, Q and ωo are known, and the ratio between and is determined, the resistance of each resistor is , , (3) Design stepsExample: It is known that Aup=5, center frequency fo=1kHz, bandwidth B=50Hz (). Try to calculate the parameters of the band-pass filter and verify.First, according to the center frequency fo, check the parameter table and determine C1, C2, and operational amplifier parameters according to the nominal value. (Aup: 1 ~10)fo=1kHz, take C1=C2=0.01uF. Since the center frequency is not high, the requirement can be met by using LM358 operational amplifier.Second, according to the value of Aup and Q, initially determine the value of and .Since Aup and Q are large, is 1.8, is 0.5, and is 3.6.Third, calculate the resistance of each resistor. The range of R1 and R3 should be between 10K and 510K, and R2 should be between 1K and 100K. Otherwise, the ratio of and needs to be reselected.Substituting the relevant parameters into the above formula, the result is:R1=229K, R3=63.7K, R2=4.18K, R4=127.4K: RF takes 36K, Rf takes 10K.Fourth, use simulation software to verify on the computer, and try to take the nominal value of each relevant resistance. The simulation schematic diagram and simulation results are shown in the figure below. The result values obtained from the AC small signal analysis and transmission characteristic analysis basically meet the requirements.Figure 13. High-Q BPF CircuitFigure 14. Voltage - Frequency SimulationFigure 15. Voltage - Time Simulation4.5 Dual-operational Amplifier BPF (High-Q)The BPF circuit with high-Q value formed by dual operational amplifiers is shown in the figure. With fewer components, a very high-Q value can be obtained when the pass band amplification factor Aup is fixed equal to 2, so it is also a commonly used BPF circuit.Figure 16. Dual-amp BPF(1) Transfer functionAccording to the rule of futility, where, , that is , where , so (2) Frequency CharacteristicsCompared with the standard form of the second-order BPF transfer function, the following parameters can be obtained:pass-band magnification , , center frequency When R4=R5,R2=R3=R,C1=C2=C, Aup=2, , （）It can be seen that when Aup=2 (that is, when R4=R5), the value of Q can be very large.(3) Design stepsAccording to the center frequency fo, check the parameter table to determine C. When C is determined, the resistance R is calculated from the center frequency. Meanwhile, etermine R1 based on the Q value. 4.6 Second-order Band Pass Filters (Voltage-controlled Type)The second-order voltage-controlled BPF is shown in the figure. Among them, R1 and C1 constitute a low-pass filter, R2 and C2 constitute a high-pass filter. (The voltage positive feedback is introduced through the voltage R3 to form a voltage-controlled band-pass filter.)Figure 17. Second-order Bandpass Filter (voltage controlled)Rf/RF cannot be 3 to avoid self-excitation.(1) Transfer FunctionWhere ，that is , , so The transfer function can be obtained by using the node current method.In order to reduce the amount of parameters matching, generally take R1=R3=R,R2=2R,C1=C2=CWhere In order to make the system stable, the coefficient of the first term in the denominator must be larger than 0, that is, 3−Auf>0, in other words, Auf<3.(2) Amplitude - frequency Characteristicswhere band-pass amplification , center frequency , Q factor It can be seen that the closer Auf is to 3, the larger the Q value. The narrower the pass band B, and the better the selectivity.(3) Design StepsAccording to the center frequency, look up the table and initially determine C1=C2=Ccalculate resistance , that is , Calculate bandwidth based on upper and lower cutoff frequencies , Calculate the quality factor Calculate by Q and determine the resistances Rf and RF.As a special case, the center frequency fo=1KHz is known, so C1=C2=C=0.01uF，R2=2R=31.8K, getting Auf=2.95, that is . If Rf=10K, calculate RF=19.5K.For high pass and band pass filters, the output of the op amp is not required to be 0 at static state. And the single power supply operating mode can be selected. In the low-pass or band-stop filter circuit, it is a DC-to-AC DC amplifier circuit, which generally requires the circuit to work in a dual power supply state. Ⅴ Band Pass Filter ApplicationsThe filtering circuit has a wide range of uses.According to different frequency amplitude characteristics, filter circuits can be divided into low pass filter circuit (LPF), high-pass filter circuit (HPF), band pass filter circuit (BPF), band stop filter circuit (BEF) and all-pass filter circuit (APF) . The BPF is mainly used to highlight signals in useful frequency bands and weaken signals or interference and noise in other frequency bands to improve the signal-to-noise ratio. Therefore, band pass filters are often used in wireless receivers and transmitters to receive useful signals while preventing unwanted frequencies from passing through.In addition to the fields of electronics and signal processing, an specific application of band pass filters is in the field of atmospheric sciences. A very common example is to use it to filter the weather data in the last 3 to 10 days, only the cyclone as a disturbance remains in the domain. Frequently Asked Questions about Band Pass Filter1. What is a bandpass filter used for?A band pass filter is an electronic circuit or device which allows only signals between specific frequencies to pass through and attenuates/rejects frequencies outside the range. Band pass filters are largely used in wireless receivers and transmitters, but are also widely used in many areas of electronics. 2. What is the bandwidth of a bandpass filter?The bandwidth of a bandpass filter is usually defined as the 3 dB bandwidth. Similarly, the 1 dB bandwidth is the point at which the signal amplitude decreases by 1 dB from its maximum value (above and below the center frequency). 3. How does bandpass filter work?A bandpass filter works to screen out frequencies that are too low or too high, giving easy passage only to frequencies within a certain range. Band-pass filters can be made by stacking a low-pass filter on the end of a high-pass filter, or vice versa. Attenuate means to reduce or diminish in amplitude. 4. How is bandpass filter calculated?So all frequencies between the low cutoff frequecny and the high cutoff frequency are the passband of the bandpass filter. The gain of the circuit is determined by the formula, gain (AV)= -R2/R1. Thus, for example, to have a gain of 10, R2 must be 10 times the value of R1. 5. What is the use of band pass filter?Bandpass filters are widely used in wireless transmitters and receivers. The main function of such a filter in a transmitter is to limit the bandwidth of the output signal to the band allocated for the transmission. This prevents the transmitter from interfering with other stations.

IntroductionLED lights cannot directly use the conventional mains grid voltage, because of the characteristics of LED lighting. In order to meet the special voltage and current requirements of LEDs, a specially designed voltage conversion device must be used to make LEDs work normally. This device is an LED driver. LED drivers are usually switching mode devices that convert the input voltage (Typically 120-220 VAC or 12 VDC) into a voltage at which the current drawn by the LED's is equal to its drive current. The drive current is regulated for optimum brightness, led service life, and battery life. A drive current lower than the maximum drive current of an LED can greatly prolong service life. As a key part of LED lighting, the quality of LED drivers directly affects the performance of LED lighting.Choose the Correct LED Drivers For LED LightsNo matter how good the quality of the LED driver is, failure and maintenance are inevitable. This article will analyze the 10 failures in LED lighting design and its application based on the relevant technology and practical experience of the LED driver.CatalogIntroductionⅠ LED Driver Failure Analysis1.1 Forward Voltage Drop (Vf) Range1.2 Power Margin and Derating Requirements1.3 LED Working Characteristics1.4 Test Session1.5 Different Load with Different Test Results1.6 LED Driver Circuit Problem1.7 Wrong Phase Wring1.8 Grid Fluctuation1.9 Frequent Line Trips1.10 Drive CoolingⅡ LED Driver Maintenance2.1 Multimeter to Detect LED Driver2.2 Identify LED Power SupplyⅢ LED Driver Circuit Modulation3.1 Pulse Width Modulation (PWM)3.2 Pulse Frequency Modulation (PFM)3.3 Sliding-Mode ModulationⅣ One Question Related to LED DriverⅠ LED Driver Failure AnalysisThe LED driver is measuring current passing through LEDs using sense resistor and then increase or decrease the voltage to maintain constant current continuously. LEDs are kind of diode so they need DC voltage to operate so most of the LED drivers are boost and can vary output supply in wide range (example, 16V to 38V). They also have dimming control by PWM signal from microcontroller OR by having a manual potentiometer to change sense resistor. According to them, LED driver failures are complex, but we can follow the steps below to analyse.1.1 Forward Voltage Drop (Vf) RangeLED lamp load end is generally composed of a number of LEDs connected in series, and its working voltage Vo=Vf×Ns, where Ns represents the number of LEDs. And the Vf of an LED varies with temperature. Generally, at a constant current, Vf becomes lower at high temperatures and becomes higher at low temperatures. The LED lamp load working voltage is VoL at high temperature, and VoH represents a value at low temperature. When selecting an LED driver, consider that the driver output voltage range is greater than VoL～VoH.If the maximum output voltage of the LED driver is lower than VoH, the maximum power of the lamp may not reach the actual power required at low temperature. If the minimum voltage of the selected LED driver is higher than VoL, the output of the driver may exceed the working range at high temperature. And LED driver will work unstable, making the lights flicker.Considering the overall cost and lamp efficiency, don’t blindly pursue the ultra-wide output voltage range of the LED driver. Because the driver voltage is only in a certain range, its efficiency is the highest. When the range is exceeded, the efficiency and power factor (PF) will deteriorate. In addition, if the design of the driver output voltage range is too wide, high costs and unoptimized efficiency will be made. 1.2 Power Margin and Derating RequirementsIn general, the nominal power of the LED driver refers to the data measured under the rated environment and rated voltage. Taking into account different applications, most LED driver suppliers will provide power derating curves in their product specifications (common load vs. ambient temperature derating curves and load vs. input voltage derating curves).As shown in Figure 1, the red curve represents the power derating curve when the input is 120Vac, and its load varies with the ambient temperature. When the ambient temperature is lower than 50℃, the LED driver is allowed to be 100% full load. When the ambient temperature is as high as 70℃, the LED driver can only be derated to 60% of the load. When the ambient temperature changes between 50℃~70℃, the driver load varies with the temperature linearly.Figure 1. Power Derating Curve (Load vs Ambient Temperature)The blue curve represents the power derating curve when the input is 230Vac or 277Vac, and its load varies with the ambient temperature. The principle is similar to the above mentioning.As shown in Figure 2, the blue curve represents the derating curve of the LED driver when the ambient temperature is 55°C, its output power varies with the input voltage. When the input voltage is 140Vac, the load of the driver is allowed to be 100%, and the input voltage will be adjusted downward. If the output power remains the same, the input current will rise, resulting in input terminal loss and lower efficiency. When the device temperature rises, exceeding the rated temperature, which may cause the device to fail.Figure 2. Power Derating Curve (Load vs Input Voltage)Therefore, when the input voltage is less than 140Vac, the output load of the LED driver is required to linearly decrease as the input voltage decreases. According to the above derating curve and corresponding requirements, when choosing a LED driver, actual applying needs are important, as well as the derating margin. 1.3 LED Working CharacteristicsWhen the required input power is a fixed value, such as a fixed error of 5%, the output current can only be adjusted to the specified power for each lamp. Due to different working ambient temperature and different lighting time, the power of each lamp will vary greatly.Although there are considerations for marketing and business factors. However, the volt-ampere characteristic of the LED lamp determines that the LED driver is a constant current source, and its output voltage varies with the series voltage Vo of the LED load. When the efficiency of the driver is basically unchanged, its input power changes with Vo. And meanwhile, the overall efficiency of the LED driver will increase after thermal equilibrium. Under the same output power, the input power will decrease compared to the boot time.Therefore, when formulating requirements, LED driver users should first understand the operating characteristics of LEDs. Avoid suggesting indicators that do not meet the principles of operating characteristics, and indicators that far exceed actual requirements, resulting in excess quality and cost waste. 1.4 Test SessionSample test problems, for example, multi-brand LED driver samples all failed during the test. The reason is that a self-dual voltage regulator is used to directly power the LED driver for testing. After power on, the voltage regulator is gradually adjusted from 0Vac to the rated operating voltage of the LED driver. This kind of test operation can easily make the LED driver start and work with the load when the input voltage is very small, but this situation will cause the input current to be far greater than the rated value. And the internal input terminal related components, such as fuses, rectifier bridges, thermistors, etc. will fail due to excessive current or overheating, damaging the LED driver.The correct test method is to adjust the voltage regulator to the rated operating voltage range of the LED driver, and then connect the driver to power-on test. Of course, technically improving the design can also avoid the failure caused by this kind of test misoperation. That is, a starting voltage limit circuit and an input undervoltage protection circuit are set at the input of the driver. When the input does not reach the start-up voltage set by the driver, the driver does not work. When the input voltage drops to the input undervoltage protection point, the driver enters the protection state. Although the driver has a self-protection function and will not fail, you must carefully understand whether the purchased LED driver product has this protection before testing (considering the actual application environment of the LED driver, most LED drivers currently do not have this set). 1.5 Different Load with Different Test ResultsOn the one hand, when the LED driver is tested with LED lights, the result is normal; on the other hand, when driver tested with an electronic load, the result may be abnormal. Usually this phenomenon has the following reasons:1) The output instantaneous voltage or power of the driver exceeds the working range of the electronic load instrument. (Especially in CV mode, the maximum test power should not exceed 70% of the maximum power of the load. Otherwise, the load may instantaneously have overpower protection when loading, causing the driver to fail to work.)2) The characteristics of the electronic load instrument used are not suitable for measuring constant-current device. And the load voltage gear jumping, result in the drive to fail to work.3) Because there is a large capacitor inside the input of the electronic load meter. The test is equivalent to connecting a large capacitor in parallel with the driver output, which may cause the driver's current sampling work to be unstable. As we all known, the LED driver is designed to meet the working characteristics of LED lamps. The most practical test method is to use the LED lamp as a load, and connects an ammeter and a voltmeter in series to test. 1.6 LED Driver Circuit ProblemThe following conditions often cause damage to the LED driver:Connect AC to the DC output terminal of the driver, causing the driver to fail.Connect AC to the DC/DC output or input of the driver, causing the driver to fail.Connect the output terminal of the constant current to the dimming light, causing the driver to fail.Connect the phase wire to the ground wire causing the driver has no output and the housing is charged. 1.7 Wrong Phase WringTake an international example: the rated working voltage between each phase line and the neutral line is 220V, and the voltage between the phase line and the phase line is 380V. If the driver is connected to two phase wires, after power on, the LED driver input voltage exceeds the rated range, which cause the product to fail.As shown in Figure 3, V1 represents the first phase voltage, V2 represents the second phase voltage, and R1 and R2 respectively represent the drivers normally installed on the line. When the neutral line (N) on the circuit is disconnected, the drivers R1 and R2 on the two branches are connected to the 380V voltage after being connected in series. Because of the difference in input internal resistance, when one of the drivers is charged to start, the internal resistance becomes smaller. Most of the voltage may be applied to another driver, causing the overvoltage damage. Therefore, it is recommended that switches or short-circuiters on the same distribution branch should be disconnected together, not just cut off the neutral line. What’s more, do not put the power distribution fuse on the neutral line to avoid bad effect of the neutral line on the circuit.Figure 3. Neutral Line Open Circuit Diagram 1.8 Grid FluctuationWhen wires of a transformer grid branch is too long and there is large power equipment on the branch, the grid voltage will fluctuate sharply when the large equipment starts and stops. It even causes the grid to be unstable. When the grid voltage exceeds 310V, the drive may be damaged (even if there is an LED lightning protection device, it is useless. Because the lightning protection device is to deal with pulse spikes of tens of uS level, and the fluctuation of the grid may reach tens of mS, or even hundreds of mS) . Therefore, special attention should be paid when there is large electric machinery on the street lighting branch power grid. It is best to monitor the fluctuation range of the power grid or to supply power to the grid transformer separately. 1.9 Frequent Line TripsToo many lights are connected on the same branch, which leads to overload on a certain phase and uneven power distribution among the phases, resulting in frequent line trips. 1.10 Drive CoolingAlthough the LED has high luminous efficiency, only a small part of the energy flowing through the LED is radiated in the form of visible light. And most of the remaining energy is consumed in the LED in the form of heat, so the LED generates more serious heat. When the driver is installed in a non-ventilated environment, the driver housing should be in contact with the lamp housing as much as possible. If possible, apply thermal glue or a thermal pad on the contact surface between the housing and the lamp housing to improve the heat dissipation of the LED driver and ensure the reliability of the driver.Ⅱ LED Driver Maintenance2.1 Multimeter to Detect LED DriverMeasuring the output voltage of the no-load LED driver with a multimeter, if the output voltage is not detected, does it mean that the driver is broken? Look at the following steps:1) The voltage of the non-isolated LED power supply in the no-load state is about 300V tested with a multimeter, and it is about 220V with a PFC.2) Isolating the LED power supply, the voltage in the no-load state, tested with a multimeter, is about 3-5V more than the total voltage of the rated LED series. However, although the output voltage can be tested under no load, it does not mean that it can be normal under load. At this time, it is necessary to connect the corresponding LED light board to see the performance of the LED lighting. If there is no flicker, the output voltage is also equal to the total voltage of LED lights in series connection. This situation can be considered normal, otherwise it fails. If there is no output voltage at no load, the power supply must be broken. 2.2 Identify LED Power SupplyThe LED power supply is widely used in many applications. So how to distinguish the quality of LED power supply is particularly important. A few methods are briefly introduced below. LED Driver ICThe power of IC drive, the quality of IC directly affects the whole power supply. The lighting manufacturer should understand the IC design solution and calculate the cost of the driver, so as to purchase power products at a reasonable price. TransformersThe control chip can be regarded as the brain center of the power supply, while the transformers determine the power and temperature resistance. The transformer is responsible for the transfer of "AC to DC". However, the energy overload will damage the device. The core of the transformer is the magnetic core and the wire package. Electrolytic Capacitors and Ceramic CapacitorsThe quality and life requirements of input electrolytic capacitors are important. However, people tend to ignore the quality requirements of the output capacitor. In fact, the life of the output capacitor also has a great impact on the life of the power supply. The output end has a switching frequency of up to 60,000 times per second, which causes the parasitic resistance of the capacitor to heat up and produce substances similar to scale. Finally, the electrolyte heats up and bursts. Ceramic capacitors: The materials are divided into X7R, X5R and Y5V, and the actual capacitance value of Y5V can only reach 1/10 of the actual value. In addition, the nominal capacitance value only refers to when a capacitor works at 0V. Therefore, this tiny chip with poor options will also lead to a price difference in cost and greatly shorten the life of the power supply. Circuit Design and Welding ProcessJudgment of the pros and cons of the design: Aside from the professional point of view, it can be distinguished by some intuitive methods, such as the neat layout of the components, and soldering points. As for flying leads and manually adding components, it is a serious lack of techniques and efficiency. As we all know, the quality of mechanized production of wave soldering process is definitely better than manual welding. Because the machining process is more neat and uniform. Identification method: whether there is red glue on the back board.The flashing phenomenon of the lamp after a period of use is basically caused by the power supply or the weak welding of the lamp beads. However, it is extremely difficult to detect the virtual welding of products through aging, so AOI must be used to detect the quality of the power supply. Batch Inspection of Aging Racks and High Temperature Aging RoomsNo matter how good the power products are controlled by materials and production processes, they still need to be tested for aging. Because the incoming inspection of electronic components and transformers is difficult to control. Only through the aging of the entire batch of power supplies and the high temperature sampling inspection of the high temperature room. This is a wide-ranging screening to determine whether the materials have safety hazards. Ⅲ LED Driver Circuit ModulationThe LED driver circuit is divided into constant-voltage type and constant-current type according to the power supply to the LED. Constant-current switch type LED driver circuit samples the current flowing through the LED lamp, and gives the output control signal to control the on and off of the switching power tube, which aims to adjust the output current as the set value. The dimming control circuit mainly includes SCR dimming circuit, pulse width modulation (PWM), pulse frequency modulation (PFM), sliding mode control, PWM_PFM, PSM, etc. Let's take pulse width modulation (PWM), pulse frequency modulation (PFM), and sliding mode modulation to introduce in detail below. 3.1 Pulse Width Modulation (PWM)Pulse width modulation, shown in the figure below, refers to the stability of the output voltage by changing the on-time of the switching power tube in each cycle at a specific frequency. That is adjusting the duty cycle to obtain stable output voltage. When the output voltage changes due to the working environment, noise and other factors, the error amplifier samples the voltage change and sends the signal to the control circuit. The control circuit adjusts the duty cycle of the switching power tube signal to maintain the stability of the output voltage.Figure 4. PWM Modulation Based on BUCK StructureFigure 4 (a). Voltage ModeFigure 4 (b). Peak Current ModeFigure 4 (c). Average Current Mode3.1.1 Advantages of PWM(1) The PWM modulation method has high efficiency under heavy load, and has a good dynamic response to load changes.(2) The output ripple voltage is small and the linearity is high.(3) The frequency is stable, the duty cycle adjustment is not restricted, the control is simple, and both the current control mode and the voltage control mode are applicable.3.1.2 Disadvantages of PWM(1) The efficiency of PWM modulation method decreases at light load.(2) The transient response is slow during constant-voltage driving, and a more complicated compensation circuit is required.(3) Accurate current detection circuit is required for constant-current driving. 3.2 Pulse Frequency Modulation (PFM)The pulse frequency modulation is shown in the figure below. Under the condition of a certain on-time of the switching power tube, the output voltage can be controlled by adjusting the off time. When the output voltage changes, the error amplifier samples the feedback signal and sends the output signal compared with the reference signal to the control circuit. The control circuit analyzes the error signal and generates a square wave signal with constant pulse width and varying frequency to control the switch power tube to maintain the stability of the output voltage.Figure 5. Pulse Frequency Modulation Based on BUCK Structure3.2.1 Advantages of PFM(1) The PFM modulation has very high efficiency, better frequency characteristics and higher voltage regulation rate at light load.(2) The PFM modulation has a relatively high transmission signal-to-noise ratio and a good anti-interference ability.(3) The output voltage has a large adjustable range and low power consumption.3.2.2 Disadvantages of PFM(1) The efficiency of the PFM modulation will decrease under heavy load.(2) The frequency spectrum of the output ripple is scattered and irregular.(3) The load adjustment range is very small, resulting in high filtering costs. 3.3 Sliding-Mode ModulationSliding-mode modulation mode, the full name is sliding mode variable structure control,  is a discontinuous control. As shown in Figure 6, the sliding mode makes the system structure change purposefully according to its current state, which force the system to make small amplitude and high frequency up and down movements along the designed trajectory under response conditions. That is, sliding mode movement. Reduce the system's sensitivity to disturbances and load jumps.Figure 6. Sliding Mode Control Based on BUCK Structure3.3.1 Advantages and Disadvantage of Sliding ModeIt has the advantages of fast dynamic response, strong robustness and wide stability range, but it also has a problem that the operating frequency is not fixed. Ⅳ One Question Related to LED Driver4.1 QuestionHow long do LED drivers last?4.2 AnswerWhile the light function of an LED may last for years, drivers can give out much sooner. This is why we recommend name brand LED bulbs for the home, especially those with 25,000 hour rated lives. In general, high power white LEDs use much more current, and need of more complicated drivers. Frequently Asked Questions about LED Drivers Failure Analysis and Maintenance1. What is a LED driver IC?They are configured as either inductorless (charge pump) or switching regulator-based LED drivers that support driving white LEDs in series, parallel or combination. ... Topologies include boost regulator, buck regulator, buck/boost, SEPIC topology LED drivers, and more. 2. What is a LED driver used for?LED drivers are electrical devices that prevent damage to LEDs by regulating the forward voltage (VF) of the LED that changes with temperature, avoiding thermal runaway while delivering a constant current to the LED. LED drivers also aid efforts to meet new energy requirements (e.g., Energy Star). 3. How do I choose an LED driver?Use an LED driver with at least the same value as your LED(s). The driver must have a higher output power than your LEDs require for extra safety. If the output is equivalent to the LED power requirements, it is running at full power. Running at full power may cause the driver to have a shorter life span. 4. Why do LED drivers fail?LED FailureThe LEDs usually fail, because they have been connected to a constant LED driver in parallel. If the LEDs have failed you may want to also replace the LED driver. We usually recommend using a model with an adjustable output, and trimming down the output voltage slightly, to avoid over powering the LEDs. 5. How long do LED drivers last?Namely, the life of the driving circuit expires prior to when the LED stops emitting light or has its brightness dropped. The typical nominal lifetime of these elements is often times less than 25,000 hours, while the lifetime of LED itself could be as long as 50,000-100,000 hours. 6. Why do my LED drivers get hot?If the LED driver is trying to draw DC (not a balanced load circuit) then that can also cause the transformer to overheat.7. What is the difference between a transformer and an LED driver?LED drivers and electronic transformers for retrofit LED lighting are not interchangeable. They differ in output and load compatibility i.e. which LED lights they will work with. The fundamental difference between the two is that LED drivers output DC while electronic halogen transformers output 12VAC.

IntroductionResistors are usually connected in a circuit in various ways, and the two most basic ways are series and parallel. This article will mainly introduce these two connection methods, including their definitions, formulas, circuit diagrams, examples and identification methods. In addition, the article also introduces Ohm's law and Kirchhoff's law, which are very important in understanding the series and parallel connections of resistors.You may need these two calculators in reading this arrticle:① Ohm's Law Calculator② Parallel and Series Resistance CalculatorThe following video explains the basics of resistors in series and parallel, which can promote your understanding of this article. But it does not matter so much if you skip this video since the article explains in detail and is comprehensive.Resistors in series and parallel - deriving the formulaCatalogIntroductionCatalogI Series Connection of ResistorsII Parallel Connection of ResistorsIII Resistor Combination(Mixed Resistor Circuit)IV Ohm's Law  4.1 What is Ohm's Law?  4.2 What is Closed Circuit Ohm's Law?  4.3 The Key Points of Studying Ohm's LawV Kirchhoff's Law  5.1 Concepts  5.2 Kirchhoff's First Law (Nodal Current Law)  5.3 Kirchhoff's Second Law (Law of Loop Voltage)  5.4 Application Note of Kirchhoff's LawVI Series and Parallel Circuit Identification MethodsVII QuizⅧ FAQI Series Connection of Resistors(1) Circuit characteristicsFigure1. Resistors in seriesThe figure shows the series connection of n resistors, and the voltage and current reference directions are related. The circuit characteristics are derived from Kirchhoff’s law:(A) The resistors are connected in sequence. According to KCL, the current flowing through the resistors is the same;(B) According to KVL, the total voltage of the circuit is equal to the sum of the voltages of the series resistors, namely:(2) Equivalent resistanceFigure2. Equivalent resistance circuitSubstituting Ohm's law into the voltage expression, we get:The above formula illustrates that the series circuit of multiple resistors in Figure (a) and the circuit of single resistor in Figure (b) have the same VCR, which is equivalent to each other.The equivalent resistance is:In conclusion:The resistors are connected in series, and the equivalent resistance is equal to the sum of the sub-resistances;The equivalent resistance is greater than any one of the series resistance.The partial pressure of series resistanceIf the total voltage across the series resistor is known, what is the divided voltage on each resistor? From figure (a) and figure (b) we know:MeetIn conclusion:Resistors are connected in series, and the voltage on each sub-resistor is proportional to the resistance value. The higher the resistance value, the higher the voltage. Therefore, the series circuit can be used as a voltage divider circuit.Example 1: Calculate the voltage across the two series resistors as shown in the figure.Figure3. Circuit of Example1Solution: From the partial pressure formula of series resistance:(Note the direction of U2)(3) PowerThe power of each resistor is:SoTotal power:Draw conclusions from the above formulas:When resistors are connected in series, the power consumed by each resistor is proportional to the size of the resistor, that is, the larger the resistance, the larger the power consumed;The power consumed by the equivalent resistance is equal to the sum of the power consumed by each series resistor.II Parallel Connection of Resistors(1) Circuit characteristicsFigure4. Parallel circuit characteristics The figure shows the parallel connection of n resistors, and the voltage and current reference directions are related. The circuit characteristics are derived from Kirchhoff's law:(a) The two ends of each resistor are connected together. According to KVL, the two ends of each resistor are at the same voltage;(b) According to KCL, the total current of the circuit is equal to the sum of the currents flowing through the parallel resistors, namely:(2) Equivalent resistanceFigure5. Equivalent resistance in parallel connectionSubstituting Ohm's law into the current expression, we get:G =1/R is the conductanceThe above formula illustrates that the parallel circuit of multiple resistors in Figure (a) and the circuit of single resistor in Figure (b) have the same VCR, which is equivalent to each other.The equivalent conductance is:Therefore,Namely,The most commonly used formula to find the equivalent resistance when two resistors are connected in parallel:In conclusion:The resistors are connected in parallel, and the equivalent conductance is equal to the sum of the conductances and greater than the partial conductance;The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the sub-resistances, and the equivalent resistance is less than any parallel sub-resistance.Current distribution of parallel resistanceIf the total current of the parallel resistance circuit is known, find the current on each sub-resistance and call it a shunt. From figure (a) and figure (b) we know:Namely,MeetFor two resistors in parallel, there are:Conclusion: When the resistors are connected in parallel, the current on each sub-resistor is inversely proportional to the resistance value, and the current divided by the larger resistance value is smaller. Therefore, the parallel resistor circuit can be used as a shunt circuit.(3) PowerThe power of each resistor is:SoTotal power:Draw conclusions from the above formulas:When resistors are connected in parallel, the power consumed by each resistor is inversely proportional to the size of the resistor, that is, the larger the resistance, the smaller the power consumed;The power consumed by the equivalent resistor is equal to the sum of the power consumed by each parallel connected resistor.consumed by each series resistor.III Resistor Combination(Mixed Resistor Circuit)A circuit with resistors connected in series and connected in parallel is called a resistor combination or mixed resistor circuit. The part where the resistors are connected in series has the characteristics of a resistor series circuit, and the part where the resistors are connected in parallel has the characteristics of a resistor parallel circuit.Example 2: The circuit is shown in the figure, please calculate the voltage and current of each branch.Figure6. Example circuit 2Solution: This is a resistor series and parallel circuit. First find the equivalent resistance Reg = 11W, and the current and voltage of each branch are:The general steps for solving series and parallel circuits can be obtained from the above examples:⚫ Find the equivalent resistance or equivalent conductance;⚫ Apply Ohm's law to find the total voltage or total current;⚫ Apply Ohm's law or voltage division and shunt formula to find the current and voltage on each resistor.Therefore, the key issue in analyzing series-parallel circuits is to distinguish the relationship between series and parallel circuits.To determine the series-parallel relationship of the circuit, the following 4 points should be mastered:⚫ Look at the structural characteristics of the circuit. If two resistors are connected end-to-end, they are connected in series;⚫ Look at the relationship between voltage and current. If the current flowing through the two resistors is the same current, it is connected in series; if the two electrical groups bear the same voltage, it is connected in parallel.⚫ Equivalent to deformation of the circuit. For example, the left branch can be twisted to the right, the upper branch can be turned down, the curved branch can be straightened, etc.; the short circuit in the circuit can be compressed and extended at will; the multi-point grounding can be connected by a short circuit . Generally, if it is really a problem with a resistor series circuit, it can be distinguished.⚫ Find the equipotential point. For circuits with symmetrical characteristics, if two points can be judged to be equipotential points, according to the concept of circuit equivalence, one is to use short wires to connect the equipotential points; the other is to break the branch that connects the equipotential points. Open (because there is no current in the branch), thus obtain the series-parallel relationship of the resistance.IV Ohm's Law4.1 What is Ohm's Law?(1) The content of Ohm's lawWhen there is a potential difference between the two ends of the conductor, an electric field appears inside the conductor, and the charge moves in a directional motion under the force of the electric field to generate current. German physicist Ohm summed up Ohm's law in 1826 through a large number of experiments: Under steady conditions, the intensity of the current passing through a section of conductor is proportional to the voltage across the conductor.(2) Mathematical expression of Ohm's law Note: The unit of the physical quantity in the formula: the unit of I is ampere (A), the unit of U is volt (V), and the unit of R is ohm (Ω).The proportional coefficient R in the formula is determined by the properties of the conductor and is called the resistance of the conductor. Unit: Ohm (Ω). The reciprocal of resistance is called conductance and is represented by G, that isUnit: Siemens (S).(3) Understanding and explanation of Ohm's law● Applicable conditions of Ohm's law: applicable to pure resistance circuits (that is, when working with electrical appliances, the consumed electrical energy is completely converted into internal energy.)● I, U and R in the formula must correspond to the same conductor or the same circuit. If it is in different time, different conductor or different section of circuit, I, U, and R can not be mixed, therefore, the three physical quantities should be marked with angles in order to distinguish under normal circumstances.● For the same conductor (that is, R does not change), I and U are proportional; for the same power source (that is, U does not change), I and R are inversely proportional.● R=ρL/S is the definition of resistance, which means that the resistance of a conductor is determined by the material, length and cross-sectional area of ​​the conductor itself. In addition, resistance is also related to factors such as temperature.● The formula transformed from Ohm's law is a measure of resistance. It indicates that the resistance of a conductor can be given by U/I, that is, the ratio of R to U and I is related, but the magnitude of R itself is related to the applied voltage U and the passing current Factors such as the size of I are irrelevant.● Knowing any two quantities among I, U and R, you can find another quantity.● Issues that need special attention and re-emphasis: I, U and R in the formula must be in the same circuit; when using the formula to calculate, the unit of each physical quantity must be unified.The above explanations are all part of Ohm’s law, which only applies to pure resistance circuits.(4) Pure resistance circuitA pure resistance circuit is a circuit with only resistance elements in addition to the power supply, or inductance and capacitance elements, but their influence on the circuit is negligible. The voltage and current have the same frequency and phase.The resistance converts all the energy obtained from the power supply into internal energy. This kind of circuit is called a pure resistance circuit. Here is a brief explanation from the energy point of view.Basically, as long as there is no conversion of electric energy other than internal energy, this circuit is a pure resistance circuit.4.2 What is Closed Circuit Ohm's Law?In an AC circuit, Ohm's law also holds, but the resistance R should be changed to impedance Z, that is, I = U/Z. If the circuit is closed and contains a power supply, it is called a full circuit, as shown in the figure below. The dotted line in the figure is the power supply, which is called an internal circuit. The circuit outside the power supply is called an external circuit. Since the power supply has internal resistance, the current not only has a voltage drop when passing through an external circuit, but also has an internal voltage drop when passing through an internal circuit. In the whole circuit, the current intensity is proportional to the electromotive force E of the power supply, and inversely proportional to the resistance (R+r) of the whole circuit (including the inner circuit and the outer circuit). This is the Ohm's law of the whole circuit, expressed by the formula:Where I- the current in the circuit, A; E- the electromotive force of the power supply, V; R- the resistance of the external circuit, Ω; r- the resistance of the internal circuit, Ω.From the above formula, in the circuit shown in the figure below, E=IR+Ir=Uouter+Uinner.Figure7. The simplest closed circuitIn the formula, U external = IR-external circuit voltage; U internal = Ir-internal circuit voltage.It should be noted that, since the internal resistance of the power supply itself and the internal resistance of the connecting wires are generally not large, the calculation results that are ignored in the calculation are basically correct. But sometimes it is necessary to calculate the internal voltage drop of the power supply, and to accurately calculate the current of the whole circuit, it is necessary to use the whole circuit Ohm's law. For example, in the figure below, if E=10V, r=0.1Ω, R=1kΩ, then:Figure8. An application example of Ohm's law of closed circuit① When S is connected to the 1 position, the circuit is in the open state,Ammeter readingThe reading of the voltmeter is U=IR=0.01×1000=10 (V), or U=E-Ir=10-0.01×0.1≈10 (V).②When S is connected to the 2 position, the circuit is in an open state, so the reading of the ammeter is 0; the reading of the voltmeter is U=E=10(V).③When S is connected to the 3 position, the circuit is in a short-circuit state, the reading of the ammeter is I=E/r=10/0.1=100(A)A; the reading of the voltmeter U=0(V).4.3 The Key Points of Studying Ohm's LawOhm's law is an important basic law in electricity. It is a law that is summarized and summarized through experiments. To master this law, we must pay attention to the following points:(1) Ohm's law applies to the entire circuit or a part of the circuit from the positive pole to the negative pole of the power supply, and it is a pure resistance circuit.(2) The current I "passing through" in Ohm's law, the voltage U at "both ends" and the resistance R of the "conductor" are all corresponding physical quantities on the same conductor or the same circuit. The above relationship does not exist between the current, voltage, and resistance of different conductors. Therefore, when using the formula I=U/R, the current, voltage, and resistance of the same conductor or the same circuit must be substituted into the calculation, and the three correspond one to one.(3) There is simultaneity among the three physical quantities in Ohm’s law. Even on the same part of the circuit, the closing or opening of the switch and the movement of the sliding position of the sliding varistor will cause the change of the circuit, which will lead to the current in the circuit. , Voltage, resistance changes, so the three quantities in the formula I=U/R are the same time value.(4) The difference between I=U/R and R=U/I:Ohm's law expression I=U/R means that the current in the conductor is related to the voltage across the conductor and the resistance in the conductor. When the resistance R is constant, the current I in the conductor is proportional to the voltage U across the conductor; when the voltage U across the conductor is constant, the current I in the conductor is inversely proportional to the resistance R of the conductor.R=U/I is derived from Ohm’s law expression. It means that the resistance value of a certain section of conductor is equal to the ratio of the voltage across the section of the conductor to the current passing through it. This ratio R is the property of the conductor itself and cannot be understood as R is directly proportional to U and inversely proportional to I. This is also the difference between physics and mathematics.(5) Ohm's law reflects the causal relationship between current intensity and voltage, and the restrictive relationship between current intensity and resistance under certain conditions. That is, when the resistance is constant, the current intensity is proportional to the voltage across the conductor; when the voltage is constant, the current intensity is inversely proportional to the resistance of the conductor. When establishing a proportional relationship, we must pay attention to its conditions. Ohm's law states that the current intensity through a conductor is determined by two factors, the voltage across the conductor and the resistance of the conductor.V Kirchhoff's LawKirchhoff's law includes the first law and the second law. They are the basic laws that are indispensable for the analysis and calculation of complex circuits.5.1 Concepts • BranchA two-terminal element connected in a circuit is a branch. Usually a certain current flows through the branch. (This definition is not universal. For example, if two components are connected in series and then connected in a circuit, it can only be regarded as a branch.)• NodeThe connection point between the branch and the branch is called a node. Usually the current diverges at the junction.• Loop loopA closed path formed by branches is called a loop.Figure9. 6 elements, 6 branches, 4 nodes, 3 independent circuits5.2 Kirchhoff's First Law (Nodal Current Law)The textual expression of KCL: For any node, the algebraic sum of the current flowing into (or out of) the node is equal to zero.Its mathematical expression:The regulation of current positive and negative: Generally, the current flowing into the node is positive, and the current flowing out of the node is negative.The physical meaning of KCL: conservation of chargeNote: KCL is not only applicable to a node, but also to a part of the circuit, as shown in the shaded part of the above figure:i3＝i65.3 Kirchhoff's Second Law (Law of Loop Voltage)KVL’s literal expression: In any closed loop of the circuit, go around a circle in a certain direction, and the algebraic sum of the voltage of each segment is zero.That is: or. When applying the law of loop voltage, the electromotive force is often written on the left side of the equation, and the voltage is written on the right side of the equation.The method for determining the sign of each electromotive force and voltage in the second expression is as follows:① First select the current direction of each branch.② Any choice of the detour direction along the loop (clockwise or counterclockwise).③ If the direction of the current flowing through the resistor is the same as the detour direction, the voltage drop on the resistor is positive, otherwise, it is negative.④ If the direction of the electromotive force is the same as the direction of the orbit, the electromotive force is positive, otherwise, it is negative.The physical meaning of KVL: energy conservation.5.4 Application Note of Kirchhoff's Law• Kirchhoff’s law is a general law that the circuit should satisfy, and has nothing to do with the specific properties of the components;• Kirchhoff’s law applies to any lumped circuit, that is, nonlinear, time-varying circuits, etc.;• Application steps:A. Divide the branch roads and number them;B. Specify the branch current and voltage reference direction, and generally need to be associated;C. Select the appropriate node according to the meaning of the question, and apply KCL;D. Or choose the appropriate circuit according to the meaning of the question, apply KVL, and pay attention to independence.Example: Use KVL to derive the relationship between the total resistance and the sub-resistance and the voltage division formula in the series resistance circuit.Apply KVL according to the current and voltage reference direction and the detour direction of the loop calibrated in the figure:-u+u1+u2+…+un = 0 or u=u1+u2+…+un Because the voltage and current of each resistor obey Ohm's law: uk=iRk, there are:u = i × R1 + i× R2 +...... +i× Rn = i× ( R1+R2+…+Rn)= i Re among them: Re=R1+R2+…+Rn, which is the total resistance or equivalent resistance.uk = iRk=( u/Re ) Rk, which is the voltage division formula of the series circuitVI Series and Parallel Circuit Identification MethodsMethod 1: Current flow method(1) Starting from the positive pole of the power supply, use arrows to mark the path of the current along the connected wires, and finally return to the negative pole of the power supply;(2) Observe whether the current has a shunt and confluence point:If there is only one path for the current in the circuit, the components are connected in series (as shown in Figure a below);If there is a shunt point and a confluence point in the circuit, that is, the direction of the current is greater than one path, the components between the shunt point and the confluence point are connected in parallel (as shown in Figure b below)Figure10. Current flow methodMethod 2: Demolition methodRemove any electrical appliances:If the other electrical appliance cannot work, the two electrical appliances are connected in series (as shown in Figure a below)If the other consumer still works without being affected, the two consumers are connected in parallel (as shown in Figure b below)Figure11. Demolition methodMethod 3: Node MethodFor other non-intuitive non-series circuits, the situation is more complicated and needs to be judged according to several steps:The first step is to mark nodes. That is, use different letters (or symbols) to mark all nodes of the circuit. As shown in the following figure (a), the four points A, B, C, and D are all nodes in the circuit.The second step is to merge the nodes. According to the characteristics of the nodes, some of the nodes you have marked may be equivalent to the same node. The letters (or symbols) belonging to the same node must be changed to the same letter (or symbol), as shown in the circuit shown in Figure (a) Point A and point C are the same node, C should be changed to A, point B and point D should be the same node, D should be rewritten as B, that is to say, the circuit shown in Figure (a) essentially has two nodes A and B .Figure12. Node MethodThe third step is to determine the connection mode of the circuit. There are usually two ways to judge:Method one:Direct judgment: as shown in the figure (a) above, both ends of the resistors R1, R2 and R3 are independently connected to nodes A and B, so R1, R2 and R3 are connected in parallel.Method Two:Drawing judgment: that is, draw the intuitive equivalent circuit diagram of the original diagram. The specific drawing method of the intuitive equivalent circuit diagram of the circuit diagram in Figure (a) is: first determine the two points A and B on the paper, and then combine the original diagrams A and B. The components between the two points B are independently connected to the newly determined points A and B, as shown in the above figure (b), that is, the equivalent circuit diagram of figure (a) is figure (b).Warm reminder: The "node method" is generally used to identify irregular and more complex circuits, which has certain difficulties. There are many ways to identify series and parallel circuits, but you can choose the most suitable method according to your own understanding of the method when using it.VII QuizThe voltage dropped across the 300 ohm resistor isA. 6V B.9V C.2V D.30VAnswer: AⅧ FAQ1. What is the difference between two resistors connected in series, and two resistors connected in parallel?When resistors are in series then net resistance is the sum of individual resistances whereas in parallel it is the sum of the reciprocal of individual resistances.When a resistor is in series the current is the same through all resistors but the voltage is different. The sum of the voltage drop across each resistor is equal to the voltage across a resistor connected in series.When the resistor is in parallel the voltage across each resistor is the same while the current through each resistor is different.In series, the net resistance is higher (sum of each resistance) while in parallel net resistance is lower (net resistance is lower than smallest resistance connected in parallel). 2. Why are resistors connected in series and parallel?Connecting resistors in series increase their total resistance and the power they can handle by distributing the applied voltage. The current flow is the same for each resistor regardless of its resistance.Connecting resistors in parallel reduce their total resistance while at the same time increasing their power they can handle by sharing the current flow in the circuit. The voltage drop across each resistor is the same regardless of its resistance. 3. What is the difference between resistors in parallel and resistors in a series?For resistors in parallel, the voltage across them is the same while the current is the sum let take a case of two resistors connected in parallel the formula 1/Req=1/R1+1/R2 further simplify Req=R1*R2/(R1+R2)While for resistors in series their current is the same but the voltage is the sum and let still take the case of two resistors connected in series to obtain their equivalent Req= R1+R2. 4. How are resistors added in series and parallel?When resistors are connected one after each other this is called connecting in series. This is shown below. To calculate the total overall resistance of a number of resistors connected in this way you add up the individual resistances. This is done using the following formula: Rtotal = R1 + R2 +R3 and so on. 5. Why is resistance different in series and parallel?When resistors are connected in parallel, more current flows from the source than would flow for any of them individually, so the total resistance is lower. Each resistor in parallel has the same full voltage of the source applied to it, but divide the total current amongst them. 6. How do you calculate resistors in parallel?Parallel Resistor EquationIf the two resistances or impedances in parallel are equal and of the same value, then the total or equivalent resistance, RT is equal to half the value of one resistor. That is equal to R/2 and for three equal resistors in parallel, R/3, etc. 7. Why is resistance less in parallel?When resistors are connected in parallel, more current flows from the source than would flow for any of them individually, so the total resistance is lower. 8. How do you sum resistors in parallel?The sum of the currents through each path is equal to the total current that flows from the source. You can find total resistance in a Parallel circuit with the following formula: 1/Rt = 1/R1 + 1/R2 + 1/R3 +... If one of the parallel paths is broken, the current will continue to flow in all the other paths. 9. What happens when you add a resistor in series?When resistors are connected in series, the total voltage (or potential difference) across all the resistors is equal to the sum of the voltages across each resistor. ... In other words, the voltages around the circuit add up to the voltage of the supply. 10. What is the difference between series connection and parallel connection?A parallel circuit refers to a circuit with two or more two paths for the current to flow. ... In a series circuit, all the components are arranged in a single line. In a parallel circuit, all the components are arranged parallel to each other. 

IntroductionIn electronics, operational amplifiers are generally dual/quadruple configurations. So users can consider using the extra amplifier as a comparator. Electrical symbols of the comparator and the operational amplifier are very similar. They are devices with one input inverting terminal and one non-inverting terminal, and one output terminal. In addition, the output voltage range of the output terminal is generally between the rail-to-rail power supply. Meanwhile, they have same features of low bias voltage, high gain and high common-mode rejection ratio. When an op amp is used as a comparator, its own gain bandwidth product, group delay, slew rate and other parameters are likely to be changed due to internal frequency compensation and saturation effects. For an optimized single device, this change can be seen as an economical solution. This article discusses the specifications and characteristics to consider when using op-amps as comparators and provides design advice. How operational amplifier be a comparator and what the difference between them.Op Amp vs ComparatorCatalogIntroductionⅠ Operational Amplifier and Comparator1.1 Electronic Op Amp1.2 Electrical ComparatorⅡ Circuit Structure Comparison2.1 Op Amp2.2 ComparatorⅢ Difference between Amplifier and Comparator3.1 Total Difference Summary3.2 Distinctions between Op-amp and ComparatorⅣ Basic Use of Comparators and Op AmpsⅤ Op-amp Comparator5.1 Technique5.2 Op Amp Comparators DisadvantagesⅥ Using Op Amps as Comparators NotesⅦ ConclusionⅠ Operational Amplifier and Comparator1.1 Electronic Op AmpThe operational amplifier is a kind of differential amplifiers with high input resistance, low output resistance, high open gain (open-loop gain), and has the function of amplifying the voltage difference between the active input pin and the negative input pin. Operational amplifiers and voltage comparators are indeed the same in principle and diagram symbol. That said, they have 5 pins: two of which are power supply (+) and supply power (-), another two pins are non-inverting input (+) and non-inverting input terminal (-), and the last pin is the output terminal.Figure 1. Op Amp Symbol1.2 Electrical ComparatorComparing two or more data items to determine whether they are equal, or determining the  relationship and arrangement order between them is called comparison. A circuit or device that can realize this is called a comparator. Specifically, it is a circuit that compares an analog voltage signal with a reference voltage. The two inputs of the comparator are analog signals, and the output is a binary signal 0 or 1. When the difference of the input voltage increases or decreases and the sign of the positive and negative remains unchanged, the output remains constant. Comparing the voltages of the two input terminals, if the voltage at the positive input terminal is a and the voltage at the negative input terminal is b, when a>b, the output is high level(logic 1); when a<b, the output is low level(logic 0). The schematic diagram is shown below (the voltage at the input terminals of the comparator is IN1 and IN2, the power supply is VCC/GND, the pull-up resistor is 1K, and the pull-up voltage is VCC.).Figure 2. Volatge ComparatorWhen output voltage IN1＞IN2, positive input is in high level with high voltage.When output voltage IN2＞IN1, negative input is in low level with high voltage.A reference voltage is usually applied to an input terminal. Then the output will indicate the  signal applied to the other input. Comparators are often used to determine whether a signal is above or below the reference level. And meawhile, the comparator can form a non-sinusoidal waveform conversion circuit and be used in fields such as analog and digital signal conversion.When the reference voltage is zero, the comparator is called a zero-crossing detector. It uses to convert a sine wave into a square wave. Two comparators can form a "window" circuit, which is used to determine whether a signal is between two limited values. In an output state of the comparator changes as quickly as possible, and sometimes the output of the comparator is required to have a certain logical relationship with the input, a dedicated strobe pulse is required. At this time, the op amp comparator only has an output during operation. In general, a dedicated comparator IC has better performance. And it replaces the operational amplifier in some applications. The most common advantage is that the comparator IC operates with a single power supply.The comparator has a wide range of uses, and can be used for discrete control of voltage signals such as thermistors and photosensitive sensors. For example, the voltage value of the photoresistor is collected by a comparator to determine whether it is day or night. What’s more, the comparator can also be used for voltage adjustment in an analog negative feedback circuit.Figure 3. TLC311 ComparatorIt can be seen from the diagram that the difference between the operational amplifier and the comparator lies in the output circuit. The operational amplifier uses a dual-transistor push-pull output. While the comparator uses only one transistor, the collector is connected to the output terminal, and the emitter is grounded. In addition, the comparator requires an external pull-up resistor from the positive power supply terminal to the output terminal, which is equivalent to the collector resistance of the transistor. Op amp can be used for linear amplifying circuit (negative feedback), as well as the non-linear signal voltage comparison (open-loop or positive feedback). The comparator can only be used for signal voltage comparison, not for linear amplifier circuits (because it has no frequency compensation). Both can be used for signal voltage comparison, but the comparator is designed as a high-speed switch, which has a faster conversion rate and a shorter delay than an operational amplifier. Ⅱ Circuit Structure Comparison2.1 Op AmpFigure 4. Op Amp CircuitOp amp circuit generally consists of input segment, gain segment, and output segment. The input  is composed of a differential amplifier section for amplifying the voltage difference between two pins. In addition, the in-phase signal component (the state where there is no potential difference between the pins and the input voltage is some) is not amplified to take a cancellation effect. If only relying on the differential amplifier circuit, the gain is insufficient, so the gain section is used to further increase the open gain of the operational amplifier.The anti-vibration phase compensation capacitor is connected between the gain section of the ordinary operational amplifier. In order to avoid changes in the characteristics of the operational amplifier due to loads such as resistors connected to the output pins, a compensation capacitor is connected with the output as a buffer.The change (distortion, voltage drop, etc.) in output characteristics caused by the load is mainly determined by the circuit structure and current capability of the output section.Generally, types of output circuit stages are A, B, C, and AB type, which are classified according to the amount of drive current flowing in the output (the difference in bias voltage). Depending on the amount of drive current, the level of distortion coefficient in the output section will change. The order of general circuit distortion from small to large is type A, type AB, type B, and type C. 2.2 ComparatorFigure 5. Comparator CircuitThe comparator circuit structure is basically the same as that of an operational amplifier. Because a negative feedback circuit is not used, there is no built-in phase compensation capacitor for vibration isolation. Owing to it can limit the operating speed between the input and output, the response time is significantly improved compared with the operational amplifier.The output circuit form of the comparator is mainly divided into open collector (open drain) type and push-pull output type. The figure shows the internal equivalent circuit of BA10393, it is also an open collector output circuit. Ⅲ Difference between Amplifier and Comparator3.1 Total Difference Summary(1) The main difference between amplifier and comparator is the closed-loop characteristic. Most of the amplifiers work in a closed loop state, so it is required that they cannot be self-excited after the closed loop. Most of the comparators work in an open loop state and pursue speed. For the case of relatively low frequencies, the amplifier can completely replace the comparator (the output level should be considered), but in most cases, the comparator cannot be used as an amplifier.In order to increase the speed, the comparator optimization will reduce the range of closed-loop stability. While the op amp is optimized for the closed-loop stable range, so the speed is reduced. If an amplifier used as a comparator, as for performance, you may pay more than an amplifier price for its closed-loop stability.In other words, whether an op amp is used as a comparator or not is to see the negative feedback depth of the circuit. Therefore, a shallow closed-loop comparator may work in the amplifier state and will not have self-excited state. However, a lot of experiments must be done to ensure that the op amp is stable under all working conditions.(2) In general speaking, the comparator is an open-loop application of the op amp, but the comparator is designed for voltage threshold comparison. The required comparison threshold must be accurate, and the rise or fall time of output edge after comparison should be short. It conforms to TTL/CMOS level/or OC, etc., does not require the accuracy of the intermediate links, in addition, the driving capability is also different. In short, using op amps as comparators cannot achieve full-scale output in most cases, or the edge time after comparison is too long. So it is better to use special comparators in the design.Figure 6. Op Amp and Comparator Symbol3.2 Distinctions between Op-amp and ComparatorAlthough the electrical symbols of the comparator and the op amp are the same on the circuit diagram, the two devices have big differences and are generally not interchangeable. The differences are as following:1. The flipping speed of the comparator is fast, on the level of ns, while the flipping speed of the op amp is generally us level(except for special high-speed op amps).2. The op amp can be connected to the negative feedback circuit, but the comparator cannot use negative feedback. Although the comparator also has two input terminals of the inverting and non-inverting phase, when connecting negative feedback, the circuit cannot work stably without phase compensation circuit inside. But it is the main reason why the comparator is much faster than the op amp.3. The output stage of the operational amplifier generally adopts a push-pull circuit and a bipolar output. The output stage of most comparators is an open collector structure, so pull-up resistors and unipolar output are needed, which are easy to connect to digital circuits.4. Based on input, many operational amplifiers have built-in protection circuits to prevent large voltages from damaging the chip. When a large differential voltage is input, the input work will become abnormal, because the differential input voltage range of the op amp is usually limited. In addition, the common-mode input voltage range of non-rail-to-rail op amps cannot reach the positive power rail, but the comparator supports the positive power rail. Op amps and comparators have many similar parameters. It is more convenient to choose op amps instead of comparators in applications that require low offset voltage, low offset current, and high common mode rejection. Ⅳ Basic Use of Comparators and Op AmpsFigure 7. Operational Amplifier and ComparatorThe comparator is an open-loop circuit. Its function is to compare the voltage of the output terminal. When the voltage at the positive input terminal is large (IN2>IN1), the output is in high level (note: The comparator is an OC output, and the output terminal needs a pull-up resistor. A few volts will be pulled up to output a few volts, otherwise, the output will be an open circuit). When the negative input terminal voltage is large (IN1>IN2), the output will be in low level (GND). The voltage comparator input signal is an analog voltage, and the output signal generally only has two steady-state voltages of high level and low level. The voltage comparator can convert various periodic signals into rectangular waves.Operational amplifier can be used in linear amplifying circuit, and can also be used in non-linear circuit (used as comparator). It is widely used in electrical circuits, such as non-inverting amplification, inverse proportional amplification, difference, addition circuit, subtraction circuit, integral and differential circuit.  Ⅴ Op-amp Comparator5.1 TechniqueThe functions of the operational amplifier are more complicated, but the comparator is relatively simple. When the frequency requirement is not high, the operational amplifier can also be used as a low-performance comparator in practical applications.In theory, an operational amplifier with an open-loop configuration (no negative feedback) can function as a low-end comparator. When the voltage of the non-inverting input terminal (V+) is higher than the inverting input terminal (V-), due to the higher open-loop gain, a positive saturation voltage +U is output. When the voltage of the inverting input terminal (V-) is higher than the positive input terminal (V+), a reverse saturation voltage -U is output. For an op amp that works in a linear negative feedback configuration and is powered by a separate voltage (±V), is different from a non-linear comparator without negative feedback. 5.2 Op Amp Comparators DisadvantagesIn practice, the use of op amp comparators has the following disadvantages compared with the use of dedicated comparators:1) The op amp is designed to work in a linear segment with negative feedback, so saturated op amps generally have a slower flip speed. Most op amps have a compensation capacitor used to limit the slew rate of high-frequency signals. This makes the op amp comparator generally have a propagation delay on the level of microseconds, but a dedicated comparator is on the level of nanoseconds.2) The op amp does not have a built-in hysteresis circuit and requires a special external network to delay the input signal. 3) The static operating current of the op amp is stable only under negative feedback conditions. When the input voltage is not equal, there will be a DC offset.   4) The function of the comparator is to generate the input signal for the digital circuit. When using the op amp comparator, it is necessary to consider the compatibility with the digital circuit interface.5) Interference may occur between different frequencies of multiple op amps.6) Many op amps have diodes connected in reverse series at the input. The input of the two poles of the op amp is generally the same, which will not cause operational problems. But the two poles of the comparator need to be connected to different voltages, which may cause unexpected breakdown of the diode.7) Integrated circuits of dedicated comparator, which better combine the characteristics of analog and digital. It provides an output representing the logic state related to two analog voltages, one of which is a fixed reference quantity. When another voltage exceeds the reference value, is less than the reference value, or is in a specified range, the comparator can send a signal. It has an optimized combination of high gain, wide bandwidth and large flip rate to quickly change the output state. And the conversion time of digital signals is usually very fast. Ⅵ Using Op Amps as Comparators NotesThere are many points should remember when using op amps as comparators in circuits. You must consider five main op-amp characteristics to ensure expected performance:1) Power SupplyIf the logic and operational amplifier share the same power supply, the rail-to-rail operational amplifier can drive CMOS and TTL logic. but if they do not share the same power supply, an additional interface circuit is required.2) Input impedance and Bias CurrentWhen the operational amplifier is used as a comparator, it must meet the high input impedance condition. The input impedance of the CMOS voltage feedback operational amplifier is in the megohm level, which meets the requirement. As for current feedback (transconductance) operational amplifiers, the inverting input terminal has extremely low impedance, which cannot be used as a comparator.3) Differential Input CharacteristicsThe original intention of operational amplifier design is to cooperate with negative feedback to reduce the differential input as much as possible. In specific applications, the actual differential input voltage and the maximum differential input voltage that the op amp can actually provide should be considered.4) Common-mode Input CharacteristicsFor the old FET-type input operational amplifier, when the input exceeds the common-mode voltage range allowed by the device, a phase reversal will occur. At present, the op amps produced by various manufacturers use various methods to prevent the op amps from phase inversion. If the actual common-mode voltage range exceeds the allowable input common-mode voltage range of the op amp, you need to actually verify whether it is working properly.5) StabilityBecause there is no negative feedback externally, the open loop gain of the op amp used as a comparator is very high. Therefore, parasitic capacitance of the PCB and ground impedance of the non-inverting input terminal may cause the output to oscillate.Figure 8. Window Comparator CircuitⅦ ConclusionAlthough op amps are not designed to be used as comparators, nevertheless, many applications where the use of an op amp as a comparator is an economical engineering decision. It is important to make an reasonable decision to ensure that the op amp chosen performs as expected.That said, it is necessary to read the data sheets carefully and to consider the effects of op amp parameters on the application. Because the op amp is being used in a nonstandard manner, it may not reflect actual behavior, and some circuit experiment is advisable. Furthermore, because not all devices are typical in their behavior, some pessimism is warranted when interpreting the experimental results. Frequently Asked Questions about Operational Amplifier as Comparator1. Can an op amp be used as a comparator?However, op amps can also be used as comparators, which causes them to operate non-linearly. The inputs are driven hard and the output voltage slams to the power supply rail. 2. How does a comparator op amp work?A comparator circuit compares two voltages and outputs either a 1 (the voltage at the plus side; VDD in the illustration) or a 0 (the voltage at the negative side) to indicate which is larger. Comparators are often used, for example, to check whether an input has reached some predetermined value. 3. How op amp can be used as comparator in open loop configuration?Thus, an op-amp operating in open loop configuration will have an output that goes to positive saturation or negative saturation level or switch between positive and negative saturation levels and thus clips the output above these levels. This principle is used in a comparator circuit with two inputs and an output. 4. What is the difference between a comparator and an amplifier?Unlike operational amplifiers that usually operate with the input voltages at the same level, comparators typically see large differential voltage swings at their inputs. But some comparators without rail-to-rail inputs are specified to have a limited common mode input voltage range. 5. What is the difference between op amp and comparator?The difference between an op-amp comparator and a voltage comparator is in the output stage as a standard op-amp has an output stage that is optimized for linear operation, while the output stage of a voltage comparator is optimized for continuous saturated operation as it is always intended to be close to one supply.

IntroductionThe relay is an electrical device regarded as a switch in the circuit. That is, the current in the control circuit depends on the "open" and "close" of relay contacts. Therefore, the reliability and service life of the relay depend on the quality and performance of the contacts greatly. The performance of the contact is affected by factors such as contact material, contact voltage, load type, operating frequency, atmospheric environment, contact configuration and bounce.  If any of these factors cannot meet the predetermined value, contact problems such as electrochemical corrosion of the metal between the contacts, contact welding, contact wear, and contact resistance may occur. The volume of the load determines the size of the voltage and current that the relay can control (The rated load of the contact refers to the voltage and current that the electromagnetic relay allows to break.). If you not pay attention to it when use, it is easy to damage the relay contacts.Relay ContactCatalogIntroductionⅠ Relay Contact Form ConfigurationⅡ Relay Contact SymbolⅢ Relay Contact Fault Analysis3.1 Terminology3.2 Contact Bonding and Fusion Welding3.3 Contact Erosion3.4 Contact Metal Migration3.5 Contact Loose and Crack3.6 Contact DustⅣ Contact Protection MethodsⅤ Frequently Asked Questions about Relay ContactⅠ Relay Contact Form Configurationa. Normally Opened ContactIt would mean the contacts are normally open when the coil of the relay is not energized or there is no magnetic field nearby in a reed switch. b. Normally Closed ContactIt would mean the contacts are normally closed when the coil of the relay is not energized or there is no magnetic field nearby in a reed switch. c. Common ContactIt would have 3 leads and would have one normally open and one normally closed circuit. This is also called a “changeover” because the common contact changes from the normally closed position to the normally open position when the coil is energized in a relay or a magnetic field is nearby in a reed switch. Ⅱ Relay Contact Symbol Ⅲ Relay Contact Fault Analysis3.1 TerminologyThere is something in which the relay contact seems to be closed, but the circuit works abnormally sometimes. This is due to the existence of the contact resistance of the relay contacts. When the current passes through the closed contact, the contact resistance will consume a certain amount of power, which will increase the temperature of the contact. If the current is large, the contact material will soften and deform, resulting in greater contact resistance, and even having welding failure in severe cases, making the closed contact unable to be disconnected. Another form of contact resistance is "membrane resistance". Because the contacts of the relay are exposed to the air for a long time, there will always be compounds produced by dust, water vapor, and chemical gas, which will adhere to the contacts to form a thin film. Because of it, the conductivity of the contacts will become worse, and even become non-conductive in severe cases. 3.2 Contact Bonding and Fusion WeldingContact bonding usually occurs when the contacts are in a static connection. Contact resistance making the temperature of the conductive spots and nearby materials increase, which leads to a great increase in the diffusion rate and a large expansion of the contact area. The molecular force formed by the mutual extrusion and penetration of metal molecules at the contact point is the internal factor leading to the contact bonding, in addition, the sliding friction between the contacts is a necessary condition for accelerating the molecular extrusion penetration and accumulating bonding force. The size of the bonding force depends on the rigidity of the contact material and the physical conditions that cause molecular extrusion and penetration. Whether the contacts are bonded depends on the bonding force is greater than the return force of the reed. Fusion welding refers to the phenomenon that the contact areas of two electrodes are united together by metal welding. According to the reasons for formation, welding can be divided into static welding and dynamic welding. The Joule heat generated by the contact resistor melts the contacts part, and the phenomenon that they are combined and cannot be disconnected is called static welding. In the process of the contacts controlling the external circuit, the contact pressure of the contacts is near zero or above, and meanwhile, the liquid metal bridge between the contacts made. The welding phenomenon that occurs owing to the arc heat flow melting the contacts is called dynamic welding. 3.3 Contact ErosionA load of contact switching is mostly inductive. When the inductive load is disconnected, its accumulated magnetic energy will generate a high back electromotive force at both ends of the contact, which will break up the air gap between the contacts to form sparks and cause electrical corrosion. Cause the contact surface to dent or stick and cannot be separated, all of them belong to poor contact, which will result in a short circuit. The main factors that affect arc erosion include the characteristics of the arc and its effect on the heat flow and force of the electrode and the response of the contact material to the heat and force of the arc. In general, there are two main forms of arc erosion: 1) Vaporization and evaporation: Under the action of arc energy, the surface material of the contact changes from solid to liquid, and then into a gaseous state to leave the contact. Except that, in certain conditions, the contact material also has a sublimation process from a solid-state to a gas state. 2) Liquid splashing: Under the action of arc energy, a certain area of the surface of the contact melts. The liquid metal splashes out in the form of tiny droplets under the action of various forces, resulting in a larger material loss. These forces include spot pressure, electrostatic field force, electromagnetic force, force and reaction force of material movement, contact surface tension, etc. The form of arc erosion varies with the contact material and load current conditions. When the load current is small, the erosion of the contact material is dominated by vaporization and evaporation. When the current is increased, not only the vaporization and evaporation of the contact material but also the splashing phenomenon of liquid metal will occur. When the current is further increased, the metal liquid splashing becomes the main form of contact erosion. Preventing electrical corrosion between the contacts can be obtained by setting up a resistance spark extinguishing circuit and a resistance-capacitance spark extinguishing circuit. Therefore, when choosing a relay, you should consider the voltage applied to the contact and the load capacity of the contact. For example a relay with a contact load of 28V(DC)×10A means that the relay’s contact can only work at a DC voltage of 28V, and the contact current is 10A. If these two ratings are exceeded, the service life of the relay will be affected, and even the contacts will be burnt and damaged. In addition, the number of circuits that the relay needs to control should be determined according to actual requirements. In the same model series of relays, there are generally a variety of contact forms for selection, and each group of contacts should be fully utilized when using. 3.4 Contact Metal MigrationDuring the working process, there is usually a mutual transfer of materials between two contacts. If this mutual transfer cannot be offset, a net transfer of materials occurs. The significant contact metal migration is a big net transfer. The asymmetry of various factors in the contact operation is the main reason for the metal migration of the contact. These factors include arc, contact material characteristics and various external forces. Details are as following: 1) The arc has various forms of energy input to the contacts. For the contact at the cathode, the kinetic energy of the ion current colliding with the cathode after being accelerated by decompression, the potential energy released by the ion current on the cathode surface and the electrons, the arc column radiation or the energy conducted to the cathode surface, and the cathode Joule heat generated by the current in the body. All of these energies will increase the temperature of the contact material, resulting in contact material melting and evaporation. 2) The contact has various forces in the working process, including electronic force, electrostatic force, electromagnetic force, the reaction force of material movement, plasma flow force, these forces may cause the metal in the molten pool on the surface of the contact Liquid splashing occurs. 3) The material properties that affect the migration of the contact metal include electrical conductivity, specific heat capacity, latent heat of melting and vaporization, melting point and boiling point, metallurgical dynamics, and so on. In addition, the size, shape, and connection form of the contacts will also affect the metal migration. 3.5 Contact Loose and CrackContacts are electrical contact parts for relays to switch loads. Some products have contacts that are press-fitted by riveting. The main drawbacks of this installing method are loose contacts, cracks in the contacts, or excessive size and so on. They will affect the contact reliability of the relay. The loosening of contacts is caused by the improper size of the mating part of the reed and the contact or the improper adjustment force by the operator. Contact cracking is caused by too high material hardness or too much pressure. Different crafts should be used for contacts of different materials, and some contact materials with higher hardness should be annealed before contact manufacturing, riveting, or welding. 3.6 Contact DustSometime after use, dust and dirt will deposit on the contacts of the relay, which will cause a black oxide film on the surface, resulting in poor contact. Therefore, the contacts need to be cleaned regularly. For example, carbon tetrachloride liquid can be used to ensure good contact performance.  Ⅳ Contact Protection MethodsFigure 1. Contact Oscillogram (contact action time, release time, rebound time and stabilization time)We know that the relay contact protection needs to be more careful than MOSFET. Generally, the load of the relay is much larger than MOSFET. Common DC motors, DC clutches and DC solenoid valves with large DC loads, these inductive load switches are often closed, because surges caused by hundreds of or even thousands of back electromotive force will shorten the life of the contacts or even completely damage them. On the contrary, if the current is small, such as around 1A, the back electromotive force will cause arc discharge, which will cause metal oxides to contaminate the contacts, leading to failure of the contacts and increasing contact resistance. Protect contacts mainly to extend the use time of the relay, because the contacts will always accumulate carbon and age, and the surface is not as clean as it was originally. What’s more, when the relay life is approaching the end, its contact resistance will increase rapidly. Generally, under normal temperature and pressure, the breakdown voltage of the key dielectric in the air is 200~300V. Therefore, our goal is generally to control the voltage below 200V or less.Figure 2. Breakdown VoltageThere generally have the following methods to do it:MethodCircuitCharacteristicComponent SelectionResistor and CapacitorIf the load is related to time, the initial leakage current may cause the load to malfunction.R: The contact voltage is 1VC: The contact current is 1A, and the value of RC varies with the relay and load.The function of the capacitor C is to suppress the excessive voltage when the inductor is discharged.The value of resistance R is determined by the test needs.The breakdown voltage of the capacitor C is 200~300V.If the load is a relay or solenoid valve, the release time will be extended. When the contact power supply voltage range is 24V~ 48V, the voltage across the load is 100 ~ 200V.DiodeThe diode (regarded as a freewheeling diode) acts as a channel for the coil to release energy and a way to dissipate heat. Compared with the RC circuit, it significantly changes the release time of the relay (2~5 times).The reverse breakdown voltage is at least 10 times the power supply voltage, and the forward current is equivalent to the load.Zener DiodeThis circuit effectively prevents the diode from affecting the release time of the relay.The breakdown voltage of the Zener diode must be consistent with the power supply voltage of the relay.VaristorBased on the characteristics of the varistor to stabilize the voltage, this circuit can prevent the contact voltage from being too high, and also slightly delay the relay release time. When the load contact power supply voltage is 24V or 48V, and the voltage across the load is 100 to 200V, the varistor is very effective. * Standard diodes can significantly extend the rebound time. Connecting conventional diodes in series with Zener diodes will affect it lightly. If it is an inductive load, when the contacts are separated, a longer rebound time prolongs the arc generation time and shortens the life of the contacts. For example, a relay with a diode connected to the coil needs 9.8ms to release the contact. Combining the Zener diode with the small signal diode can shorten the time to 1.9ms. In addition, the return time of the relay without a diode connected to the coil is 1.5ms. Although the inductive load is not easy to handle than the resistive load, the use of effective protection will make the performance better. There are two methods that can’t be used.Figure 3. Capacitor and Relay CircuitIn the actual circuit, the protection device (diode, resistor, capacitor, varistor, etc.) and the load should have a certain distance. If the two are too far apart, the effect of the protective device may be weakened. Generally, the distance between the two should be within 50cm. DC loads at higher frequencies will cause abnormal switch corrosion (electric spark generation). When the DC solenoid valve or clutch is controlled at a higher frequency, the contacts may have corrosion. The reason for this is that when an electric spark (arc discharge) is generated, the reaction between nitrogen and oxygen causes contact corrosion. Ⅴ Frequently Asked Questions about Relay Contact1. How do relay contacts work?A relay is an electrically operated switch. They commonly use an electromagnet (coil) to operate their internal mechanical switching mechanism (contacts). When a relay contact is open, this will switch power ON for a circuit when the coil is activated. 2. What is a relay contact output?A relay contact output works basically like an on/off switch. To simplify, if the output is "off" the circuit will be broken (open). If the output is "on" the contact will be made, completing the circuit. Therefore, the controller does not supply any current or voltage itself. 3. Why do relay contacts weld?Consequently, when the contacts are ON again, short-circuited current from the capacitance may cause contact weld. This circuit effectively suppresses arcs when the contacts are OFF. When the contacts are ON again, however, charge current flows to the capacitor, which may result in contact weld. 4. How do I protect my relay contacts?Various ways to protect relay contacts from the effects of switching an inductive load – from left to right: a diode, a spark quench capacitor, Zener diodes or a transil, a varistor. 5. What is a contact form relay?Contact Form: The arrangement of the contacts in the relay. This determines how many circuits the relay can operate. Form 1A (or “1 Form A): One circuit is opened and closed with the contacts in a Normally Open position. 6. What is a relay contact?Relays control one electrical circuit by opening and closing contacts in another circuit. ... When a relay contact is Normally Closed (NC), there is a closed contact when the relay is not energized. In either case, applying electrical current to the contacts will change their state. 7. How many contacts does a relay have?Two. A simple electromagnetic relay consists of a coil of wire wrapped around a soft iron core, an iron yoke that provides a low reluctance path for magnetic flux, a movable iron armature, and one or more sets of contacts. 8. What is the difference between relay and contactor?A contactor joins 2 poles together, without a common circuit between them, while a relay has a common contact that connects to a neutral position. Additionally, contactors are commonly rated for up to 1000V, while relays are usually rated to the only 250V. 9. What is the purpose of contactor or relay?A contactor is a large relay, usually used to switch current to an electric motor or another high-power load. Large electric motors can be protected from overcurrent damage through the use of overload heaters and overload contacts. 10. What are the three major parts of a contactor or relay?There are three major parts of a contactor or relay: the coil, mechanical linkage and contacts. The coil is used to create a magnetic field and is rated based on voltage (24 V, 120 V, 208/204 V, 480 V). The mechanical linkage connects the armature to the contacts when the coil is energized, completing the circuit. Recommended ReadingBasic Knowledge of Relay Electronics Tutorial with VideoThe Role of the Relay and Its Working PrincipleHow Relays Work? Relay Functions and Applications

IntroductionSimply put, an oscillator is a device that can convert DC power into AC power without external signal excitation. The so-called "oscillation" implies alternating current. This article will mainly explain the circuits of different sine wave oscillators, including their working principles, how to realize their functions, circuit composition and comparison of advantages and disadvantages of different forms of circuits. This article uses a large number of circuit diagrams and formulas to explain in detail, which can help you understand in a better way.Basics of oscillators and their different typesCatalogIntroductionCatalogI The Principle of Feedback Oscillator1.1 How Does the Feedback Oscillator Work?1.2 Equilibrium Conditions1.3 Starting Conditions of the Oscillator1.4 Stable Conditions of the Oscillator1.5 General Composition of Sine Wave OscillatorII LC Oscillator Circuit2.1 The Composition Principle of the Oscillator2.2 Capacitive Feedback Oscillator2.3 Inductive feedback oscillatorIII RC Oscillator Circuit3.1 Brief Introduction of RC Oscillator and its Circuit3.2 RC Phase Shift Oscillator3.3 Wien Bridge OscillatorIV Quartz Crystal Oscillator Circuit4.1 What is a Quartz Crystal Oscillator?4.2 Quartz Crystal4.3 Quartz Crystal Oscillator CircuitV Non-sine Wave Generating Circuit5.1 What is a Non-sine Wave Generating Circuit?5.2 Rectangular Wave Generator5.3 Triangle Wave and Sawtooth Wave Signal GeneratorVI QuizⅦ FAQI The Principle of Feedback Oscillator1.1 How Does the Feedback Oscillator Work?The feedback oscillator is when the power is turned on, the various electrical disturbance signals in the loop are selected by the frequency selection network, and the signal of a certain frequency is fed back to the input terminal, and then the cycle of amplification → feedback → amplification → feedback , The amplitude of the signal increases continuously, and the oscillation is established from small to large. As the signal amplitude increases, the amplifier will enter a non-linear state, and the gain will decrease. When the feedback voltage is exactly equal to the input voltage, the oscillation amplitude will no longer increase and enter a balanced state. As can be seen from the figure below, the feedback oscillator is a closed loop composed of an amplifier and a feedback network. The amplifier is usually a tuned amplifier with an oscillation circuit as a load. The feedback network is generally a linear network composed of passive components.Figure1. Block Diagram of Feedback OscillatorIn order to generate self-oscillation, there must be positive feedback, that is, the signal fed back to the input terminal and the signal at the input terminal of the amplifier have the same phase. For the above figure, suppose the voltage amplification factor of the amplifier is K(s), the voltage feedback coefficient of the feedback network is F(s), and the closed-loop voltage amplification factor is Ku(s), thenby We can writeIf a certain frequency ω1=ω, then T(jω1) is equal to 1. From the above formula, we can see that Ku(jω) will tend to infinity. This shows that there is no external signal, and self-excited to produce signal output, namely self-oscillation. Therefore, the condition of self-oscillation is that the loop gain is 1.Definition:1.2 Equilibrium ConditionsThe equilibrium condition of the oscillator isthis can also be expressed asIf a certain frequency ω1=ω, then T(jω1) is equal to 1. From the above formula, we can see that Ku(jω) will tend to infinity. This shows that there is no external signal, and self-excited to produce signal output, namely self-oscillation. Therefore, the condition of self-oscillation is that the loop gain is 1. The above two formulas are the amplitude and the phase equilibrium conditions respectively. Equilibrium conditions are also called "two conditions for maintaining self-oscillation". The amplitude balance condition determines the amplitude of the oscillator output signal, and the phase equilibrium condition determines the frequency of the oscillator output signal. But it must be pointed out that the loop can only meet the phase equilibrium condition at a certain frequency (f), which is the resonant frequency (f0) of the loop.1.3 Starting Conditions of the OscillatorWhen the oscillator is in actual application, there should be no external signal Us(s) shown in Figure 1. The initial source of oscillation is electrical signals such as electrical shock and various thermal noises that inevitably exist when the oscillator is switched on.It can be seen from the establishment process of the oscillation that in order to make the oscillator start-up, the feedback voltage Uf and the input voltage Ui should be in phase at the beginning of the oscillation (that is, positive feedback); Uf>Ui should be required in amplitude, that is:Vibration conditions: φA+φF=2nπ(n=0,1,2,•••)AF>1 Simply put, as we know, the condition of unity gain must be met to make the oscillation continue. But to start the oscillation, the voltage gain of the positive feedback loop must be greater than 1, so that the amplitude of the output voltage can reach the required potential. Then the gain must be reduced to 1, so that the output voltage can be maintained at the required potential and the oscillation phenomenon can continue. Transition from |T(jω)|>1 to |T(jω)|=1 when the oscillator is workingThe amplifier must work in the linear amplification region of the transistor when amplifying small signals.When the oscillation is started, the amplifier works in the linear region. At this time, the output of the amplifier increases linearly with the increase of the input signal; as the amplitude of the input signal increases, the amplifier gradually enters the saturation or cut-off region from the amplification region, and enters a nonlinear state. The closed-loop gain of will decrease with the increase of the input signal, as shown in the figure below:Figure2. Graphical Representation of Amplitude ConditionsWhen the loop gain drops to |T(jω)|=1, the growth process of the amplitude will stop, and the oscillator will reach a balanced state and perform constant amplitude oscillation. It can be seen that the transition of the oscillator from amplified oscillation to steady amplitude oscillation is realized by the non-linear characteristics of the amplifier. When the oscillating circuit is powered on, the current of the transistor increases abruptly from zero, and the sudden change current contains a wide spectrum component. The start-up process of the circuit is very short! As long as the circuit satisfies the starting conditions, after the oscillator is powered on, there will be an output signal with stable amplitude at the output.Figure3. Circuit Start-up Process1.4 Stable Conditions of the OscillatorIf the loop gain characteristic has two equilibrium points A and B, among them, point A is stable and point B is unstable.Figure4. Stable Conditions of the OscillatorIt can be seen from the above discussion that in order to stabilize the equilibrium point, |T(ω0)| must have a negative slope change near UiA.Stable conditions are divided into amplitude stable conditions and phase stable conditionsTo make the amplitude stable, the oscillator must have the ability to prevent amplitude changes at its equilibrium point. Then the amplitude stability condition should beSince the feedback network is a linear network, which means the size of the feedback coefficient does not change with the input signal, so the amplitude stability condition can be written asThe phase stability depends on the increase of ω, and the decrease of , meaning that the phase characteristic of the parallel oscillator circuit ensures the phase stability.Therefore, the phase stability condition is. The higher the Q value of the loop,  the larger of the value of , and the better phase stability.1.5 General Composition of Sine Wave Oscillator(1) Amplifying circuit-realize energy control.(2) Positive feedback network-meets the conditions for starting vibration.(3) Frequency selection network-only one frequency satisfies the oscillation condition to obtain a sine wave output of a single frequency. Commonly used frequency selection networks include RC frequency selection and LC frequency selection(4) Amplitude stabilization link-makes the circuit easy to start and oscillate stably, with little waveform distortion. Examples of oscillation circuits:High frequency resonant amplifier and sine wave oscillatorFigure5. High Frequency Small Signal Resonant AmplifierFigure6. Mutual Inductance Coupled OscillatorII LC Oscillator CircuitLC oscillators can be divided into three types: mutual inductance coupled oscillators, inductive feedback oscillators and capacitive feedback oscillators according to their different feedback networks.This section focuses on different types of feedback LC oscillators and three-point oscillators.2.1 The Composition Principle of the OscillatorFigure7. General Form of Three-terminal OscillatorThe basic circuit is the so-called three-terminal (also called three-point) oscillator, which means the circuit formed by connecting the three terminals of the LC loop and the three electrodes of the transistor respectively, as shown in the figure. The three-terminal LC oscillator is a feedback type LC oscillator. In order to obtain positive feedback, the feedback circuit must make the instantaneous polarity of the transistor's AC voltage meet a certain phase relationship: when Vbe is negative, Vce should be positive, namely, Vbe and Vce are in reverse phase, and Veb and Vce are in phase. Only when the reactance Xce and Xeb have the same properties can they be guaranteed to be in phase. When the resistance of the loop element is very small, its influence can be ignored, and the influence of the input impedance and output impedance of the transistor can also be ignored. To maintain oscillation, the circuit must meet the requirements. Otherwise, the loop resonance condition cannot be met.The criteria for the three-terminal oscillator circuit to meet the phase equilibrium condition is as follows:(1) The reactance properties of Xce and Xeb are the same, but the reactance properties of Xcb are opposite. That is, ce and be are the same resisting piece, and cb resisting piece.(2) The oscillation frequency should satisfy 1Xo+Xcl-XolBased on this criterion, it can be quickly judged whether the oscillating circuit composition is reasonable or not.Three-terminal LC oscillatorThe three-terminal LC oscillation circuit is often used, and its operating frequency is about a few MHz to a few hundred MHz. The frequency stability is also higher than that of the transformer coupled oscillation circuit, which is about 10-3~10-4. After some frequency stabilization measures, it can be higher. There are many types of three-terminal LC oscillators, mainly: Inductance three-terminal type, also known as Hartley oscillator; capacitor three-terminal type, also known as Colpitts oscillator; series type improved capacitor three-terminal type, also known as Clapp parallel type improved capacitor three-terminal type , Also known as Sellier oscillator. The three-terminal oscillator has two basic circuits, as shown in the figure below.Figure8. Capacitive Feedback Oscillator and Inductive Feedback Oscillator2.2 Capacitive Feedback OscillatorCapacitive feedback three-terminal oscillator is an electronic component, also called Colpitts oscillator, which is a kind of self-excited oscillator. It is composed of a series capacitor, an inductance circuit and a positive feedback amplifier. It is named because the three end points of the two series capacitors of the oscillating circuit are connected to the three pins of the oscillating tube respectively.Figure9. Capacitive Feedback OscillatorAs shown in the figure, use C2 to feed back part of the voltage of the resonant tank to the base. The three end points of the LC resonant tank are respectively connected to the three electrodes of the transistor, so it is called a capacitive feedback three-terminal oscillator, or Colpitts oscillator. The vector analysis method can be used to prove that the circuit meets the phase balance condition. As long as the ratio of C1 and C2 is appropriately selected and the amplifier has enough amplification, the circuit can oscillate.Figure10. Capacitive Feedback OscillatorAdvantages of Colpitts circuit:(1) Good oscillation waveform;(2) The frequency stability of the circuit is high. If the capacitance of the circuit is increased appropriately, the influence of unstable factors on the oscillation frequency can be reduced;(3) The operating frequency of the three-terminal circuit of the capacitor can be made higher. The output and input capacitors of the oscillator tube can be directly used as the oscillation capacitor of the loop, and the operating frequency can reach a very high frequency range of tens of MHz to hundreds of МHz. Disadvantages of Colpitts circuit:When adjusting C1 and C2 to change the oscillation frequency, the feedback coefficient will also change, which will affect the starting conditions and working status. But as long as a variable capacitor is connected to both ends of L and C1 and C2 are fixed capacitors, the feedback coefficient will not be affected when the frequency is adjusted.2.3 Inductive feedback oscillator(1) Circuit compositionIn order to overcome the shortcomings that the transformer primary coil and the secondary coil in the transformer feedback oscillation circuit are not tightly coupled, the N1 and N2 of the transformer feedback oscillation circuit can be combined into one coil. As shown in the figure below, in order to strengthen the resonance effect, the capacitor C is connected across the entire coil. This is the inductive feedback oscillator circuit, or Harley oscillator.Figure11. Inductive Feedback Oscillator Circuit(2) Working principle✿The circuit includes four parts: amplifier circuit, frequency selection network, feedback network and non-linear element (transistor), and the amplifier circuit can work normally.✿Use the instantaneous polarity method to judge whether the circuit meets the phase condition of sine wave oscillation: disconnect the feedback, add the input voltage with frequency f0, give its polarity, and judge that the polarity of the feedback voltage obtained from N2 is the same as the input voltage , So the circuit satisfies the phase condition of sine wave oscillation.✿As long as the circuit parameters are selected properly, the circuit can meet the amplitude condition and produce sine wave oscillation. The following figure shows the AC path of the inductive feedback oscillation circuit. The three ends of the primary coil are connected to the three poles of the transistor, so the inductive feedback oscillation circuit is called an inductive three-point circuit.Figure12. AC Path of Inductive Feedback Oscillator Circuit(3) Advantages and disadvantagesThe coupling between N2 and N1 in the inductance feedback oscillation circuit is tight, the amplitude is large, and it is easy to oscillate; when C uses a variable capacitor, a wide adjustment range of oscillation frequency can be obtained, and the highest oscillation frequency can reach tens of MHz. Since the feedback voltage is taken from inductance, it has greater reactance to high-frequency signals, and the feedback signal contains more high-order harmonic components, and the output voltage waveform is not good. The following introduces two improved capacitor three-terminal oscillation circuits:Clap oscillator:The following figure (a) is the principle circuit of the Krapper oscillator, and (b) is its AC equivalent circuit. Its characteristic is that a capacitor C3 is added to the inductance branch of the aforementioned capacitive three-point oscillating resonant tank. Its value is relatively small, requiring C3<< C1, C3<< C2.Figure13. Clapp OscillatorRegardless of the influence of the capacitance between the poles, the total capacitance CΣ of the resonant circuit is the series connection of C1, C2 and C3, namely. Thus, the oscillation frequency is .The condition for the above formula to be true is that C1 and C2 must be selected relatively large. It can be seen that the influence of C1 and C2 on the oscillation frequency is significantly reduced, so the influence of the capacitance between the transistors connected in parallel with C1 and C2 is also very large. It is smaller, and the stability of the oscillation frequency is improved. Sellier oscillator:Figure14. Sellier Oscillator so the oscillation frequency:L is the inductance of the inductance coil of the resonant amplifier circuit; C is the total capacitance of the resonant circuit. In the LC resonance circuit, the inductance L(H)/capacitance C(F)=105~106, which can achieve better results.III RC Oscillator Circuit3.1 Brief Introduction of RC Oscillator and its Circuit● What is an RC oscillator?(1) The sine wave oscillator has no input signal and is a positive feedback amplifier with a frequency selection network. If resistors and capacitors are used to form a frequency selection network, it is called an RC oscillator, which is generally used to generate 1Hz-1MHz low-frequency signals. The frequency selection effect of the RC frequency selection network is not as good as that of the LC resonant circuit, so the waveform and stability of the RC oscillator are worse than that of the LC oscillator.(2) RC oscillator can be divided into sine wave oscillator and non-sine wave oscillator according to whether the output wave type is sine wave.(3) There are many kinds of RC oscillation circuits: bridge type, phase shift type, double T type, the most commonly used is bridge type oscillation circuit, namely RC series-parallel frequency selection network. ● Features of RC oscillator(1) RC phase-shift oscillator features: simple, poor frequency selection, unstable amplitude, inconvenient frequency adjustment, generally used in occasions with fixed frequency and low stability requirements. Frequency range: several hertz-tens of kilohertz(2) RC series-parallel network oscillator features: it can easily and continuously change the oscillation frequency, it is convenient to add negative feedback to stabilize the amplitude, and it is easy to get a good oscillation waveform.(3) Double T frequency selective network oscillator characteristics: good frequency selection characteristics, difficult frequency modulation, suitable for generating single frequency oscillation. ● RC oscillator circuitThe oscillating circuit composed of RC frequency selection network is called RC oscillating circuit, which is suitable for low-frequency oscillation, and is generally used to generate low-frequency signals of 1Hz~1MHz. The circuit is composed of four parts: amplifier circuit, frequency selection network, positive feedback network, and amplitude stabilization link. The main advantage is simple structure, economic and convenient. According to the different forms of the RC frequency selection network, the RC oscillator circuit can be divided into an RC lead (or lag) phase shift oscillator circuit and a Wien circuit oscillator circuit. For RC oscillator circuits, increasing the resistance R can reduce the oscillation frequency, and increasing the resistance does not need to increase the cost. The frequency of the sine wave generated by the commonly used LC oscillator circuit is relatively high. If a sine wave with a lower frequency is to be generated, the oscillation circuit must have a larger inductance and capacitance. This will not only cause the components to be bulky, heavy and inconvenient to install, but also difficult to manufacture. high cost.  Therefore, the sinusoidal oscillation circuit below 200kHz generally adopts an RC oscillation circuit with a lower oscillation frequency.3.2 RC Phase Shift OscillatorThe phase shift oscillator is an oscillator composed of an advanced phase shift or a lag phase shift circuit as a frequency selection network and an inverting amplifier. It has the advantages of simple circuit, economy and convenience, but the effect of frequency selection is poor, the amplitude is not stable enough, and the frequency adjustment is inconvenient. Therefore, it is generally used for occasions with fixed frequency and low stability requirements. Its oscillation frequency is:Figure15. RC Phase Shift Oscillator Schematic Diagram3.3 Wien Bridge OscillatorThe RC series-parallel frequency selection network and amplifier can be combined to form an RC oscillator circuit, and the amplifier part can be an integrated operational amplifier. As shown in the figure, the RC series-parallel frequency selection network is connected between the output of the operational amplifier and the non-inverting input to form positive feedback. Rt and R1 are connected between the output of the operational amplifier and the inverting input to form negative feedback. . The positive feedback circuit and the negative feedback circuit constitute a Wien bridge circuit, and the input and output ends of the operational amplifier are respectively connected across the diagonal of the bridge. Therefore, this kind of oscillation circuit is called a Wien bridge oscillation circuit.Figure16. Wien Bridge OscillatorThe oscillating signal is input from the non-inverting terminal, so a non-inverting amplifier is formed. The output voltage is in phase with the input voltage, and the closed-loop voltage amplification factor is equal to: When the RC series-parallel frequency selection network is ω=ω0=1/RC, Fu=1/3, εf=0, so as long as |Au|=1+(Rt/R1)>3, that is, Rt>2R1, oscillation The circuit can meet the self-excited oscillation amplitude and phase start-up conditions to produce self-excited oscillation, the oscillation frequency f0=1/2πRC. Using double adjustable potentiometer or double adjustable capacitor can easily adjust the oscillation frequency. In the commonly used RC oscillator circuit, the high stability capacitor is generally used to switch the frequency band (coarse frequency adjustment), and then the double variable potentiometer is used to fine-tune the frequency.IV Quartz Crystal Oscillator Circuit4.1 What is a Quartz Crystal Oscillator?Quartz crystal oscillator refers to a device made on the principle that the crystal resonates due to the piezoelectric effect when the frequency of the electrical signal is equal to the natural frequency of the quartz crystal. It is a key component of crystal oscillators and narrow-band filters.Although the appearance, size and frequency of the quartz crystal oscillator are different, the structure principle is basically the same. In order to improve the stable and reliable operation of the quartz crystal, the shell components of the quartz crystal oscillator will be sealed and evacuated. Or fill with nitrogen.4.2 Quartz Crystal(1) StructureFigure17. Structure of the Quartz Crystal(2) Basic characteristicsApplying an electric field between the plates→mechanical deformation of the crystalMechanical force is applied between the plates → the crystal generates an electric fieldPiezoelectric effect: alternating voltage → mechanical vibration → alternating voltageWhen the alternating voltage frequency = natural frequency, the amplitude is the largest → piezoelectric resonanceThe natural frequency of mechanical vibration is related to the size of the wafer, and the stability is high.4.3 Quartz Crystal Oscillator CircuitThe high quality factor of quartz crystal is used to form an LC oscillator circuit.(1) Parallel Type quartz crystal oscillatorFigure18. Parallel Type Quartz Crystal Oscillator Quartz crystal works between fs and fp, which is quite a large inductance, and forms a capacitive three-point oscillator with C1 and C2. Because the Q value of the quartz crystal is very high, which can reach more than several thousand, the circuit can obtain high oscillation frequency stability.Figure19. Frequency Characteristics of Parallel Quartz Crystal Oscillator (2) Series type quartz crystal oscillatorFigure20. Series Type Quartz Crystal Oscillator Circuit The quartz crystal works at fs, which is resistive and has the smallest impedance, the strongest positive feedback, and zero phase shift, which meets the phase balance condition of oscillation.For frequencies other than fs, the impedance of the quartz crystal increases, and the phase shift is not zero, then the oscillation condition is not met, and the circuit does not oscillate.Figure21. Frequency Characteristics of Series Quartz Crystal OscillatorV Non-sine Wave Generating Circuit5.1 What is a Non-sine Wave Generating Circuit?It is composed of an integrating circuit and a hysteresis comparator circuit. The role of the integrator circuit is to produce a transient process. The hysteresis comparator acts as a switch, that is, the steady state is destroyed by the continuous closing of the switch, and a transient process is generated.Commonly used non-sine wave generating circuits include rectangular wave generating circuits, triangular wave generating circuits and sawtooth wave generating circuits, etc. They are often used as signal sources in pulse and digital systems.5.2 Rectangular Wave GeneratorIt is composed of hysteresis comparison circuit and RC timing circuit. The output has no steady state and there are two transient states; if the output is high level, it is defined as the first transient state, and the output is low level as the second transient state.Basic components:(1) Switching circuit: The output has only two situations of high level and low level, called two states; therefore, a voltage comparator is used.(2) Feedback network: self-control, when the output is in a certain state, it breeds the condition of turning into another state. Feedback should be introduced.(3) Delay link: Make the two states maintain a certain period of time and determine the oscillation frequency. Use RC circuit to achieve.Circuit composition:Figure22. Rectangular Wave Generating Circuit5.3 Triangle Wave and Sawtooth Wave Signal GeneratorThe circuit structure of the triangle wave generator: hysteresis comparator + inverting integratorworking principle:Figure23. Circuit of Triangle Wave Generator Sawtooth wave generator: change the forward and reverse charging time constant of the integrator, thereby changing the duty cycle.Figure24. Circuit Diagram of Sawtooth Generator uo1=+UZ, D is cut off, charging time constant: R4C.uo1=-UZ, D is on, charging time constant: (R6∥R4)C≈R6C.Figure25. The Waveform of the Sawtooth GeneratorVI QuizLC resonant circuits are used in:a) RF and ultrasonic oscillators.b) AF and ultrasonic oscillators.c) LF sweep oscillators.d) Variable frequency crystal oscillators. Answer: aⅦ FAQ1. What are the uses of an oscillator?Oscillators have very high precision and accuracy usually <100 ppm variation at a max. So with this kind of accuracy, the oscillator can be used as a clock of the microcontroller (the clock is the most essential part of the microcontroller, without an accurate clock, the functionality will be erratic because we cannot expect the output at the same time we have designed it for). All the quartz-based watches use an Oscillator (32kHz quartz crystal) to keep the time. SO if your timekeeping devices are running with an oscillator, you can imagine the accuracy.Oscillators can additionally be used to generate waveforms required in test benches. In almost all the applications where timing and synchronization are very essential, an oscillator finds its place. For example, in communication systems (whichever electronic communication you consider let it be a telephone, lan, anything) an oscillator is the heart.An oscillator can be used in power systems to generate accurate power waveforms. 2. What is the function of a local oscillator?A local oscillator is used in transmitters and receivers to add or subtract an amount to a basic carrier and modulation. Very handy, as it’s easiest to build up a carrier and modulate it at a low frequency, like 445Kc or 10.7MHz, and then add to it a “LO” to get it up to the FM band or the Gigahertz Wifi or radar bands. The same thing on receive, you first use a 'LO' to subtract down to an intermediate frequency where it’s so much easier to amplify and filter. 3. How do you make a crystal oscillator?The simplest is to use a logic inverter. Put a crystal between the input and output. Some schematics show some caps from the crystal legs to the ground and some show a series resistor. 4. Which type of circuit is used in the oscillator?Types of Oscillators: Harmonic Oscillators & Crystal Oscillators. Harmonic or linear oscillators produce a sinusoidal output where a signal increases and decreases at a predictable level over time. Two basic types are RC, or resistor/capacitor circuits, as well as LC, or inductor-capacitor circuits. 5. What is an Oscillator and the types of oscillators?An oscillator is a type of circuit that controls the repetitive discharge of a signal, and there are two main types of the oscillator; a relaxation, or a harmonic oscillator. This signal is often used in devices that require a measured, continual motion that can be used for some other purpose. 6. What is the basic principle of an oscillator?There are many types of electronic oscillators, but they all operate according to the same basic principle: an oscillator always employs a sensitive amplifier whose output is fed back to the input in phase. Thus, the signal regenerates and sustains itself. This is known as positive feedback. 7. What is the working of the oscillator?Oscillators convert direct current (DC) from a power supply to an alternating current (AC) signal. They are widely used in many electronic devices ranging from simplest clock generators to digital instruments (like calculators) and complex computers and peripherals etc. 8. How does an oscillator work without input?An oscillator circuit uses a vacuum tube or a transistor to generate an AC output. ... For continuously generating output without the requirement of any input from the preceding stage, a feedback circuit is used. From the above block diagram, the oscillator circuit produces oscillations that are further amplified by the amplifier. 9. What causes oscillation?If a constant force such as gravity is added to the system, the point of equilibrium is shifted. ... In the spring-mass system, oscillations occur because, at the static equilibrium displacement, the mass has kinetic energy which is converted into potential energy stored in the spring at the extremes of its path. 10. What is the difference between oscillator and inverter?The oscillator is a generalized term for an active circuit that produces a periodic waveform. The inverter is a specialized term for a system that contains an oscillator and produces large amounts of power(such as AC) from a source (like a DC battery). The oscillator has no input and produces an oscillating wave as output.