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IntroductionRLC circuit is a circuit structure composed of resistance (R), inductance (L), and capacitance (C). The LC circuit is a simple example. RLC circuits are also called second-order circuits. The voltage or current in the circuit is the solution of a second-order differential equation, and its coefficients are determined by the circuit structure.If the circuit components are regarded as linear components, an RLC circuit can be regarded as an electronic harmonic oscillator.The natural frequency of this circuit is generally expressed as: (unit: Hz)RLC circuits are often used as band-pass filters or band-stop filters, and the Q factor can be obtained by the following formula:There are generally two types of RLC circuit composition: series and parallel.The animation above demonstrates the operation of the LC circuit (RLC circuit without resistors). The charge is transferred back and forth between the capacitor plate and the inductor. The energy oscillates back and forth between the electric field (E) of the capacitor and the magnetic field (B) of the inductor. The RLC circuit works similarly. The difference is that the oscillating current decays to zero over time due to the resistance in the circuit.CatalogIntroductionCatalogI RLC Series Circuit 1.1 What is Series RLC Circuit? 1.2 What is Transient Response of RLC Circuit? 1.3 Laplacian Domain 1.4 RLC Series Resonance Formula   1.5 Phasor Diagram of RLC Series CircuitII RLC Parallel CircuitIII The Difference Between Series Resonant Circuit and Parallel Resonant Circuit 3.1 Series Resonance 3.2 Parallel ResonanceIV Application of RLC Circuit Resonance 4.1 Application of Series Resonance Circuit 4.2 Application of Parallel Resonance CircuitV Frequently Asked Questions about RLC CircuitI RLC Series Circuit1.1 What is Series RLC Circuit?Figure1. RLC Series CircuitV-supply voltageI-circuit currentR-resistanceL-InductanceC-capacitanceIn this circuit, all three elements are connected in series with the voltage. The main differential equations can be obtained by substituting the constitutive equations of the three elements into Kirchhoff's voltage law (KVL). From Kirchhoff's voltage law:are the voltages across R, L, and C respectively, and V(t) is the voltage of the power supply that changes with time. Substituting the constitutive equation to get:In the case of a constant supply voltage, take the derivative of the above formula and divide by L to obtain the following second-order differential equation:This equation can be written in a more common form:α is called "attenuation", which is used to measure the attenuation rate of the transient response of this circuit when the external input is removed. ω0 is the angular resonance frequency. These two coefficients are given by:The damping coefficient ζ is another commonly used parameter, defined as the ratio of α to ω0:1.2 What is Transient Response of RLC Circuit?Figure2. Transient ResponseThe figure shows the underdamped and overdamped responses of the series RLC circuit. The critical damping is drawn with a thick red curve. These drawings are unified when L = 1, C = 1 and ω0=1. According to the value of different damping coefficient ζ, the solution of the differential equation has three different situations, namely: under-damping (ζ<1), over-damping (ζ>1), and critical damping (ζ=1).The characteristic equation of the differential equation is:The roots of this equation are:The general solution of this differential equation is the linear superposition of two exponential functions:The coefficients A1 and A2 are given by the boundary conditions of the specific problem.The following video introduces how to analyze RLC circuits by way of second order differential equations. Both parallel and series RLC configurations are discussed in it, looking primarily at Natural Response, but also touching on Step Response.RLC Circuit Response Explanation1.2.1 Over-damped responseThe over-damped response (ζ>1) is:Overdamping response is a transient current without oscillation attenuation.1.2.2 Underdamped responseThe underdamped response (ζ<1) is:Through the trigonometric identities, these two trigonometric functions can be expressed by a phased sine function:The underdamped response is an attenuated oscillation with a frequency of ωd. The rate of oscillation decay is α. The α in the index describes the envelope function of the oscillation. B1 and B2 (or B3 and phase difference φ in the second form) are arbitrary constants and are determined by boundary conditions. The frequency ωd is given by:This is the so-called damped resonance frequency or damped natural frequency. It is the frequency at which the circuit naturally vibrates when driven by no external source. The resonant frequency ω0 is the resonant frequency of the circuit when it is driven by an external source, and is often called the undamped resonant frequency in order to facilitate the distinction.1.2.3 Critical damping responseThe critical damping response (ζ=1) is:1.3 Laplacian DomainThe Laplace transform can be used to analyze the AC transient and steady-state behavior of the RLC series circuit. If the waveform generated by the above voltage source is V(s) after Laplace transform (where s is the complex frequency s=σ+iω), then Kirchhoff’s voltage law is applied in the Laplace domain:Among them, I(s) is the current after Laplace transform. Solve for I(s):After rearranging, the following formula can be obtained:1.3.1 Laplace admittanceSolve for Laplace admittance Y(s):The above formula can be simplified by using the parameters α and ωo defined in the above content, and we can get:1.3.2 Pole and zeroThe zero point of Y(s) is s such that Y(s)=0: s=0 and |s|⟶ ∞; the pole of Y(s) is s such that Y(s)⟶ ∞. Solve the quadratic equation. Get:The poles of Y(s) are the roots s1 and s2 of the characteristic equation of the differential equation mentioned above.1.3.3 Sine steady stateThe sine steady state can be represented by letting s=jω, where j is the imaginary unit. Substitute this into the amplitude of the above equation:The function of the current with ω as the variable isThere is a peak.In this special case, ω in this peak is equal to the undamped natural resonance frequency:1.4 RLC Series Resonance FormulaThe so-called series resonance formula refers to the study of the energy value of the voltage and current of the series circuit to reach the same phase, and the inductance of the inductance in the circuit and the capacitive reactance in the capacitor are equal in value. Therefore, in the study of the resistance characteristics of the circuit, In the case of a given terminal voltage, the maximum current is released, and the active power consumed will also be the maximum.Figure3. RLC series resonance formulaResonance definition: The energy of the L and C_ elements in the circuit are equal. When a reactance element in the circuit releases energy, the other reactance element must absorb the same energy, that is, energy pulsation occurs between the two reactance elements.  When series resonance occurs:Inductive reactance XL = capacitive reactance XCSource voltage U = resistance voltage URInductor voltage UL = Capacitor voltage UCInductor's reactive power QL = Capacitor's reactive power QCTotal circuit impedance Z=resistance value RApparent power S = resistance power PExplanation: When the circuit resonates, it must have two components: inductor L and capacitor C, and the frequency corresponding to resonance is called "resonant frequency" or resonant frequency, generally we use fr to indicate.1.5 Phasor Diagram of RLC Series Circuit(1) Phasor diagram of voltage and currentU&=U&R+U&L+U&CFigure4. Phasor diagram of voltage and currentFigure5. Phasor diagram of voltage and current(2) Voltage triangleThe relationship between the voltage triangle and the impedance triangle: divide the effective value of the voltage triangle by I to get the impedance triangle.Figure6. Voltage triangle● The relationship between the total voltage and the effective value of each part of the voltage:● The effective value relationship between total voltage and total current: U=I|Z|● The phase difference relationship between total voltage and total current:II RLC Parallel CircuitFigure7. RLC Parallel CircuitV-supply voltageI-circuit currentR-resistanceL-InductanceC-capacitanceThe characteristics of the RLC parallel circuit can be handled by the duality (electrical circuits) of the circuit. The RLC parallel circuit is treated as the dual impedance of the RLC series circuit, so it can be analyzed in a similar way to the RLC series circuit.The attenuation α of the RLC parallel circuit can be obtained by the following formula:If the factor of 1/2 is not considered, the damping coefficient of the RLC parallel circuit is exactly the reciprocal of the damping coefficient of the RLC series circuit.Frequency domainAdd the admittance of each element in parallel to obtain the admittance of this circuit:After capacitors, resistors, and inductors are connected in parallel, the impedance at the resonance frequency is the maximum, which is the opposite of the case where capacitors, resistors, and inductors are connected in series. The RLC parallel circuit is an antiresonator.In the figure below, it can be seen that if a constant voltage is used for driving, the frequency response of the current has a minimum value at the resonance frequency ω0=1/√LC. If it is driven by a constant current, the frequency response of the voltage has a maximum value at the resonance frequency, which is similar to the frequency response graph of the current in an RLC series circuit.Figure8. Sinusoidal steady state analysisNormalize with R = 1 ohm, C = 1 Farad, L = 1 Henry, and V = 1.0 VoltIII The Difference Between Series Resonant Circuit and Parallel Resonant CircuitIn an AC circuit containing resistance, inductance and capacitance, the voltage at both ends of the circuit and its current are generally out of phase. If the circuit parameters or the power supply frequency are adjusted to make the current and the power supply voltage in phase, the circuit is resistive, which is called resonance for the working state of the circuit at this time.Resonance is a specific phenomenon of sinusoidal AC circuits. It is widely used in electronics and communication engineering. However, in power systems, resonance may damage the normal operation of the system.Resonance is generally divided into series resonance and parallel resonance. As the name implies, series resonance is the resonance that occurs in a series circuit. Parallel resonance is the resonance that occurs in a parallel circuit.3.1 Series Resonance3.1.1 IntroductionIn a series circuit composed of resistance, inductance and capacitance, when the capacitive reactance XC and the inductive reactance XL are equal, that is, XC=XL, the voltage U and the current I in the circuit have the same phase, and the circuit presents pure resistivity. This phenomenon is called series resonance. When the circuit is in series resonance, the total impedance in the circuit is the smallest, and the current will reach the maximum. 3.1.2 Conditions for the occurrence of series resonanceIn order to resonate in a series circuit, certain conditions must be met.When UL=UC, that is, XL=XC,. Voltage and current are in phase, and series resonance occurs in the circuit. From ωL=1/ωC, ω0=1/√LC can be obtained, and the resonance frequency is f=f0=1/2π√LC. 3.1.3 Characteristics of series resonance circuit● Minimum total impedance● When the power supply voltage is constant, the current is the largest● The circuit is resistive, and the voltage on the capacitor or inductor may be higher than the power supply voltage 3.1.4 Energy changes in the circuit at resonanceThe circuit absorbs Q=0 from the power supply, and the circuit energy exchanges between the electric field and the magnetic field inside the circuit during resonance. The power supply only provides energy to R.High voltage may damage the device. Series resonance should be avoided in the power system. And series resonance is widely used in radio engineering.3.2 Parallel Resonance3.2.1 IntroductionIn a circuit where an inductance and a capacitor are connected in parallel, when the size of the capacitor just makes the voltage and current in the circuit have the same phase, that is, when the power supply is consumed by resistance and becomes a resistance circuit, it is called parallel resonance.Parallel resonance is a complete compensation. The power supply does not need to provide reactive power, only the active power required by the resistance. At resonance, the total current of the circuit is the smallest, and the current of the branch is often greater than the total current of the circuit. Therefore, parallel resonance is also called current resonance.When parallel resonance occurs, a large current flows in the inductance and capacitance components, which will cause the fuse of the circuit to blow or burn the electrical equipment; however, it is often used in radio engineering to select signals and eliminate interference. 3.2.2 Parallel resonance conditionsIn the following two types of circuitsFigure9. Two types of circuitsThe resonant frequency formula of (a) has been discussed above, and (b) is determined by,We can get.Under normal circumstances, the coil resistance R is much smaller than XL, therefore, ignoring R we can getthat is f=f0=1/2π√LC. 3.2.3 Features of parallel resonant circuit● When the voltage is constant, the current is the smallest at resonance● Maximum total impedance● The circuit is resistive, and the branch current may be greater than the total currentIV Application of RLC Circuit Resonance4.1 Application of Series Resonance CircuitThe use of series resonance to generate power frequency high voltage, which is used in high voltage technology to do withstand voltage test for power equipment such as transformers, can effectively find dangerous concentrated defects in the equipment, and is the most effective and direct way to test the insulation strength of electrical equipment Methods. Used in radio engineering, series resonance is often used to obtain a higher voltage.In the radio, the series resonance circuit is often used to select the radio signal. This process is called tuning. The following figure shows a typical circuit.Figure10. A typical circuit for tuningWhen the electric waves of various signals of different frequencies generate electric signals of different frequencies on the antenna, they are induced to the coil 2L through the coil 1L. If the oscillation circuit resonates to a certain signal frequency, the current of the signal in the loop is the largest, and a voltage CU higher than the signal voltage Q times is generated across the capacitor. For other signals of various frequencies, because no resonance occurs, the current in the loop is very small, which is suppressed by the circuit. Therefore, the capacitor C can be changed to change the resonant frequency of the loop to select the desired radio signal.4.2 Application of Parallel Resonance CircuitThe application of LC parallel resonant circuit in communication electronic circuit is determined by its characteristics. Specifically, it mainly includes three categories. One is working in resonance, as a frequency-selective network application. At this time, it appears as a large resistance and outputs a larger voltage under the excitation of current; the second is working in detuning The state, present as inductive or capacitive at this time, together with other inductances and capacitors in the circuit, satisfies the oscillation conditions of the three-point oscillation circuit to form a sine wave oscillator; the third is to work in a detuned state, that is, to work on the amplitude-frequency characteristic curve Or one side of the phase-frequency characteristic curve to realize amplitude-frequency conversion, frequency-amplitude conversion, frequency-phase conversion, and phase-frequency conversion to form an angle modulation and demodulation circuit. (1) LC parallel resonant circuit used as frequency selective matching networkFrequency selection is to select useful frequency components from the input signal and suppress useless frequency components or noise. In communication electronic circuits, the LC parallel resonant circuit is the most commonly used as a frequency selection network. It is widely used in high-frequency small-signal amplifiers, Class C high-frequency power amplifiers, mixers and other circuits. The common feature of these circuits is that the LC resonant circuit is not only a frequency-selective network. Through the connection of the transformer, it also plays the role of impedance transformation, reducing the impact of the amplifier tube or the load on the resonant circuit, and obtaining better selectivity. . (2) The LC parallel resonant circuit of the overtone crystal oscillator as a capacitorUnder the action of the applied alternating voltage, in the mechanical vibration generated by the quartz crystal, in addition to the fundamental frequency mechanical vibration, there are many odd frequency overtones. When a crystal oscillator with a very high operating frequency is required, overtone crystal oscillators are often used. The figure below shows the overtone crystal oscillator.Figure11. Circuit composition and reactance curve of L1C1 circuitIn the above figure, the quartz crystal and the CL branch are inductive. The quartz crystal, C2, and L1C1 loop together form a three-point oscillator. According to the composition principle of the three-point oscillator (shooting the same), the L1C1 resonant circuit should be capacitive. Assuming that the quartz crystal in the figure is working at the 5th overtone frequency, the nominal frequency is 5 MHz. In order to suppress the parasitic oscillation of the fundamental frequency and 3rd overtone, the L1C1 loop should be tuned between the 3rd and 5th overtone frequency, that is, 3~ Between 5 MHz.  From the reactance characteristic curve of the L1C1 resonant circuit shown in Figure (b), it can be seen that for the 5th overtone frequency of 5 MHz, the L1C1 circuit is capacitive, and the circuit meets the three-point oscillation condition and can oscillate. For the fundamental and third harmonics that are less than the resonance frequency of the L1C1 loop, the loop has an inductive characteristic, which does not conform to the principle of different components and cannot produce oscillation. For overtones of 7 times and above, although the L1C1 circuit is also capacitive, the equivalent capacitance at this time is too large, the amplitude starting conditions cannot be met, and the oscillation cannot be generated. (3) LC parallel resonant circuit that realizes the functions of amplitude-frequency conversion and frequency-phase conversionThe phase-frequency characteristic of the impedance of the LC parallel resonant circuit is a monotonous curve with a negative slope. The linear part of the curve can be used to perform a linear conversion between frequency and phase. This is mainly used in the phase frequency discrimination circuit; the same, the LC parallel resonant circuit The linear part of the impedance's amplitude-frequency characteristic curve can also perform the linear conversion between frequency and amplitude, so it has also been applied in the slope frequency discrimination circuit.V Frequently Asked Questions about RLC Circuit1. Is LCR and RLC circuit the same?Yes. An RLC circuit (also known as a resonant circuit, tuned circuit, or LCR circuit) is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. This configuration forms a harmonic oscillator. 2. What is the resonant frequency of the RLC circuit?What is Resonance in the RLC circuit? Resonance is the phenomenon in the electrical circuit, where the output of the circuit is maximum at one particular frequency. And that frequency is known as the resonant frequency. At the resonant frequency, The capacitive reactance and inductive reactance are equal. 3. Is the RLC circuit linear?In an RLC circuit, the most fundamental elements of a resistor, inductor and capacitor are connected across a voltage supply. All of these elements are linear and passive in nature. 4. What is the bandwidth of the RLC circuit?The bandwidth of any system is the range of frequencies for which the current or output voltage is equal to 70.7% of its value at the resonant frequency, and it is denoted by BW. 5. What is the second-order circuit?A second-order circuit is characterized by a second-order differential equation. It consists of resistors and the equivalent of two energy storage elements. 6. What is the first-order circuit?A first-order circuit can only contain one. energy storage element (a capacitor or an. inductor). The circuit will also contain. 7. What is the half-power frequency?The frequencies for which current in a series RLC (or a series tuned) circuit is equal to 1/√2 (i.e. 70.71%) of the maximum current (current at resonance)are known as Half Power Frequencies. 8. What is the natural response of the RC circuit?The natural response tells us what the circuit does as its internal stored energy (the initial voltage on the capacitor) is allowed to dissipate. It does this by ignoring the forcing input (the voltage step caused by the switch closing). The "destination" of the natural response is always zero voltage and zero current. 9. What is the difference between first-order and second-order filters?The main difference between a 1st and 2nd order low pass filter is that the stopband roll-off will be twice the 1st order filters at 40dB/decade (12dB/octave) as the operating frequency increases above the cut-off frequency ƒc, point as shown. 10. What is the use of a resonant circuit?One use for resonance is to establish a condition of stable frequency in circuits designed to produce AC signals. Usually, a parallel (tank) circuit is used for this purpose, with the capacitor and inductor directly connected together, exchanging energy between each other. 

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.

2026 Executive Summary: Discharging a capacitor safely is a critical maintenance step to prevent severe electrical shocks and equipment damage. In 2026, with the rapid expansion of high-voltage EV inverters and renewable energy grid systems, proper discharge protocols using dedicated resistors or discharge tools are more important than ever. This guide covers the working principles, safety procedures, and step-by-step methods for discharging both low and high-voltage capacitors safely.IntroductionMaintenance technicians and electronics hobbyists frequently experience electrical shocks from devices long after they have been unplugged. The primary component responsible for this dangerous phenomenon is the capacitor. From industrial power capacitors and modern EV inverter filter capacitors to the graphite coating of legacy CRT televisions, capacitors can store lethal amounts of electrical charge (often exceeding 300V) in fractions of a second. If maintenance personnel accidentally touch a charged terminal, the resulting electric shock can cause severe secondary injuries, such as falls or involuntary contact with other live circuits. Therefore, verifying zero energy state and manually discharging the capacitor is a mandatory safety protocol before beginning any repair work. This article details the industry-standard methods for safely discharging capacitors, explains the underlying physics of capacitance, and outlines the working principles of various capacitor types used in 2026. If you need to calculate the exact discharge rate of a capacitor under a known capacitance and charge it through a fixed value resistor, we recommend using Apogeeweb's Capacitor Safety Discharge Calculator.Figure 1. Apogeeweb's Capacitor Safety Discharge CalculatorTable of ContentsIntroductionTable of ContentsI. How Does a Capacitor Charge and Discharge?II. How to Safely Discharge a Capacitor?  2.1 Discharge Method After the Capacitor is Cut Off  2.2 Critical Safety Notes for Capacitor Discharge  2.3 The Physics of the Charging and Discharging ProcessIII. Three Methods to Discharge High Voltage Capacitors  3.1 What is a High Voltage Capacitor?  3.2 Step-by-Step High Voltage Discharge MethodsIV. How to Discharge Low Voltage Capacitors?  4.1 Short-circuiting with Wires  4.2 Using a Digital Multimeter  4.3 Safety PrecautionsV. How to Discharge a Filter Capacitor?  5.1 Discharge Techniques for Filter Capacitors  5.2 Calculating Charge and Discharge Time ConstantsVI. Fast Discharge Methods for Power Compensation and Electrolytic CapacitorsVII. How Does a Capacitor Bank Discharge Coil Work?  7.1 Principle of Capacitor Bank Discharge Coils  7.2 Influence of the Connection ModeVIII. How to Test Capacitors Using the Discharge PrincipleIX. Test Your Knowledge: Capacitor QuizX. Frequently Asked QuestionsI. How Does a Capacitor Charge and Discharge?When a capacitor charges, it stores electrical energy in an electrostatic field between two conductive plates, and when it discharges, it releases this stored energy back into the circuit to power a load. A capacitor is a passive electronic component composed of two conductive parallel plates separated by an insulating dielectric material.Figure 2. The Function of CapacitorsDuring the charging process, the power supply forces charged particles through the circuit, causing the potential difference between the two plates to gradually approach the voltage of the power source. Ultimately, opposite polarities of charge accumulate on the plates, bound by the dielectric, storing electrical energy as an electrostatic field. During the discharge process, the capacitor acts as a temporary power source. It moves the stored charged particles through a closed circuit, neutralizing the potential difference between the plates. The electrostatic field collapses, and the stored energy is converted into work consumed by the connected electrical load.II. How to Safely Discharge a Capacitor?To safely discharge a capacitor, you must create a controlled closed loop using a high-wattage resistor or a dedicated discharge tool to slowly neutralize the stored potential difference without creating dangerous sparks. Watch this demonstration video first:A practical capacitor lesson demonstrating the effects of uncontrolled discharge.2.1 Discharge Method After the Capacitor is Cut OffWhen a capacitor is disconnected from an energized circuit, it retains its stored voltage. If the circuit contains bleed resistors or other continuous loads, it will discharge slowly. Otherwise, it must be discharged manually by creating a short circuit through a resistive load (or a direct wire for very low voltages). When discharging, the external circuit and the capacitor form a closed loop. The excess electrons (negative charges) travel toward the positive electrode to achieve electrostatic balance. This current flow neutralizes the charges on both ends of the capacitor. Once neutralization is complete, the electric field disappears. However, because real-world circuits always contain some resistance, the charge decays exponentially. It trends infinitely toward zero but technically never reaches absolute zero, though it quickly drops to safe handling levels.Figure 3. Discharge Tools2.2 Critical Safety Notes for Capacitor DischargeAfter the capacitor is disconnected from the main bus, it must be discharged through a high-wattage discharge resistor or a special voltage transformer.Discharge must occur between the lead wires of the capacitor, and subsequently between the lead wires and the metal casing.The capacitor should be physically grounded only after the initial resistive discharge is complete.Before handling the capacitor, a test discharge must be performed by holding the discharge rod on the terminals for several seconds.Even if both sides of a capacitor bank are grounded, residual charges can remain. Each individual capacitor in a parallel group must be discharged separately.Exercise extreme caution with damaged capacitors. Internal disconnections can prevent standard grounding devices from fully discharging the unit.If the capacitor enclosure features an interlocking safety device, ensure the protective fence is only opened after the entire system is verified as grounded.2.3 The Physics of the Charging and Discharging ProcessSuppose a capacitor has upper and lower plates, with the upper plate connected to the positive electrode and the lower plate to the negative electrode. Upon connection to a DC power supply, a potential difference forms. The positive charges remain stationary in the atomic lattice, while the negative charges (electrons) are repelled from the negative terminal of the supply and accumulate on the bottom plate. This electron movement creates a growing potential difference across the plates. The voltage increases until it perfectly matches the power supply voltage, at which point the capacitor is fully charged and current ceases to flow. After disconnecting the power, the dielectric insulation prevents the charges from recombining. The potential difference persists until a conductive path is provided. When we discharge the capacitor by connecting the plates with a wire or resistor, electrons flow from the negatively charged plate back to the positive plate until electrostatic equilibrium is restored.Figure 4. Charge and DischargeIII. Three Methods to Discharge High Voltage Capacitors3.1 What is a High Voltage Capacitor?High-voltage capacitors are heavy-duty components designed to handle extreme electrical loads, commonly found in microwave ovens, medical imaging equipment, and modern EV charging infrastructure. They consist of outlet porcelain bushings, capacitive element groups, and a sealed steel shell. The internal elements use capacitor paper, film-paper composites, or pure synthetic films as the dielectric, with aluminum or platinum plates. To meet high withstand voltage requirements (often exceeding 10kV), internal capacitive elements are connected in series or parallel. Many modern high-voltage capacitors are equipped with internal bleed resistors designed to reduce residual voltage below 75V within 10 minutes of disconnection, though manual discharge remains a mandatory safety requirement.Figure 5. Microwave High Voltage Capacitor3.2 Step-by-Step High Voltage Discharge MethodsHigh-voltage capacitors must never be short-circuited directly with a screwdriver, as the massive instantaneous current can melt the contacts, vaporize the metal, and cause an explosion. Instead, the energy must be dissipated slowly using a resistive load. Here are three safe methods:Method 1: The High-Wattage Resistor MethodFirst, unplug the electrical power and verify the equipment is isolated from the mains.Obtain a 20,000-ohm, 2-watt (or higher, such as 5W) wire-wound resistor.Using insulated pliers, hold the resistor and touch its probes across the two terminals of the capacitor for several seconds.If the capacitor has three terminals, discharge between the outer terminal and the center terminal, then repeat for the remaining outer terminal.Method 2: The Alligator Clip MethodConnect one end of a high-wattage resistor to an insulated test lead and the other end to an insulated alligator clip. Wrap exposed connections in electrical tape.Clamp the alligator clip securely to the equipment's chassis ground wire.Use the test lead probe to touch the positive terminal of the capacitor. This routes the discharge safely to ground without generating sparks.Note: If discharging multiple capacitors consecutively, the resistor will generate significant heat. Use a 5W or 10W resistor for heavy-duty applications.Method 3: The Bulb or Soldering Iron MethodConstruct a discharge rig using a 100-200 watt incandescent bulb (or a 60-80W electric soldering iron) connected to two insulated probes.Touch the probes to the capacitor terminals. The bulb will flash brightly and dim as the capacitor discharges, providing a visual indicator of the voltage drop.Once the bulb is completely dark, verify the voltage is zero using a multimeter.IV. How to Discharge Low Voltage Capacitors?4.1 Short-circuiting with WiresFor low-voltage capacitors operating below 50V or with a capacity under 1μF, you can safely discharge them by directly short-circuiting the two poles with an insulated wire or screwdriver. While a screwdriver is common, it can leave carbonized burn marks on the terminals. Never use this direct short-circuit method for high-voltage or large-capacity capacitors, as the rapid energy release will create dangerous sparks and potentially damage the component.Figure 6. Shortcircuit4.2 Using a Digital MultimeterYou can safely discharge small capacitors using the resistance setting (Ohms) on a digital multimeter. Set the multimeter to a high resistance range (e.g., 100K or 200K ohms) and place the probes on the capacitor terminals. The internal battery of the multimeter will interact with the capacitor, and you will see the resistance reading climb or drop until it stabilizes, indicating the charge has been neutralized. Disconnect the probes immediately after the reading stabilizes to prevent reverse charging.Figure 7. Multimeter4.3 Safety PrecautionsBecause capacitors exhibit dielectric absorption (often called "battery action"), they can slowly rebuild a small residual charge even after being discharged. Always manually discharge a capacitor immediately before handling it, even if the equipment has been unplugged for days. When working with industrial capacitor banks, ensure the circuit breaker and isolation switches are open, and wear appropriately rated insulating gloves.V. How to Discharge a Filter Capacitor?5.1 Discharge Techniques for Filter CapacitorsA filter capacitor is an energy storage device installed at the output of a rectifier circuit to smooth out AC pulsations and provide a stable DC output. In a standard 220V AC to DC power supply, the voltage across the primary filter capacitor can reach approximately 310V DC. To discharge a 310V filter capacitor, the best tool is a 25W electric soldering iron or a dedicated power resistor. A 25W soldering iron has an internal resistance of about 2.2KΩ. According to Ohm's Law (I = U/R), the maximum initial discharge current is 310V / 2200Ω = 140mA. This low current safely drains a several-hundred microfarad capacitor in a few seconds without generating sparks. Avoid using a 25W incandescent bulb for 310V filter capacitors. The cold resistance of a 25W tungsten filament is only about 160Ω, resulting in an instantaneous current surge of nearly 2 amps, which can instantly burn out the filament.Figure 8. Filter Capacitors5.2 Calculating Charge and Discharge Time ConstantsThe charging and discharging time of a filter capacitor is dictated by the RC time constant (T = R × C), where R is the circuit resistance and C is the capacitance. The time required for the capacitor voltage to reach 63.2% of the supply voltage is one time constant. After 5 time constants (5T), the capacitor is considered 99.3% fully charged or discharged. Charging Calculation: If a rectifier diode has an internal forward resistance of 30Ω and the filter capacitor is 2200μF, the charging time constant is Tc = 30Ω × 0.0022F = 0.066 seconds (66ms). Discharging Calculation: If the connected load has a resistance of 300Ω, the discharge time constant is Td = 300Ω × 0.0022F = 0.66 seconds (660ms). It will take approximately 3.3 seconds (5 × 660ms) for the capacitor to fully discharge through the load once power is removed.Figure 9. (a) Charging Curve (b) Discharging CurveFigure 10. Bridge Rectifier CircuitRelated recommendation: Apogeeweb's time constant calculator.VI. Fast Discharge Methods for Power Compensation and Electrolytic Capacitors(1) Power Factor Compensation CapacitorsPower factor compensation capacitors, rated in kVAR, are large non-polar capacitors used to stabilize industrial power grids. Modern units are equipped with internal discharge resistors designed to drop the voltage below 50V within 3 minutes of disconnection. However, technicians must still manually discharge them using a high-power resistor probe before maintenance, as they operate at grid voltages (220V to 480V+).Figure 11. Reactive Power Compensation Supplied by Capacitors(2) Operating Skills for Electrolytic CapacitorsSmall Lead-Type: Can be directly short-circuited, though using a 100-ohm resistor is always safer for the component's lifespan.Snap-in/Horn Type: Use a 220V/60W bulb or a dedicated 1KΩ 5W resistor to discharge slowly.Large Bolt-Type: For high-voltage industrial electrolytics, use a dedicated discharge coil. Alternatively, a long (5-meter) coiled wire with alligator clips can be used; the length and coiling provide enough inductive and resistive load to dissipate the energy as heat safely.VII. How Does a Capacitor Bank Discharge Coil Work?A discharge coil is a mandatory safety device installed in parallel with high-voltage capacitor banks in substations. It rapidly drains the residual charge from the capacitors when they are disconnected from the grid, preventing dangerous overvoltage conditions during re-closing and ensuring the safety of maintenance personnel.7.1 Principle of Capacitor Bank Discharge CoilsThe discharge coil acts as a voltage transformer. Its primary winding is connected across the capacitor bank, bearing the full operating voltage. When the power is cut, the coil provides a low-resistance path for the DC charge to dissipate rapidly. For large capacity capacitor banks (≥1.7Mvar), a dedicated discharge coil must be used instead of a standard voltage transformer (PT) to prevent the PT from overheating and exploding under the massive discharge current.7.2 Influence of the Connection ModeDischarge coils are typically used in 66kV and below power systems. Their secondary windings are often wired in an open delta configuration to provide internal fault protection for the capacitor bank. If the discharge coil is used to directly monitor the capacitor's terminal voltage, jumper connection methods cannot be used, as they would distort the voltage readings required for accurate protective relaying.VIII. How to Test Capacitors Using the Discharge PrincipleYou can test the health of a capacitor (checking for breakdown, leakage, or failure) using an analog multimeter. This test relies on the multimeter's internal battery charging the capacitor, and the subsequent discharge behavior.Normal: The multimeter pointer swings rapidly to the right (low resistance) as the capacitor charges, then slowly returns to "∞" (infinite resistance) as it fully charges and blocks DC current.Leakage: The pointer swings to the right but fails to return all the way to "∞", stopping at a specific resistance value. This indicates the dielectric is leaking current.Open Circuit: The pointer does not move at all and stays at "∞". (Note: Very small capacitors under 5000pF may not show a visible swing on standard meters).Short Circuit: The pointer swings to "0" ohms and stays there, indicating the internal dielectric has completely failed.Figure 12. (a) Normal; (b) Breakdown; (c) FailureIX. Test Your Knowledge: Capacitor QuizWhich of the following determines the charging and discharging rate of a capacitor?a) Time constantb) Currentc) Powerd) VoltageAnswer: aExplanation: The time constant (T = R × C) in an RC circuit dictates the speed of charge and discharge. A smaller time constant results in a faster charging and discharging rate. Frequently Asked QuestionsWhat is the safest tool to discharge a capacitor?The safest tool to discharge a capacitor is a dedicated capacitor discharge pen or a high-wattage resistor (such as a 20,000-ohm, 5-watt resistor) connected to insulated alligator clips. These tools safely dissipate the stored electrical energy as heat without creating dangerous sparks or damaging the capacitor terminals.How long does it take for a capacitor to discharge naturally?A disconnected capacitor can take anywhere from a few minutes to several months to discharge naturally, depending on its internal leakage resistance and dielectric material. Because high-voltage capacitors can retain lethal charges for weeks, you must always manually discharge and verify them with a multimeter before handling.Why shouldn't I use a screwdriver to discharge a capacitor?Using a screwdriver to short-circuit a capacitor causes an instantaneous, uncontrolled energy release. This rapid discharge can generate dangerous sparks, melt the capacitor's terminals, damage the screwdriver, and potentially cause the capacitor to explode. Always use a proper resistive load to control the discharge rate safely.Can a capacitor hold a charge without power?Yes, a capacitor is specifically designed to store electrical energy and will hold its charge long after the main power supply is disconnected. This residual charge acts like a temporary battery, which is why capacitors pose a severe shock hazard in unplugged electronic devices and power supplies.{ "@context": "https://schema.org", "@graph":[ { "@type": "Article", "headline": "How to Safely Discharge a Capacitor: 2026 Guide", "datePublished": "2020-09-10", "dateModified": "2026-03-20", "author": { "@type": "Organization", "name": "Apogeeweb" }, "publisher": { "@type": "Organization", "name": "Apogeeweb" }, "description": "A comprehensive 2026 guide on how to safely discharge high and low voltage capacitors, including step-by-step methods, safety tools, and the physics of RC time constants." }, { "@type": "FAQPage", "mainEntity":[ { "@type": "Question", "name": "What is the safest tool to discharge a capacitor?", "acceptedAnswer": { "@type": "Answer", "text": "The safest tool to discharge a capacitor is a dedicated capacitor discharge pen or a high-wattage resistor (such as a 20,000-ohm, 5-watt resistor) connected to insulated alligator clips. These tools safely dissipate the stored electrical energy as heat without creating dangerous sparks or damaging the capacitor terminals." } }, { "@type": "Question", "name": "How long does it take for a capacitor to discharge naturally?", "acceptedAnswer": { "@type": "Answer", "text": "A disconnected capacitor can take anywhere from a few minutes to several months to discharge naturally, depending on its internal leakage resistance and dielectric material. Because high-voltage capacitors can retain lethal charges for weeks, you must always manually discharge and verify them with a multimeter before handling." } }, { "@type": "Question", "name": "Why shouldn't I use a screwdriver to discharge a capacitor?", "acceptedAnswer": { "@type": "Answer", "text": "Using a screwdriver to short-circuit a capacitor causes an instantaneous, uncontrolled energy release. This rapid discharge can generate dangerous sparks, melt the capacitor's terminals, damage the screwdriver, and potentially cause the capacitor to explode. Always use a proper resistive load to control the discharge rate safely." } }, { "@type": "Question", "name": "Can a capacitor hold a charge without power?", "acceptedAnswer": { "@type": "Answer", "text": "Yes, a capacitor is specifically designed to store electrical energy and will hold its charge long after the main power supply is disconnected. This residual charge acts like a temporary battery, which is why capacitors pose a severe shock hazard in unplugged electronic devices and power supplies." } } ] }, { "@type": "HowTo", "name": "How to Discharge a High Voltage Capacitor", "description": "Step-by-step instructions for safely discharging a high voltage capacitor using a high-wattage resistor.", "step":[ { "@type": "HowToStep", "name": "Isolate Power", "text": "First, unplug the electrical power and verify the equipment is isolated from the mains." }, { "@type": "HowToStep", "name": "Prepare the Resistor", "text": "Obtain a 20,000-ohm, 2-watt (or higher, such as 5W) wire-wound resistor." }, { "@type": "HowToStep", "name": "Discharge the Terminals", "text": "Using insulated pliers, hold the resistor and touch its probes across the two terminals of the capacitor for several seconds." }, { "@type": "HowToStep", "name": "Discharge Multi-Terminal Capacitors", "text": "If the capacitor has three terminals, discharge between the outer terminal and the center terminal, then repeat for the remaining outer terminal." } ] } ]}

IntroductionThe hard disk interface is the connecting part between the hard disk and the host computer system, and its function is to transmit data between the hard disk cache and the host memory. Different hard disk interfaces determine the data transmission speed between the hard disk and the computer. In the entire system, the quality of the hard disk interface directly affects the speed of the program and the performance of the system. From this article, you can understand the connector concepts of IDE, SATA, SCSI, Fibre Channel (FC) and SAS and their development process, and finally two important interface protocols: AHCI and NVMe.SAS, SATA, SCSI, FC, and IDE ExplainedCatalogIntroductionⅠ Bus Interface TypesⅡ What is IDE?2.1 Integrated Drive Electronics Definition2.2 IDE Mode2.3 IDE Advantages and DisadvantagesⅢ What is SCSI?3.1 SCSI Basics3.2 SCSI VersionⅣ What is Fiber Channel (FC)?4.1 Overview of Fibre Channel4.2 Fibre Channel ProtocolⅤ What is SATA?5.1 Serial ATA Definition5.2 SATA Interface5.3 IDE vs SATA InterfaceⅥ What is M.2?Ⅶ What is SAS?Ⅷ Tech Guide: AHCI and NVMe Protocol8.1 AHCI Protocol8.2 NVMe Protocol8.3 Tech NoteⅠ Bus Interface TypesFrom an overall point of view, hard disk interfaces are divided into five types: parallel ATA (PATA, also called IDE or EIDE), SATA, SCSI, Fibre Channel, and SAS. IDE is mostly used in household products. And some of it are used in website servers. SCSI is mainly used in the server market. While Fibre Channel is only used in high-end servers and is expensive. SATA is now the mainstream hard disk. Most notebook computers and desktop computers use it, and solid state hard drives also use it. SAS is generally used in servers. It has fast transmission speed and strong reliability. Under the broad categories of IDE and SCSI, there has a variety of specific interface types that can be divided according to different technical specification and transmission speed. Ⅱ What is IDE?2.1 Integrated Drive Electronics DefinitionThe full name of IDE is "Integrated Drive Electronics", and its original meaning refers to the hard disk drive that integrates the "hard disk controller" and the "disk body". This approach reduces the number and length of cables for the hard disk interface, enhances the reliability of data transmission, and makes hard disk manufacturing easier. Many hard disks used to have IDE interfaces, but now almost all hard disk interfaces are standard with SATA.IDE represents a type of hard disk interfaces, but in actual applications, people are also used to call it the first IDE-type hard disk ATA-1. This type of interface has been eliminated with the development of technology. With the time passes, more types of hard disk interfaces are developed, such as ATA, Ultra ATA, DMA, Ultra DMA and other interfaces are all IDE hard disk interfaces.2.2 IDE ModeThere are three transmission modes for IDE: PIO (Programmed I/O), DMA (Driect Memory Access), and Ultra DMA (UDMA).The biggest drawback of PIO mode is that it consumes a lot of CPU resources. The IDE interface running in PIO mode has a data transfer rate ranging from 3.3MB/s (PIO mode 0) to 16.6MB/s (PIO mode 4). There are two types of DMA modes: Single-Word DMA and Multi-Word DMA. The highest transfer rate of Single-Word DMA mode is 8.33MB/s, and Multi-Word DMA (Double Word) can reach 16.66MB/s. The biggest difference between the DMA and the PIO is that the DMA mode does not rely too much on CPU instructions to run, which can save the processor's operating code.Due to the emergence and rapid popularity of the UDMA mode, PIO and DMA are immediately replaced by UDMA. UDMA is a standard protocol under the Ultra ATA system, which is based on the 16-bit Multi-Word DMA mode. One of the advantages of UDMA is that in addition to the advantages of DMA mode, it also applies CRC (Cyclic Redundancy Check) technology to enhance the performance of error detection and debugging during data transmission. Since the introduction of the Ultra ATA standard, its interface has applied DDR (Double Data Rate) technology to double the transmission speed, with a transmission speed of up to 100MB/s. 2.3 IDE Advantages and DisadvantagesAdvantages: Compatible and cost-effective.Disadvantages: slow data transmission speed, short cable length, fewer connected devices, no support for hot swap, poor upgrading ability of interface speed. Ⅲ What is SCSI?3.1 SCSI BasicsThe full name of SCSI is "Small Computer System Interface", which is a completely different interface from IDE. SCSI is not specifically designed for hard disks, but a high-speed data transmission technology widely used in minicomputers. It has the advantages of wide application range, multitask, large bandwidth, low CPU occupancy rate, and hot swap. So SCSI is mainly used in medium and high-end servers and high-end workstations. But the higher price makes it difficult to popularize like IDE. SCSI also has some potential problems. It has limited system BIOS support, and it has to be set for each computer. There's also no common SCSI software interface.Figure 1. SCSI Interface3.2 SCSI VersionSCSI VersionDescriptionsSCSI-1developed in 1986(obsolete)Introduced in 1979, supported synchronous and asynchronous SCSI peripherals.SCSI-2adopted in 1994Introduced in 1992, also known as fast SCSI, supported any SCSI device.SCSI-3debuted in 1995It is the standard currently in use. Ⅳ What is Fiber Channel (FC)?4.1 Overview of Fibre ChannelFibre Channel is the same as SCSI. It is not originally an interface technology developed for hard disk design and development, but specifically designed for network systems. However, as storage systems develop, they are gradually applied to hard disk systems. Fibre Channel is developed to improve the speed and flexibility of multi-disk storage systems. And it greatly improves the communication speed of multi-disk systems. The main characteristics of Fibre Channel are: hot swap, high-speed bandwidth, remote connection, large number of connected devices, etc. It can meet the high data transmission rate requirements of high-end workstations, servers, mass storage sub-networks, and peripherals for bidirectional and serial data communication through hubs, switches and point-to-point connection.4.2 Fibre Channel ProtocolFiber Channel ProtocolDescriptionsFC-0Physical layer, customizes different media, set transmission distance and signal mechanism standards, defines optical fiber, copper interfaces, and cable indicatorsFC-1Encode/DecodeFC-2Framing protocol /flow controlFC-3common services such as data encryption and compressionFC-4Protocol mapping layer, which defines the interface between fibre channel and upper-layer protocol. Upper-layer applications such as SCSI protocol, HBA FC-4 interface functions. FC-4 supports multiple protocols, such as FCP-SCSI, FC-IP, and FC-VI. Ⅴ What is SATA?5.1 Serial ATA DefinitionSATA stands for "Serial Advanced Technology Attachment" or "Serial ATA". It is an interface used to connect ATA hard drives to a computer's motherboard. SATA adopts serial connection mode. Serial ATA bus uses embedded clock signal, which has stronger error correction ability. Compared with the past, its biggest difference is that it can check transmission instructions (not just data). Errors are automatically corrected, which greatly improves the reliability of data transmission.Now the general interface is SATA interfaces. The reason why it can replace IDE is because the performance of the SATA is much better than that of the IDE. SATA speed is also much higher than IDE, and it also supports hot swap/hot-plugging.5.2 SATA InterfaceMost of the computers we use are also SATA interfaces. The current SATA interface has three versions 1.0, 2.0, and 3.0. The larger the version number, the later it appears, the better the performance, which mainly due to the faster data transfer rate. SATA 3.0 is the most common interface used today, though there have been four revisions since its introduction, namely 3.1 through 3.4. The SATA interface version is backward compatible, and the higher version is compatible with the lower. Some SATA hard disks provide jumpers. Due to the jumper settings are different, the version number of the SATA interface of the same hard disk is different. In addition, the actual transfer rate of the interface requires the support of the SATA motherboard.SSD has better performance, smaller size, and higher interface requirements. High-performance SSDs have basically switched to M.2, U.2 and PCIe, but SATA interfaces will not be eliminated in a short time. It is still in mainstream market, especially the HDD market. The SATA 3.3 specification upgraded by SATA-IO also brings some new features, optimizing the support of SMR, and can be powered off remotely. SMR shingled magnetic recording technology can increase the storage density of HDD by 25%.The SATA interface entered the 6Gbps era from the 3.0 standard in 2009. In 2011, SATA 3.1 was updated, SATA 3.2 was updated in 2013, and then SATA 3.3 was updated in 2016. These subversion upgraded have not brought many new functions. After all, the bottleneck of HDDs is not the speed, and it is difficult to make big improvements from the interface. 5.3 IDE vs SATA InterfaceSATA hard disk has a new design structure, fast data transmission, save space, and many other advantages over IDE hard disk:1) SATA hard disk has a higher transmission speed than IDE hard disk. SATA can provide a peak transfer rate of 150MB/s. It will reach 300 MB/s and 600 MB/s with the development. At that time, we will get a transfer rate nearly 10 times faster than IDE hard drives.2) Compared with the PATA40-pin data cable of IDE hard disks, the SATA cable is small and thin. And the transmission distance is long, which can be extended to 1 meter, making it easier to install equipment and wiring in the machine. Because the size of the connector is small, this kind of cable effectively improves the air flow inside the computer and also speedsthe heat dissipation in the case.3) Thepower consumption has been reduced. SATA hard drives can work with 500 mA of current.4) SATA can be backward compatible with PATA devices by using multi-purpose chipsets or serial-parallel converters. Since SATA and PATA can use the same drive, there is no need to upgrade or change the operating system.5) SATA does not need to set the master and slave disk jumpers. The BIOS will number it in the order of 1, 2, 3. Whilethe IDE hard disk needs to set the master and slave disks through jumpers.6) SATA also supports hot plugging and can be used like a U disk. IDE hard disks do not support hot swap. Ⅵ What is M.2?The M.2 interface is a new interface specification. It is a new standard tailored for Ultrabooks to replace the original mSATA interface. Whether it is a smaller size or higher transmission performance, M.2 is far better than mSATA.M.2 interfaces are generally divided into two types. When buying M.2 SSDs, you need to pay attention to internal agreements. One is to use the traditional SATA AHCI protocol, which has no difference in performance with ordinary SATA solid hard drives; another is to use the brand-new NVMe protocol, which can provide SSD performance up to 3000MB/s or more. Ⅶ What is SAS?SAS (Serial Attached SCSI) is a new generation of SCS technology, which is the same as the current popular SATA technology. It uses serial technology to obtain higher transmission speed and improves internal space by shortening the cable. SAS is a new interface developed after the parallel SCSI. This interface is designed to improve the performance, availability, and expandability of the storage system, and to provide compatibility with the SATA.SAS technology can be backward compatible with SATA. Specifically, the compatibility of the two is mainly reflected in the compatibility of the physical part and the protocol. At the physical layer, the SAS interface and the SATA interface are fully compatible, and the SATA hard disk can be directly used in the SAS environment. In terms of interface standards, SATA is a sub-standard of SAS, so the SAS controller can directly control SATA hard drives, but SAS cannot be directly used in the SATA environment. Because the SATA controller cannot control the SAS hard disk. As for the protocol, SAS is composed of three types of protocols, which use corresponding protocols for data transmission according to different devices. Among them, the serial SCSI protocol (SSP) is used to transmit SCSI commands, the SCSI management protocol (SMP) is used to maintain and manage connected devices, and the SATA channel protocol (STP) is used to transfer data between SAS and SATA. Therefore, under the cooperation of three protocols, SAS can seamlessly work with SATA and some SCSI devices.The backplane of the SAS system can be connected to dual-port, high-performance SAS drives and high-capacity, low-cost SATA drives. So SAS drives and SATA drives can exist in a storage system at the same time. But it should be noted that the SATA system is not compatible with SAS, so SAS drives cannot be connected to the SATA backplane. Due to the compatibility of the SAS system, users can use hard drives with different interfaces to meet the capacity or performance requirements of various applications. So they have more flexibility when expanding the storage system, allowing storage devices to maximize application benefits.In the system, each SAS port can connect up to 16256 external devices, and SAS adopts a point-to-point serial transmission directly with a transmission rate of up to 3Gbps. It is estimated that there will be 6Gbps or even 12Gbps high-speed interfaces in the future. The SAS interface performance has also been greatly improved. It also provides 3.5-inch and 2.5-inch interfaces, so it can meet the requirements of different server environments. SAS relies on SAS expanders to connect more devices. Most expanders have 12 ports.Compare with the traditional parallel SCSI, SAS has a significant increase in interface speed. With the use of serial cables, it not only can achieve a longer connection distance, but also improve the anti-interference ability. In addition, this cable can also significantly improve the heat dissipation inside the chassis. Ⅷ Tech Guide: AHCI and NVMe ProtocolHere we will focus on the AHCI protocol and NVMe protocol of the solid state drive (SSD).There are two mainstream transmission protocols for SSD (Solid State Drive): One is the AHCI protocol, and the other is the NVMe protocol.8.1 AHCI ProtocolAdvanced Host Controller Interface (AHCI), sets the operation of Serial ATA (SATA) host controllers in a non-implementation-specific manner in its motherboard chipsets. That is, AHCI allows storage drivers to connect advanced SATA functions. When we use SATA SSD, we must enable AHCI mode in the motherboard settings. This is because when the AHCI mode is turned on, the number of useless seeks of the SSD can be greatly shortened and the data search time can be reduced. So that the SSD under multi-tasking can exert all the performance and effects. According to related performance tests, after the AHCI mode is turned on, the SSD read and write performance is increased by about 30%. However, with the gradual enhancement of SSD performance, these standards have also become a major bottleneck restricting solid state drives. Because the AHCI standard designed for hard disk drives is not suitable for low-latency solid state drives.8.2 NVMe ProtocolAnother transmission protocol is the NVMe protocol that represents the future performance trend. The so-called NVMe protocol is to make full use of the low latency and parallelism of PCI-E channels, greatly improve the read and write performance of SSDs under controllable storage costs. It reduces the high latency caused by the AHCI, and completely liberates ultimate performance of SATA SSD.NVMe Specification1.0 (March 2011)1.1 (October 2012)1.2 (November 2014)Fabric's NVMe (2014)NVM-MI (November 2015)1.3 (April 2017)1.4 (July 2019)Due to the flash memory particles and the main control, the SSD(solid state drives) price with M.2 NVMe protocol is very high, which is about twice the price of SATA SSD. So buy the corresponding level of solid state hard drive based on the configuration and requirements of the computer. Otherwise it will cause performance waste.In terms of software layer, the delay of NVMe standard is less than half of AHCI. NVMe streamlines the calling method and does not need to read registers when executing commands. Each command of AHCI needs to read registers 4 times, which consumes 8000 CPU times in total loop, causing a delay of about 2.5 ms. NVMe can support receiving commands and prioritizing requests from multi-core processors at the same time.NVMe has automatic power state switching and dynamic power management functions. The device can switch to Power State 1 after being idle for 50ms from Power State 0. If it continues to be idle, it will enter Power State 2 with lower power consumption after 500ms. There will be a short delay when switching. The SSD can be controlled at a very low level when it is idle. In terms of power management, the NVMe SSD will have a greater advantage than the AHCI SSD. This is important for mobile devices, which can significantly increase the power endurance of notebooks. Moreover, NVMe SSD can be easily matched to different platforms and systems, and can work normally without the corresponding driver provided by the manufacturer. At present, Windows, Linux, Solaris, Unix, VMware, UEFI, etc, support the NVMe SSD.PCIe SSDs based on the NVMe protocol far exceed the traditional AHCI-based SATA SSDs in terms of performance and practicability. It can be said to be the future of the development of the SSD industry. But the traditional SATA interface will become the first choice for ordinary machine installations under the background of reduced manufacturing costs.8.3 Tech Note8.3.1 PCI-E BasicPCI-E (peripheral component interconnect express) is a high-speed serial computer expansion bus standard. Its original name is "3GIO". It was proposed by Intel in 2001 to replace the old PCI, PCI-X, and AGP bus standard. It belongs to high-speed serial point-to-point high-bandwidth dual-channel transmission. The connected devices allocate exclusive channel bandwidth and do not share bus bandwidth. It mainly supports active power management, error reporting, end-to-end reliable transmission, hot plugging, quality of service ( QOS), and other functions. PCI-E also has a variety of specifications, from PCI-E x1 to PCI-E x32, which can meet the needs of low-speed devices and high-speed devices in a certain period of time in the future.The PCI-E bus protocol can be directly connected to the CPU with almost no delay, making it an excellent companion to the NVMe standard. In the era of the AHCI standard, the actual performance of PCIe can hardly be exerted due to the agreement limit.Table: PCle VersionVersionYearDescriptionPCIe 1.0a2003The data rate per channel is 250 MB/s, and the transmission rate is 2.5 GT/s.PCIe 1.12005The data rate has not changed and it is fully compatible with PCIe 1.0a.PCIe 2.02007It doubles the transfer rate from PCIe 1.0 to 5 GT/s, and the throughput per channel rises from 250 MB/s to 500 MB/s.PCIe 2.12009Its speed is the same as PCIe 2.0, supporting troubleshooting system.PCIe 3.02010Transmitter and receiver equalization, PLL improvements, clock data recovery, and channels are all improved.PCIe 3.12014Various improvements based on the PCIe 3.0 specifications.PCIe 4.02016Double the bandwidth provided by PCIe 3.0, maintain software support, and have backward compatibility for the used mechanical interfaces.PCI-E SD 7.02018A new generation of SD 7.0 standard specifications 8.3.2 Interface Size IntroductionThe size and application of the hard disk can be divided into:0.85 inches, mostly used in portable devices such as mobile phones.1 inch, mostly used in digital cameras (CF type II interface).1.8 inches, used in some notebook computers and external hard disk enclosures.2.5 inches, commonly used in notebook computers and external hard disk enclosures.3.5 inches, mostly used in desktop computers. External hard drive enclosures with 3.5-inch requires an external power supply. Frequently Asked Questions about Hard Disk Drive Interface1. Which is a hard disk interface?Today's hard drives use SATA or SAS interfaces, which are the serial versions of their PATA and SCSI predecessors. SATA drives are found in every personal computer, and SAS drives, which are enterprise class, are found in servers and high-end workstations. 2. What are the three most common types of hard drive interfaces?There are three different kinds of hard drives: SATA, SSD and NVMe. 3. What is the fastest hard drive interface?PCIe provides a faster interface speed than SATA. An SSD connected via a PCIe 3.0 x16 interface can have a link speed of 16 Gb/s. In contrast the SATA 3.0 standard only provides 6.0 Gb/s. Solid State Drives (SSDs) come in a number of different form factors and are available with different interface connects. 4. What are the types of drive interfaces?Hard disk drives are accessed over one of a number of bus types, including parallel ATA (PATA, also called IDE or EIDE; described before the introduction of SATA as ATA), Serial ATA (SATA), SCSI, Serial Attached SCSI (SAS), and Fibre Channel. 5. What is PATA hard disk?Parallel ATA (Parallel Advanced Technology Attachment or PATA) is a standard for connecting hard drives into computer systems. As its name implies, PATA is based on parallel signaling technology, unlike serial ATA (SATA) devices that use serial signaling technology. 6. Can I connect a SATA hard drive to an IDE motherboard?Yes now you can connect the SATA hard drive to an IDE motherboard very easy. Just visit your near computer hardware shop or amazon to search “SATA bilateral IDE” card. This card will covert the SATA hard desk to IDE. After this your hard desk can be connected IDE motherboard. 7. Why is SCSI still used?It's a fast bus that can connect lots of devices to a computer at the same time, including hard drives, scanners, CD-ROM/RW drives, printers and tape drives. Other technologies, like serial-ATA (SATA), have largely replaced it in new systems, but SCSI is still in use. 8. Can I replace an ATA drive with a SATA drive?Replacing the ATA drive with a SATA drive you will need the SATA drivers for your system unless the bios is set to IDE emulation. Windows won't recognize the drive without the drivers installed or IDE emulation turned on. 9. Is NVMe and M 2 the same?NVMe stands for Non-Volatile Memory Express, and it refers to the way in which data is moved, rather than the shape of the drive itself. ... There are some NVMe drives that are designed to fit into a standard PCIe motherboard slot much like a graphics card, but most NVMe drives use the M. 2 form factor. 10. What is a m2 SATA drive?M. 2 is a form factor for SSDs (solid-state drives) that's shaped like a stick of gum. These SSDs are generally faster but more expensive than traditional, 2.5-inch SSDs. Thin laptops are increasingly using M. 2 SSDs because they take up less room than 2.5-inch SSDs or hard drives.

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.