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IntroductionAs we all know, the most basic passive linear components are resistors (R), capacitors (C) and inductive components (L). These components can be used to form 4 different circuits: RC circuit, RL circuit, LC circuit and RLC circuit. They have some important properties for analog electronics, and can be used as passive filters. In practice, capacitors (and RC circuits) are usually used instead of inductors to form filter circuits. This is because capacitors are easier to manufacture with smaller size. This article mainly introduces the RC Circuit in series and parallel state.RC circuit (resistor–capacitor circuit), also called RC filter or RC network, has a resistor and a capacitor in series connection. When connected to a DC voltage source, the capacitor charges exponentially in time. That is, a capacitor can store energy, and when a resistor placed in series with it will control the rate at which it charges or discharges. This produces a characteristic time dependence that turns out to be exponential.RC Circuits Basic ExplainedCatalogIntroductionⅠ RC Circuit Basics1.1 What is RC Circuit?1.2 RC Circuit CharacteristicsⅡ How to Calculate RC Circuit?Ⅲ RC Circuits Classification3.1 Series and Parallel Circuits3.2 Example: RC Low Pass FilterⅣ Visualizing Filter Response4.1 Frequency Response4.2 Low Pass Filter Phase Shift4.3 Second-order Low-pass FilterⅤ ConclusionⅠ RC Circuit Basics1.1 What is RC Circuit?For a RC circuit (resistor-capacitor circuit), the primary composes of a resistor and a capacitor. According to the arrangement of resistors and capacitors, it can be divided into a RC series circuit and a RC parallel circuit. In addition, simple RC parallel circuits cannot resonate, because resistor does not store energy. However, LC parallel circuits can resonate. RC circuits are widely used in analog circuits and pulse digital circuits. If a RC parallel circuit connected in series in the circuit, it can attenuate low-frequency signals, and if it connected in parallel in the circuit, it can attenuate high-frequency signals. That is filtering.RC circuit is common element in electronic devices. It also play an important role in the transmission of electrical signals in nerve cells. A capacitor can store energy and a resistor placed in series with it will control the rate at which it charges or discharges.Figure 1. Passive Low-pass RC Circuit1.2 RC Circuit CharacteristicsIn the analog circuit, the passive RC filter circuit can be divided into a low-pass filter circuit and a high-pass filter circuit according to the connection and size of the capacitor.The low-pass filter circuit is somewhat equal to the integrator circuit (capacitor C is in parallel at the output.), but both circuits are applied to different requirements. The integrator circuit mainly uses the integration effect of the capacitor C when it is charged. In the case of square wave input, periodic sawtooth wave (triangular wave) will generate, so the capacitor C and resistor R are selected according to the square wave. While the low-pass filter circuit bypasses the higher frequency signal (because XC=1/( 2πfC), when f is larger, XC is smaller, which is equivalent to a short circuit), so the value of capacitor C is determined by referring to the value of the low frequency. For the filter circuit of the power supply, theoretically the larger the value of C, the better.Figure 2. Low Pass Filter CircuitThe high-pass filter circuit has the same form as the differential circuit or the coupling circuit. In the pulse digital circuit, due to the different relationship between RC and pulse width, it is divided into a differential circuit and a coupling circuit. In an analog circuit, choosing an appropriate capacitance C value can pass higher frequency signals selectively, even block DC and low-frequency signals. For example, a capacitor connected in series with a tweeter, is to prevent the low pitch from entering the tweeter to avoid burnout. What’s more, in the multi-stage AC amplifier circuit, the high-pass filter circuit is also a coupling circuit.Figure 3. High Pass Filter CircuitⅡ How to Calculate RC Circuit?From a mathematical point of view, suppose that the RC circuit has been connected to a DC power supply with a voltage value of U0. The voltage on the capacitor is equal to the power supply’s, and at a certain moment t0 the left end S of the resistor is grounded, then the capacitor discharges. In the theoretical analysis, the time t0 is taken as the zero point of time.According to KVL's law, establish the circuit equation: The initial condition is .This is a first-order homogeneous differential equation, and its general solution is .After substituting into the original equation: The characteristic equation is .The characteristic root is .According to , get .Therefore, the required initial value of the differential equation is It can be seen that the voltage attenuation speed on the capacitor depends on the , and its size only depends on the circuit structure and component parameters.When the unit of resistance is Ω and the unit of capacitance is F, the unit of product RC is seconds (s), which is represented by τ, then the capacitor voltage can be written as .tτ2τ3τ4τ5τ...∞uc(t)Uo0.368Uo0.135Uo0.05Uo0.018Uo0.0067Uo...∞0The τ time constant is the time it takes for the capacitor voltage to drop to 1/e=36.8% of the initial value. Specifically, it is the time required to charge the capacitor, through the resistor, from an initial charge voltage of zero to approximately 63.2% of the value of an applied DC voltage, or to discharge the capacitor through the same resistor to approximately 36.8% of its initial charge voltage. When t=4t, the capacitor voltage is very small, and it is generally considered that the circuit enters a steady state, which is also called the zero input response of the RC first-order circuit. Ⅲ RC Circuits Classification3.1 Series and Parallel CircuitsRC Series CircuitIn circuit, the capacitor cannot flow DC current, and R & C have an obstructive effect on the current. So the total impedance is determined by the resistance and capacitive reactance, and it changes with frequency. RC series circuit has a turning frequency: f0=1/2πR1C1. When the input signal frequency is greater than f0, the total impedance is basically unchanged, and it is equal to R1.RC Parallel CircuitThe RC parallel circuit can pass both DC and AC signals. It has the same turning frequency as the RC series circuit: f0=1/2πR1C1. On the one hand, when the input signal frequency is less than f0, the total impedance of the circuit is equal to R1, on the other hand, when the input signal frequency is greater than f0, the capacitive reactance of C1 is relatively small, and the total impedance is the sum of resistance and capacitance. In addition, when the frequency is high to a certain level, the total impedance is zero.Introduction to Parallel RC CircuitWhat’s more, as frequency increases, the capacitor will act like a short circuit to high frequency current in its path. At low frequencies, the capacitor tends to block current flow.3.2 Example: RC Low Pass FilterCircuit AnalysisTo create a passive low-pass filter, we need to combine the resistor elements with the reactance elements. That is a circuit consisting of a resistor and a capacitor or an inductor. Theoretically speaking, the RL low-pass topology is equivalent to the RC low-pass topology in terms of filtering ability. However, in practice, RC circuits are more common.Figure 4. RC Low-pass FilterAs shown in the figure, connecting a resistor in series with the signal path and a capacitor in parallel with the load, an RC low-pass response can be generated. In the figure, the load is a single part, but in actual circuits, it may be more complicated, such as the input stage of an analog-to-digital converter, amplifier, or oscilloscope to measure the response of the filter.If a resistor and a capacitor form a frequency-dependent voltage divider circuit, we can intuitively analyze the filtering function of the RC low-pass circuit.Figure 5. Change RC Low-pass Filter into a Voltage DividerWhen the frequency of the input signal is low, the impedance of the capacitor is high than the resistor. Therefore, most of the input voltage will drop on the capacitor (and both ends of the load, which is in parallel with the capacitor). When the input frequency is higher, the impedance of the capacitor is lower than the impedance of the resistor, which means that the resistor voltage decreases and less voltage is transferred to the load. Therefore, low frequencies pass and high frequencies are blocked.Cutoff FrequencyWhere the filter does not cause significant attenuation for a frequency range is called the passband, and the opposite is called the stopband. Analog filters, such as RC low-pass filters, always gradually transit from the passband to the stopband. This means that it cannot be recognized that the filter stops passing the signal and starts blocking one frequency of the signal. This is why the cutoff frequency concept introduced.When checking the frequency response graph of the RC filter, the signal spectrum is "cut" into two halves of the image, one of which is retained and one is discarded. Because as the frequency moves from below the cutoff point to above the cutoff value, the attenuation gradually increases.The cut-off frequency of the RC low-pass filter is actually the frequency at which the input signal amplitude is reduced by 3dB (this value is chosen because a 3dB reduction is equal to a 50% reduction in power). Therefore, the cutoff frequency is also called -3dB frequency. The term bandwidth refers to the width of the passband of the filter. For a low-pass filter, its bandwidth is equal to the -3dB frequency (as shown in the figure below).Figure 6. Cutoff Frequency -3dBFilter Response CalculationWe can discuss the theoretical behavior of the low-pass filter by a typical voltage divider. The output of the resistor divider is expressed as following:The RC filter uses an equivalent structure, using a capacitor XC replace R2. Then we need to calculate the total impedance and place it in the denominator, so there is The reactance of a capacitor represents the opposite amount of current, but unlike resistance, the opposite amount depends on the frequency of the signal passing through the capacitor. Therefore, we must calculate the reactance at a specific frequency. The equation we use for this as follows: In the above design example: R≈160Ω and C=10nF. We assume that the magnitude of VIN is 1V, so we can simply remove VIN from the calculation. First, let's calculate the amplitude of VOUT with a sine wave frequency: While suppressing noise, the amplitude of the sine wave is basically unchanged. Because the cutoff frequency (100kHz) we chose is much higher than the sine wave frequency (5kHz).Let’s see how the filter successfully attenuates the noise component.The noise amplitude is only about 20% of its original value. Ⅳ Visualizing Filter Response4.1 Frequency ResponseThe most convenient way to assess the effect of a filter on a signal is to examine the frequency response graph. That is Bode plot, which has amplitude (in decibels) on the vertical axis and frequency on the horizontal axis; the horizontal axis usually has a logarithmic scale so that the physical distance between 1Hz and 10Hz is the same as 10Hz to 100Hz and 100Hz to 1kHz. This configuration allows us to quickly and accurately evaluate the behavior of the filter over a large frequency range.Figure 7. Bode PlotEach point on the curve represents the amplitude that the output signal is 1V and the frequency is equal to the corresponding value on the horizontal axis. For example, when the input frequency is 1MHz, the output amplitude (assuming the input amplitude is 1V) will be 0.1V (because -20dB corresponds to a tenfold reduction factor).The curve in the passband is almost completely flat, and then as the input frequency approaches the cutoff frequency, it starts to drop faster. Finally, the rate of change of attenuation becomes stable, that is, for every ten times the input frequency increases, the amplitude of the output signal decreases by 20dB. 4.2 Low Pass Filter Phase ShiftThe way in which the filter modifies the amplitude of various frequency components in the signal has been discussed above. However, in addition to amplitude effects, reactive circuit elements always involve phase shifts.The concept of phase refers to the value of the periodic signal at a specific moment in the cycle. Therefore, when we say that a circuit causes a phase shift, we mean that it creates a misalignment between the input signal and the output signal. That is the input and output signals no longer start and end their periods at the same time. The phase shift value, such as 45° or 90°, indicates how much misalignment has been created.Each reactance element in the circuit introduces a 90° phase shift, but this phase shift does not occur at the same time. The phase of the output signal is the same as the amplitude of the output signal, and it changes gradually as the input frequency increases. In the RC low-pass filter, we have a reactive element (capacitor), so the circuit will eventually introduce a 90° phase shift.As with the amplitude response, the phase response can be most easily evaluated by examining the graph on the horizontal axis which represents the logarithmic frequency. The following description is the general pattern.The phase shift is initially 0°, and it gradually increases until it reaches 45° at the cutoff frequency. During this part of the response, the rate of change is increasing. With time, the phase shift continues to increase, but the rate of change is decreasing. As the phase shift approaches 90°, the change of rate becomes very small.Figure 8. Phase Shift4.3 Second-order Low-pass FilterAs above mentioned, we have assumed that the RC low-pass filter consists of a resistor and a capacitor. This configuration is a first-order filter. The "order" of passive filters is determined by the number of reactive components (ie capacitors or inductors) in the circuit. Higher-order filters have more reactive components, which lead to more phase shift and steeper roll-off.Second-order filters are usually built a resonant circuit consisting of inductors and capacitors (this topology is called "RLC", or resistor-inductor-capacitor circuit). However, it is also possible to create a second-order RC filter. As shown in the figure below, all we need to do is to cascade two first-order RC filters.Figure 9. Second-order Filter CircuitAlthough this topology can produce a second-order response, it is not widely used. Because its frequency response is usually not as good as a second-order active filter or a second-order RLC filter.Frequency ResponseWe can try to create a second-order RC low-pass filter by designing a first-order filter based on the required cutoff frequency, that is connecting two first-order stages in series. This set has a similar overall frequency response, with a maximum roll-off of 40dB/decade instead of 20dB/decade.However, we cannot simply connect these two stages together and analyze the circuit as a second-order low-pass filter. In addition, even if we insert a buffer between the two stages so that the first RC stage and the second RC stage can be used as independent filters, the attenuation at the original cut-off frequency will be 6dB instead of 3dB. Because the two stages work independently.Figure 10. Frequency Response of RC-RC FilterA limitation of the second-order RC low-pass filter is that the designer cannot tune the conversion from passband to stopband by adjusting the Q factor (this parameter indicates the degree of damping of the frequency response.) of the filter. If two identical RC low-pass filters are cascaded, the overall transfer function corresponds to the second-order response, but the Q factor is always 0.5. When Q = 0.5, the filter is at the boundary of over-damping, which results in a "sag" frequency response in the transition region. While second-order active filters and second-order resonant filters do not have this limitation, designers can control the frequency response of the transition region. Ⅴ ConclusionAll electrical signals contain a mixture of requiring frequency and unwanted ones. Undesirable frequency components are usually caused by noise and interference, and in some cases they have a negative impact on the performance of the system.Filters are circuits that react to different parts of the signal spectrum in different ways. The low-pass filter is designed to pass low frequency components and block high frequency components. The output voltage of an RC low-pass filter can be calculated by considering the circuit as a voltage divider (frequency-independent) composed of resistance and reactance.The graph of amplitude (in dB, on the vertical axis) vs. log frequency (in Hz, on the horizontal axis) is a convenient and effective way to check the theoretical behavior of the filter. You can also use phase and log frequency graph determines the amount of phase shift that will be applied to the input signal.The second-order filter provides a steeper roll-off, and its response is useful when the signal cannot provide broadband separation between the desired frequency and the unwanted one. You can make a second-order RC low-pass filter by connecting two identical first-order RC low-pass filters, but the overall -3 dB frequency will be lower than expected.In RC filtering circuit, the capacitor can store energy, and the resistor placed in series with it can control the charge-discharge rate. And this produces a characteristic time dependence that turns out to be exponential. Frequently Asked Questions about RC Filter Circuit1. What does an RC filter do?RC circuits can be used to filter a signal by blocking certain frequencies and passing others. The two most common RC filters are the high-pass filters and low-pass filters; band-pass filters and band-stop filters usually require RLC filters, though crude ones can be made with RC filters. 2. What is RC filter in electronics?A resistor–capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit composed of resistors and capacitors. ... A first order RC circuit is composed of one resistor and one capacitor and is the simplest type of RC circuit. 3. How do you calculate RC circuit?The (real value) impedance is the real part of the complex impedance Z. For a series RC circuit, we get Z=√R2+(1ωC)2 Z = R 2 + ( 1 ω C ) 2 . We see that the amplitude of the current will be V/Z=V√R2+(1ωC)2 V / Z = V R 2 + ( 1 ω C ) 2. 4. What is RC circuit used for?The RC circuit has thousands of uses and is a very important circuit to study. Not only can it be used to time circuits, it can also be used to filter out unwanted frequencies in a circuit and used in power supplies, like the one for your computer, to help turn ac voltage to dc voltage. 5. What is RC series circuit?A circuit that contains pure resistance R ohms connected in series with a pure capacitor of capacitance C farads is known as RC Series Circuit. A sinusoidal voltage is applied and current I flows through the resistance (R) and the capacitance (C) of the circuit.

IntroductionOperational amplifier (op amp for short) is basically a voltage amplifying device designed to be used with components like capacitors and resistors, between its in/out terminals, or is simply a linear Integrated Circuit (IC) having multiple-terminals. In electronics, the open-loop voltage gain of the actual operational amplifier is very large, which can be seen a differential amplifier with infinite open loop gain, infinite input resistance and zero output resistance. In addition, it has positive and negative inputs which allow circuits that use feedback to achieve a wide range of functions. And meanwhile, it can be further simplified into an ideal op amp model, referred to as an ideal op amp (also called ideal OPAMP).CatalogIntroductionⅠ Ideal Op Amp Characteristics1.1 Infinite Input Resistance1.2 Zero Output Impedance1.3 Infinite Open-loop Gain1.4 Infinite Common-mode Rejection Ratio1.5 Infinite BandwidthⅡ Assumptions of Ideal Op AmpⅢ Working Characteristics of Ideal Operational Amplifiers3.1 Work in Linear Region3.2 Work in Nonlinear RegionⅣ Analysis of Ideal Operational Amplifier CharacteristicsⅤ Balanced Resistance Presets5.1 The Role of Balanced Resistance5.2 Input Balancing Resistor ExplanationⅥ Ideal Op Amp EquationsⅦ Several Common Op Amp CircuitsⅧ Difference Between Ideal Op-amp and Practical Op-ampⅠ Ideal Op Amp CharacteristicsWhen analyzing various application circuits of operational amplifiers, the integrated operational amplifier is often regarded as an ideal operational amplifier. The so-called ideal op amp is to idealize various technical indicators of op amps, and it must have the following characteristics.Characteristics of An Ideal Op-Amp1.1 Infinite Input ResistanceThe input terminal of an ideal operational amplifier does not have any current to flow in. In electronics, op amps are voltage gain devices. They amplify a voltage fed into the op amp and give out the same signal as output with a much larger gain. In order for an op amp to receive the voltage signal as its input, the voltage signal must be dropped across the op amp. If you know the concept of a voltage divider, voltage drops primarily across components with high impedances, proportionally according to ohm’s law by the formula V=IR. So the greater the resistance (or impedance) of a device, the greater the voltage drop across that device is. To make sure that the voltage signal drops fully on the op amp, it must have a very high input impedance, so that the voltage drops fully across it. If it had a low input impedance, the voltage may not drop across it and it would not receive the signal. This is why op amps must have high-input impedances.It’s also easy to make the input impedance lower (put a resistor in parallel) or the source impedance higher (put a resistor in series).Figure 1. Ideal Op Amp Symbol and Transfer Characteristic Curve 1.2 Zero Output ImpedanceThe output of an ideal op amp is a perfect voltage source, no matter how the current flowing to the amplifier load changes, the output voltage of the amplifier is always a certain value, that is, the output impedance is zero. In practice, zero output impedance is actually a distinct property from infinite input impedance, but for a very long time infinite input impedance was approached only with compromises in offset voltage and noise. 1.3 Infinite Open-loop GainIn an open-loop state, the differential signal at the input has an infinite voltage gain. This feature makes the operational amplifier very suitable for practical applications with upper negative feedback configuration. 1.4 Infinite Common-mode Rejection RatioAn ideal operational amplifier can only respond to the difference between the voltages at both ends of V+ and V-. In addition, the same part of the two input signals (ie common mode signal) will be completely ignored. What’s more, a high CMRR is required when a differential signal must be amplified in the presence of a possibly large common-mode input, such as strong electromagnetic interference (EMI). An example is audio transmission over balanced line in sound reinforcement or recording. 1.5 Infinite BandwidthThe ideal operational amplifier will amplify the input signal of any frequency with the same differential gain, which will not change with the change of signal frequency.Ⅱ Assumptions of Ideal Op AmpThe op amp can be considered a voltage controlled current source, or it is an integrated circuit that can amplify weak electric signals. Based on it, for an ideal OPAMP, what is the relationship between it and these electrical signals?First, assume that the current flowing into the input of the op amp is zero. This assumption is almost completely correct for FET op amps, because the input current for FET op amps is below 1pA. But for dual high-speed op amps, this assumption is not always correct, because the input current of it can sometimes reach tens of microamperes.Second, assume that the gain of the op amp is infinite, so the op amp can swing the output voltage to any value to meet the input requirements. It means that the output voltage of the op amp can reach any value. In fact, when the output voltage is close to the power supply voltage, the op amp will saturate. Maybe this hypothesis does exit, but needs a limit in practical. For example, at higher frequencies, the internal junction capacitors of transistor come into play, thus reducing the output and therefore the gain of amplifier. The capacitor reactance decreases with increase in frequency bypassing the majority of output. The opamp is in saturation state.Figure 2. Op Amp SaturationFor example, as per datasheet of LM741, large signal voltage gain is 200V/mv. It means an open loop gain of 200,000. If you operate an op-amp in open-loop condition(i.e. without negative feedback) ,even microvolts of input voltage (input offset voltage of LM741 is 3mv) will drive the output to saturation.In most of the amplifier circuits op-amp is configured to use negative feedback which greatly reduces the voltage gain (i.e. closed loop gain). In oscillators and schmit triggers, Op-amp is configured to use positive feedback. Comparator circuit is an example of the circuit which utilizes open-loop gain of op-amp. Its output will be always at saturation either positive or negative saturation. In an integrator circuit, the DC gain should be limited by adding a feed back resistor in parallel with capacitor ;else the output will get saturated .Even in amplifier circuits, the amplitude of the input signal and the voltage gain of the circuit should be balanced so that the output voltage does not exceed power supply voltage . For example for a non-inverting amplifier with a voltage gain of 100, the maximum permissible input voltage will be 150 mv if the VCC is 15 Volts. If you apply a signal of 200 mv ,the op-amp output will goto saturation as the required output will be 20 volts which exceeds the VCC of 15 Volts.Third, the assumption of infinite gain also means that the input signal must be zero. The gain of the op amp will drive the output voltage until the voltage (error voltage) between the two input terminals is zero. The voltage between the two input terminals is zero. The zero voltage between two input terminals means that if one input terminal is connected to a hard voltage source like ground, the other input terminal will also be at the same potential. In addition, since the current flowing into the input terminal is zero, the input impedance of the op amp is infinite.Fourth, of course, the output resistance of an ideal op amp is zero. An ideal op amp can drive any load without any voltage drop due to its output impedance. At low currents, the output impedance of most op amps is in the range of a few tenths an ohm, so this assumption is true in most cases. Ⅲ Working Characteristics of Ideal Operational Amplifiers3.1 Work in Linear RegionWhen the ideal op amp works in the linear region, the output and the input voltage show a linear relationship. Where u0 is the output voltage of the integrated op amp; u+ and u- are the voltages at the non-inverting input terminal and the inverting input terminal, respectively. Auo is the open loop differential voltage magnification. According to the characteristics of the ideal op amp, two important characteristics of the ideal op amp in the linear region.1) Zero differential input voltageSince the open-loop differential voltage magnification of an ideal op amp is equal to infinity, and the output voltage is a certain value, the voltage values at the non-inverting input terminal and the inverting input terminal are approximately equal. Just like short circuit between input and output, but it is fake. Because it is an equivalent short circuit, not a real short circuit, so this phenomenon is called "virtual short".2) Zero input currentSince the open-loop input resistance of an ideal op amp is infinite, no current flows into the op amp at either input. At this time, the current at the non-inverting input terminal and the inverting input terminal are both equal to zero. Like an disconnection, but an equivalent disconnection, so this phenomenon is called "virtual break". Virtual short and virtual break are two important concepts for analyzing the ideal op amp working in the linear region.In fact, the ideal operational amplifier has the characteristics of "virtual short" and "virtual break". These two characteristics are very useful for analyzing linear amplifier circuits. The necessary condition for virtual short is negative feedback. When negative feedback is introduced, at this time, if the forward terminal voltage is slightly higher than the reverse terminal voltage, the output terminal will output a high voltage equivalent to the power supply voltage after the amplification of the op amp. In fact, the op amp has a respond time changing from the original output state to the high-level state (the golden rule of analyzing analog circuits: the change of the signal is a continuous change process). Due to the feedback resistance of the reverse end change will inevitably affect its voltage, when the reverse end voltage infinitely close to the forward end voltage, the circuit reaches a balanced state. The output voltage does not change anymore, that is, the voltage at the forward end and the reverse end is always close. (Note: The analysis method is the same when the voltage decreases.) 3.2 Work in Nonlinear RegionWhen the op-amp operates in the nonlinear region, the output voltage no longer increases linearly with the input voltage, but saturates. The ideal op amp also has two important characteristics when operating in the nonlinear region.1) When u+ ≠ u-, the output voltage of the ideal op amp reaches the saturation value.When u+ > u-, the op-amp operates works in positive saturation region with a positive output voltage.When u+ < u-, the op-amp operates works in negative saturation region with a negative output voltage.Ideal op amp operates in the nonlinear region, u+ ≠ u-, there is no “virtual short”.2) The input current is equal to zero.Although the input voltage u+ ≠ u- above, the input current is considered to be zero. Ⅳ Analysis of Ideal Operational Amplifier CharacteristicsAs for Op-amp, there's probably a description like this: three-terminal element (circuit structure with double-ended input, single-ended output), ideal transistor, high-gain DC amplifier.(1) High input resistanceUnder this situation, the current flowing into the input terminal is close to 0, almost no signal source current is used, which is close to the voltage control characteristic. And virtual break is derived from this.(2) Lower output resistanceIt has the characteristics of adapting to any load. And the impedance of the subsequent load circuit will not affect the output voltage.(3) Infinite voltage amplification(4) Under a certain supply voltage condition, the amplifier can only work in closed-loop (negative feedback) mode, and the actual amplification is limited. Because op-amps themselves don't have a 0V connection but their design assumes the typical signals will be more towards the center of their positive and negative supplies. Thus, if your input voltage is right at one extreme or forces the output toward one supply, chances are it won't work properly. Working in open-loop mode is the like a comparator, and the output is high level orlow level.In the closed-loop (limited amplification) state, the amplifier is randomly compare the potentials of the two input terminals. The output stage makes immediate adjustments when they are not equal. So the final purpose of amplification is to make the potentials of the two input terminals equal. And virtual short is derived from this. Ⅴ Balanced Resistance Presets5.1 The Role of Balanced Resistance1) A suitable resistance is generally required to ensure that the input impedance is matched.2) In order to reduce the input current imbalance, the in-phase resistor should be equal to the parallel value of the two resistors at the reverse end in theory. In practice, as a result of the closed loop, especially in deep negative feedback conditions, the misalignment is not obvious at the output. And there is no need of in-phase grounding resistor when the misalignment is not the main problem. Because a balanced resistor is the starting point for an ideal op amp. In-phase grounding resistance is useful for bipolar op amps, and has no meanings for MOS-type op amps.3) Ground input termination resistance: it is necessary for impedance matching and high frequency setting.4) Bias current and offset current.For operational amplifiers with bias current greater than offset current, input resistance matching can be reduced, and precision circuits can compensate bias current to a minimum. If the bias current and offset current are similar, the matching resistance will increase the error.5) Set for the bias current at the input, the purpose of which is to equalize the impedance of the invertingand non-inverting inputs, so that two inputs with equal bias currents are assumed to have equal voltage drops, thereby counteraction can be made. 5.2 Input Balancing Resistor ExplanationA op-amp is connected to an inverting amplifier:Set the input resistance for R1, feedback resistance for Rfi,Assume that the non-inverting end is not connected to a balanced resistor, but grounded directly.Set the input bias current for the op-amp IB (same voltage in inverting and non-inverting end).The current flows through R1 and Rf are represented by I1 and If.Inverting voltage is V-, The op-amp gain is A.Use KCL in the inverting end (set the input signal to 0).Where (0-V-)/R1- (A+1)V- /Rf=IBFrom the above equation, it follows that V-=-(IB×R1×Rf/(Rf+(A+1)R1))At this time, the output voltage of the op-amp is Vo=A×(IB×R1×Rf/(Rf+(A+1)R1))The above formula can be approximated as Vo=IB×((A×R1)/Rf)If the in-phase terminal passes through a resistor R2 to ground and R2=R1/Rf, then the voltage at the in-phase terminal is V+=-IB×R2KCL is applied to the inverted terminal, where (0-V-)/R1+(A×(V+-V-)-V-)/Rf=IBAt this time the output voltage of the op-amp is Vo=0. Ⅵ Ideal Op Amp EquationsUnderstanding the basic conditions of an ideal op amp, and combining it with the Kirchhoff's current law (KCL) node voltage method and the superposition theorem of the node, is an effective method to analyze the ideal op amp circuit.As shown below, find the output voltage uoFigure 3. OPAMP Circuit1) Equation based on KCLFrom the concept of virtual break, i+=i-=0, then i1=i2, i3=i4, so (a)Based on virtual break, u+=u-, then (b)2) Node voltage methodList the node voltage equations for node 1 and node 2, and get (c)Note: Because the output current of the op amp is unknown at 1) and 2), it is not possible to list the KCL equation or node voltage equation at the output of the op amp. In addition, the op amp output uo in 2) should be treated as an independent voltage source. 3) Superposition theoremWhen there are multiple signal inputs, choosing the superposition theorem to solve can simplify the analysis and calculation process. The size of the output signal uo can be regarded as the superposition of the output signal obtained by the independent action of u1 and u2. When u1 acts alone, the u2 terminal is grounded, and the op amp output is: (d)Therefore, the final output of the operational amplifier is:   (e) Ⅶ Several Common Op Amp CircuitsNon-inverting Amplifier CircuitA non-inverting amplifier is an op-amp circuit configuration which produces an amplified output signal. It provides a high input impedance along with all the advantages gained from using an operational amplifier. Inverting Amplifier CircuitAn inverting amplifier (also known as an inverting operational amplifier or an inverting op-amp) is a type of operational amplifier circuit which produces an output which is out of phase with respect to its input by 180 degrees out of phase with respect to input signal. In the following figure, two external resistors to create feedback circuit and make a closed loop circuit across the amplifier. Op-amp as AdderAn adder circuit can be made by connecting more inputs to the inverting op amp. The circuit diagram of a summing amplifier is as shown in the following figure. Differential AmplifierDifferential amplifier is an analog circuit with two inputs and and one output in which the output is ideally proportional to the difference between the two voltages. It is a very useful op-amp circuit and by adding more resistors in parallel with the input resistors as shown in the following. Composite AmplifierThe composite amplifier is termed as a combination of multiple operational amplifiers that are cascaded together with a negative-feedback loop around the entire network. The resistance in the circuit is generally selected at the K ohm level, the ratio of the resistance affects the gain and bias, in addition, the supply current, frequency response and capacitive load driving capability of the op amp determine their specific values in circuits. If it is used in a high-frequency circuit, the resistance needs to be reduced to obtain a better high-frequency response, but it will increase the input bias current, thereby increasing the current of the power supply. Ⅷ Difference Between Ideal Op-amp and Practical Op-ampIdeal op amps use no power, have infinite input impedance, unlimited gain-bandwidth and slew rate, no input bias current, and no input offset. They have unlimited voltage compliance.Practical op amps consume some power, have very high input impedance have limited gain-bandwidth and limited slew rate, have some input bias current and input offset voltage. Voltage compliance is limited by the power supply rail, or frequently even less.Still practical op amps are very useful because most of the limitations listed above are way better than what your circuit needs.For an ideal amplifier, it does not draw any current at all from its input. Assuming a two input amplifier the signal current in both input probes is zero. In other words the input impedance must be infinite. The output, should operate as the output of an ideal voltage source. This means that the potential between the output and the ground must be A(v2−v1), no matter how much current would a load connected to the output would draw. In other words the output impedance must be zero.For a real amplifier, the input impedance must be as large as possible while the output impedance must be as low as possible.In fact, An op-amp in real life, however, cannot operate with zero current flow. Frequently Asked Questions about Ideal Op Amp1. What is characteristic of ideal opamp?Ideal op amps will have infinite voltage gain, infinitely high impedance, zero output impedance, its gain is independent of input frequency, it has zero voltage offset, its output can swing positive or negative to the same voltages as the supply rails, and its output swings instantly to the correct value. 2. How does an ideal op amp work?An operational amplifier, or op amp, generally comprises a differential-input stage with high input impedance, an intermediate-gain stage, and a push-pull output stage with a low output impedance (no greater than 100 Ω). ... Open-loop voltage gain runs very high, on the order of 1 million. 3. Why are op amps not ideal?Op-amps with FET inputs have an Ibias that is so small that this method becomes less practical. Instead of measuring the voltage drop across a resistor, one can monitor the change in voltage across a capacitor as it is charged by the bias current. 4. How are real op amps different from ideal op amps?In real op amps, the amplified signal will not fully reach the DC supply rails. They will fall short of it. In an ideal op amp, the output will swing instantly to the amplified voltage value. There will be no time delay between the time the voltage is input into the op amp till the time it is output. 5. What are the four main ideal characteristics of an open-loop op amp?An ideal op amp is usually considered to have the following characteristics:Infinite open-loop gain G = vout / vInfinite input impedance Rin, and so zero input currentZero input offset voltageInfinite output voltage rangeInfinite bandwidth with zero phase shift and infinite slew rateZero output impedance R

IntroductionSemiconductor diode, also known as crystal diode, has obvious unidirectional conductivity. It is a kind of electronic components widely used in electrical equipment for protection, rectification, switching, and many other applications. So it is pretty common to see diodes in daily electronic circuits, such as Zener diodes, light-emitting diodes, photodiodes, etc. Therefore, it is necessary to know how to test whether a diode is properly working or not.How to Test a Diode Using a MultimeterCatalogIntroductionⅠ Diode Basics1.1 To Figure Out Diode Anode and Cathode1.2 What Would Cause a Diode to Fail?1.3 Common Diode Failures AnalysisⅡ How to Test Diode with a Multimeter?2.1 Digital Multimeter and Analog Multimeter2.2 Common Diodes Testing Rules2.3 Testing Methods of Types of DiodesⅢ Example Analysis3.1 Test a Diode in Circuit3.2 Power-off and Power-on Testing Methods3.3 ConclusionⅠ Diode Basics1.1 To Figure Out Diode Anode and CathodeThe anode and cathode of diode can be distinguished by screen printing on PCB board, which are as shown in the following:1) The notched end is the cathode of diode.2) The end with a horizontal bar is the cathode.3) The end with white parallel bars is the cathode.4) One end of the triangle arrow is the cathode.5) The small end of the plug-in diode is the cathode, and another big end is the anode.1.2 What Would Cause a Diode to Fail?The common reasons for a diode failure are open circuit, short circuit and unstable voltage regulation. Among these three types of failures, there may be signs. For example, the power supply voltage rises, the supply voltage drops to zero or the output is unstable. Therefore, specific problems must be analyzed in detail for the diode test.The common measurement tool for diode is a multimeter, including on-circuit measurement (the diode is on the circuit board) and off-circuit measurement (the diode is not on the circuit board). As for the basic principle of diode measurement, the forward resistance and the reverse resistance of the PN junction are measured, and the basic judgment is based on the values of them. Therefore, to do a good job in diode test, it is necessary to understand the basic structure and working principle of diodes, and then to understand the main fault characteristics of the diode. 1.3 Common Diode Failures Analysis1) open circuitThis means that the positive and negative electrodes of the diode have been disconnected, and the forward and reverse resistance of the diode have become infinite. After the diode is open, the circuit is in an open state.2) voltage breakdownThis means that there is a path between the positive and negative electrodes of the diode, and the forward and reverse resistance are as large as or close to each other(but not infinite). After a diode breaks down, the action between the positive and negative electrodes may always exit, because there are different manifestations in different circuits.3) forward voltageIf the forward resistance of the diode is too large, the voltage drop of the signal on the diode will increase, which will cause the output signal to decrease, and the diode will be damaged due to the heat. After the forward resistance becomes larger, the unidirectional conductivity of the diode will become poor.4) reverse voltageThe reverse resistance of the diode becomes smaller, which means the unidirectional conductivity of the diode be effected.5) performance degradationUnder this circumstance, the diode does not have obvious failures such as open circuit or breakdown. However, when the situation is getting worse, the stability of the circuit will deteriorate or the output signal voltage of the circuit will drop. Ⅱ How to Test Diode with a Multimeter?2.1 Digital Multimeter and Analog MultimeterWhen using a digital multimeter to test a diode, the red probe connects with the anode and the black probe connects with the cathode. At this time, the measured resistance is the forward conduction resistance of the diode, which is just the opposite of the test result of an analog multimeter. 2.2 Common Diodes Testing Rules(1) The forward resistance of the low-power germanium diode is 300Ω～500Ω, and the silicon diode is lkΩ or more. The former reverse resistance is tens of thousand ohms, and the latter is above 500kΩ (the value of high-power diode is smaller).(2) The polarity of the diode can be judged according to the resistance values (small forward resistance and large reverse resistance). Set the multimeter to the ohm block (Usually use R×100 or R×1k block, do not use R×1 block or R×10k block. The R×1 block is in a large current, it is easy to burn the tube, while using R×10k block may cause the tube broken down with high voltage). Connect the two polarities of the diode with the test probes respectively, and measure the two resistance values. When the measured resistance value is smaller, the end connected to the black lead is the anode. In the same way, when the measured resistance value is larger, the end connected to the black probe is the cathode. If the measured reverse resistance is small, it means that the diode is short-circuited, on the contrary, if the forward resistance is large, it means that the tube is open. In both cases, the diode can’t be work normally.(3) Silicon diodes generally have a forward voltage drop of 0.6V～0.7V, and the forward voltage drop of a germanium diode is 0.IV～0.3V. By measuring the forward voltage of the diode, it can be judged that the tested diode is a silicon tube or a germanium tube. This method is to connect a resistor (lkΩ) behind the power supply, and then connect with the diode according to the polarity characteristic to make the diode forward conducting. At this time, use a multimeter to measure the tube voltage drop. In addition, it is more convenient if it is used in energized dynamic measurement. 2.3 Testing Methods of Types of DiodesZener DiodesHow to test a Zener diode? The following here is to give some ideas.(1) Generally use the low-resistance block to test the Zener diode with a multimeter. Since the battery in the meter is 1.5V, this voltage is not enough to make the Zener diode reverse breakdown. So the forward and reverse resistance should be the same as a normal diode.(2) Measurement of the voltage stabilization value Vz of the Zener diode. When measuring diode, the power supply voltage must be greater than the stable voltage of the tube under test. In this way, the high-resistance block of the multimeter (R×10k) must be used. At this time, the battery in the meter has a higher voltage. When the multimeter's range is set to high barrier, measure diode reverse resistance. If the measured resistance is Rx, the voltage regulation value of the Zener diode is:In the formula, n is the override of the gear used. For example, if the highest electrical barrier ofR0 is the central resistance of the multimeter.E0 is the highest battery voltage value of the multimeter used.Example: Use an MF50 multimeter to measure a 2CW14 diode.R0=10Ω, the highest electrical barrier is R×10k.E0=15V, the measured reverse resistance is 75kΩ, then its voltage regulation value is:If the measured resistance is very large (close to infinite), it means that the voltage Vz under test is greater than E0, therefore, tube will not break down. If the measured resistance is very small (0 or only a few ohms), it means that the test probes are connected reversely, and then just swap the test probes. Light-emitting Diodes (LED)A light-emitting diode is a semiconductor device that converts electrical energy into light energy. It has the characteristics of small size, low working voltage and low working current.(1) There is a PN junction inside the light-emitting diode, so LED has the same characteristic of unidirectional conductivity. Its detection is similar to the measurement of ordinary diodes.(2) Use the R×1k or R×10k gear, and the forward and reverse resistance values are measured. Generally, the forward resistance is less than 50kΩ, and the reverse resistance is greater than 200kΩ.(3) The working current of the light-emitting diode is an important parameter. If the working current is too small, the light-emitting diode will not light up, and it is too large, the light-emitting diode will be easily damaged.(4) The forward turn-on voltage of the light-emitting diode is 1.2V ~ 2.5V, and the reverse breakdown voltage is about 5V. PhotodiodesPhotodiode is a semiconductor device that can convert light intensity into electrical signals.(1) There is a window on the top of the photodiode that can inject light, and the light irradiates the die through it. Under the excitation of the light, a large number of photoelectric particles are generated in the photodiode, which greatly enhances its conductivity and reduces internal resistance.(2) The photodiode is similar to the Zener diode. It also works in the reverse state, with reverse voltage.(3) The forward resistance of the photodiode does not change with the light. Its reverse resistance is larger when there is no light, and becomes smaller when it is exposed to light. That is, the stronger the light, the smaller the reverse resistance. Without light, the reverse resistance will return to the original value.(4) According to the related principle, use a multimeter to measure the reverse resistance of the photodiode. Change the light intensity when measuring, and observe the change of the reverse resistance of the photodiode. If there is no change or less change of the reverse resistance when light changes, it indicates that the tube has failed. High-speed Switching DiodesThe method of detecting high-speed silicon switching diodes is the same as that of ordinary diodes. The difference is that the forward resistance of this tube is relatively large. Measuring with Rxlk block, the forward resistance value is 5k ~ 10k in general, and the reverse resistance value is infinite. Fast Recovery Diodes / Ultrafast Recovery DiodesDetecting fast recovery and ultra-fast recovery diodes with a multimeter is basically the same as that of detecting plastic-encapsulated silicon rectifier diodes. That is, first use the Rxlk block to test its unidirectional conductivity. Generally, the size of forward resistance is about 4 ~ 5k, and the reverse resistance is infinite. And then use the Rxl block to repeat the test, at this time, the forward resistance is several ohms, and the reverse resistance is still infinite. DIAC (Diode for Alternating Current) DiodesUse the Rxlk block, and measure the forward and reverse resistance values of diac, which should be infinite. If the test probes are exchanged to measure, the pointer swings to the right, which indicates that the test tube has a leakage fault. Another method is placing the multimeter in the DC voltage block. During the test, shake the megohmmeter, and the voltage value indicated by the multimeter is the VBO value of the tube. Then change the two pins of the tested tube, and measure the VBR value in the same way. Finally, compare VBO and VBR. The smaller the difference between the absolute values of the two, the better the symmetry of the diac diode. TVS DiodesFor the dual TVS, resistance values between the two pins should be infinite when the red and black test probes of multimeter are exchanged at random. Otherwise, the tube has poor performance or has been damaged. High-frequency Varistor Diodesa. Identify Diode PolarityThe difference between high-frequency varistor diodes and ordinary diodes is that their color code is different. It is generally black of ordinary diodes, while high-frequency varistor diodes’ is light. Its polarity rule is similar to that of ordinary diodes. That is, the end with the green ring is the cathode, otherwise it is the anode.b. Measure Forward and Reverse ResistanceThe specific method is the same as the method of measuring ordinary diodes. Using the Rxlk block of a AM-500 multimeter, the forward resistance is 5k～55k, and the reverse resistance is infinite. Varactor DiodesUsing Rx10k block, no matter how the red and black test leads are exchanged for measurement, the resistance between the two pins of the varactor diode should be infinite. During the measurement, if the multimeter swings slightly to the right or the resistance value is zero, it means that the varactor diode under test has a leakage fault or has been broken down. No matter the loss of varactor diode capacity or internal open-circuit fault, it is impossible to detect them with a multimeter. When necessary, the replacement method can be used for inspection to make judgment. Infrared Light Emitting Diodes (IRED)Put the multimeter in the Rxlk block and measure the forward and reverse resistance of the IRED diode. Generally, the forward resistance should be about 30k, and the reverse resistance should be above 500k. It means the tube can work normally. The larger the reverse resistance, the better. IR Receiver Diodesa. Appearance Identification: Diode Cathode / Anode(1) Common infrared receiving diodes are black in appearance. In addition, there is a small oblique plane at the top of the tube body of the infrared receiving diode. Usually, the pin with one end of the oblique plane is the negative pole and the other end is the positive pole.(2) Use the Rxlk block to test the resistances between two pins. When a diode works normally, the resistance value of two pins are different. And exchange the test leads several times to get some pairs of values. According to the smaller resistance value, the pin connected to the red probe is the cathode, and the pin connected to the black probe is the anode.b. Performance DetectionUse a multimeter to measure the forward and reverse resistance of the infrared receiving diode. According to the resistance values, whether the diode is damaged can be judged preliminarily. Laser DiodesUse the Rxlk block of multimeter, and determine the order of the pins of the laser diode according to the method of detecting ordinary diodes. Because the forward voltage drop of the laser diode is larger than that of the ordinary diode, when detecting the forward resistance, the pointer of the multimeter is slightly deflected to the right, and the reverse resistance is infinite. Unijunction Transistor (UJT)a. Discrimination of ElectrodesBased on the R×1k block, use two meter pens to measure the forward and reverse resistance between any two of the three electrodes ( base B1 and base B2, and emitter E) of the ujt diode. The measured resistance values between the two electrodes are both 2~10kΩ, in addition, B1 and B2 will be different.b. Performance JudgmentThe performance of an ujt diode can be judged by measuring whether the resistance between its pins is normal. Use the R×1k barrier, the black test lead connect to the emitter E, and the red test lead connect to the two base electrodes in turn. Normally, a resistance value should be several thousand to ten thousand ohms. On the contrary, the red test lead connects to the emitter E, and the black test lead connects to the two base electrodes in turn, and the resistance should be infinite under normal conditions. The forward and reverse resistance values between the two bases are both in the range of 2~10kΩ. If they differ greatly from the normal value, the diode is damaged. Ⅲ Example Analysis3.1 Test a Diode in Circuita. Diode Test UsingAnalog MultimeterThe following measurements are all based on silicon diodes. If it is a germanium diode, the forward and reverse resistance of the diode will decrease.1) Measure forward resistance FRThe following figure is a wiring schematic diagram for measuring the forward resistance of a diode with an analog multimeter:Give the result as follows:IndicatorDescriptionUse the R×1k block to measure the diode, the forward resistance is several thousand ohms, and the pointer indicates stability. If the pointer swings slightly, it indicates that the thermal stability of the diode is poor.If the pointer indicates hundreds of kiloohms when measuring the forward resistance, it means that the diode is open.If the pointer indicates tens of kiloohms, it indicates that the diode has a large forward resistance and poor diode performance. Description of measurement of forward resistance:Forward Resistance (FR)DescriptionThousands of ohmsNormalZero or much less than a few thousand ohmsBreakdownHundreds of kilosLarge FR, the diode is openDozens of kilohmsLarge FR, bad forward characteristicsThe pointer is unstablePoor stability 2) Measure reverse resistance RRThe following figure is a wiring schematic diagram for measuring the reverse resistance of a diode with an analog multimeter:Give the result as follows:IndicatorDescriptionWhen measuring the reverse resistance, the value should be several hundred kiloohms. The larger the resistance value is, the better the indicator should be stable.If the reverse resistance is only a few thousand ohms, it means that the diode has broken down and has lost its unidirectional conductivity. Description of measurement of reverse resistanceReverse ResistanceDescriptionHundreds of kilosNormalZeroBreakdownMuch less than a few hundred thousand ohmsDiode’s reverse characteristic is not good.Pointer does not moveThe diode is open. Note: The reverse resistance of some diodes is very large, at this time, it is not certain that the diode is open, so that its forward resistance should be measured. If the value is normal, it means that the diode is not open.Pointer is unstableThe pointer cannot be stabilized at a certain resistance value during measurement, indicating that the diode has poor stability. 3.2 Power-off and Power-on Testing MethodsDiode in-circuit measurement is divided into two situations: Power-off and Power-on statea. Power-off MeasurementThere are something should be noted the method of this test.The influence of the external circuit on the test result is the same as the resistance and capacitance measured of internal circuit. And the influence of the measured forward resistance by the external circuit is lower than the reverse resistance.If there is any doubt about the measuring result, the diode should be removed from the circuit and measured separately. b. Power- on MeasurementWhen the circuit board is powered on, the test point is the tube voltage drop. Because the diode has a very important characteristic: when it is turned on, the tube voltage drop is basically unchanged. So the voltage drop is normal after being turned on, that is to say, the diode is normal.Measurement method: The diagram below shows the connection diagram of the tube voltage drop after the diode in the DC circuit. Setting multimeter in DC voltage 1 V block, the red probe is connected to the cathode of the diode, and the voltage indicated is the forward voltage drop of the diode. Diode forward voltage drop measurement results are analyzed as follows:DiodeDescriptionSilicon diode0.6VThe diode is normal and in a forward conducting state.> 0.6VThe diode is not in the conducting state.Close to 0The diode is in a breakdown state, the current in the loop will increase.Germanium diode0.2VThe diode is normal and in a forward conducting state.> 0.2VThe diode is off or is faulty.Close to 0In the breakdown state, the loop current increases significantly, without unidirectional conductivity. 3.3 ConclusionThe following points should be noted when measuring diodes:1) The diode in AC is in the cut-off state, because the diode is in the reverse state, and the reverse voltage at both ends is very large. The average voltage across the diode measured by the DC block is negative at this time.2) Use different blocks of the same multimeter to measure positive and negative resistance of one diode, their values will different. The forward and reverse resistances of the same diode measured with different multimeters are also different.3) When measuring the forward resistance of a diode, if the pointer cannot stop at a certain resistance value and constantly swings, it indicates that the thermal stability of the diode is not good.4) Some multimeters will provide a “diode check” function that displays the actual forward voltage of the diode when its conducting current. Such meters typically indicate a slightly lower forward voltage than what is “nominal state” for a diode, due to the very small amount of current used during the measurement. Frequently Asked Questions about Diode Test1. What is a diode test?A diode is best tested by measuring the voltage drop across the diode when it is forward-biased. ... A multimeter's Diode Test mode produces a small voltage between test leads. The multimeter then displays the voltage drop when the test leads are connected across a diode when forward-biased. 2. How do you test a rectifier diode?Touch the red (positive) probe of the multimeter to the positive terminal of the diode closet to the welder case interior. Touch the black (negative) probe of the multimeter to the negative terminal of the same diode. The multimeter should read a resistance between 0 and 1 ohm, or the diode is faulty. 3. How can you tell if a diode is positive or negative?Sometimes it's easiest to just use a multimeter to test for polarity. Turn the multimeter to the diode setting (usually indicated by a diode symbol), and touch each probe to one of the LED terminals. If the LED lights up, the positive probe is touching the anode, and the negative probe is touching the cathode. 4. How do you test a Schottky diode?Connect the red positive test lead to the anode of the Schottky diode and the black common test lead to the cathode of the diode. Listen for a “beep” or a “buzz” from the multimeter. If the Schottky diode responds as expected, the multimeter will sound a tone. 5. Can I test a diode in circuit?A diode is best tested by measuring the voltage drop across the diode when it is forward-biased. A forward-biased diode acts as a closed switch, permitting current to flow. A multimeter's Diode Test mode produces a small voltage between test leads. ... Voltage may be present in the circuit due to charged capacitors. 6. How do you check a diode?Diode PolarityThe polarity of both diodes is indicated with a stripe on one end of the body. The stripe corresponds to the line in the schematic symbol, indicating the cathode. The other end (no stripe) is the anode, indicated by the triangle in the schematic symbol. 7. What happens when a diode fails?However, a failed diode can short out too. In this case, the diode will exhibit a small resistance in both directions. The common reasons for a diode failure are excessive forward current and a large reverse voltage. Usually, large reverse voltage leads to a shorted diode while overcurrent makes it fail open. 8. How can you tell if a diode is blown?Turn the dial to “diode test” mode.This level of current is high enough to produce a reading, yet not so high that the diode will fail. It may also be labeled as “diode check” on your multimeter and is usually indicated by a small diode symbol. The diode symbol will look like a triangle pointing towards a line.

IntroductionTime relay refers to a kind of relay whose output circuit needs to make an obvious change (or contact action) after adding (or removing) the input action signal in a specified and accurate time. It is an electrical component used in a circuit with a lower voltage or a smaller current to switch on or off a circuit with a higher voltage and larger current.  With the development of electronic technology, electronic time relays have become mainstream products in time relays. Electronic intelligent digital display time relays using large-scale integrated circuit technology have many working modes, which can not only achieve long delay time but also have high time-delay accuracy, small size, convenient adjustment and long service life, making the control system simpler and more reliable. The time relay also has the function of automatic monitoring. Time relay and other equipment together can form a program space route to realize the automatic operation of the equipment.Time Relay Basics ExplainedCatalogIntroductionⅠ Time Relay Basics  1.1 What is a Time Delay Relay?  1.2 Time-delay Relay Working Principle  1.3 Timer Relay Structure  1.4 Timer Relay Parameters  1.5 Four-type Time Relay Contacts Ⅱ Understanding Time Delay in Relay CircuitⅢ Time Relay Classifications  3.1 According to Working Principle  3.2 According to the Delay ModesⅣ How to Wire Time Relay?Ⅴ Time Relay ApplicationsⅥ Time Relay SelectionⅦ Timer Relay Using Instructions  7.1 General Ideas  7.2 Two Points for Attention in Using Time RelaysⅧ Case Study: Time Relay Switch in Light CircuitⅨ Frequently Asked Questions about Time Delay Relay BasicsⅠ Time Relay Basics1.1 What is a Time Delay Relay?The time relay is a very important component in the electrical control system. In many control systems, use the time relay to achieve delay control. Time relay is an automatic control electrical appliance that uses the principle of electromagnetic or mechanical action to delay the closing or opening of contacts. Its characteristic is that there is a delay from the time the attracting coil gets the signal to the action of the contact. The time relay is generally used to control the motor starting process with time function. As above mentioned, the main function of the time delay is as an executive device in simple program control. When it receives the start signal, it starts timing. After the timing ends, its working contact opens or closes to promote the subsequent circuit work. Generally speaking, the delay performance of the time relay can be adjusted within the range of design, so as to facilitate the adjustment of its delay time. In addition, a time relay alone may not be able to do close. After closing for a period of time, it will open again. It is a cycle of time-delay closing and opening. However, configuring a certain number of time relays and intermediate relays can do it. 1.2 Time-delay Relay Working PrincipleTime relay is widely used in remote control, telecommunication, automatic control and other electronic equipment, and is one of the most important control components. When the coil is energized, the armature and the pallet are attracted by the core and move down instantaneously, making the action contact close or open. However, the piston rod and the lever cannot fall with the armature at the same time, because the upper end of the piston rod is connected to the rubber film in the air chamber.  When the piston rod starts to move downward under the action of the released spring, the rubber film is concave downward. The air in the air chamber becomes thinner, causing the piston rod to be damped and slowly descend. After a certain period of time, the piston rod descends to a certain position, and then the delay contact action is pushed through the lever to make the moving contacts open and close. The time from when the coil is energized to when the delay contact completes the action is the delay time of the relay. The length of the delay time can be changed by adjusting the size of the air inlet hole of the air chamber with a screw. After the suction coil is de-energized, the relay relies on the spring to recover. And the air is quickly expelled through the air outlet. 1.3 Time Relay StructureFigure 1. Air-damping Time Relay1 Coil5 Push plate9 Weak Spring13 Adjusting Screw2 Iron Core6 Piston rod10 Rubber Film14 Air Inlet3 Armature7 Lever11 Air Chamber Wall15 Micro Switch4 Reaction Spring8 Spring12 Piston16 Micro Switch 1.4 Time Relay ParametersTechnical parameters include rated voltage, contact working current, contact type and quantity, delay time, accuracy, ambient temperature, mechanical life and electrical life, etc. Now take the SJ23 series air-type time relay as an example, its technical parameters are as follows:1) Rated control capacity: AC300VA, DC60W (30W delay contact assembly).2) Rated voltage level: AC380V, 220V; DC220V, 110V.3) Rated voltage of the coil: AC110V, 220V and 380V.4) Maximum operating current of the contact: 0.79A at AC380V, 0.27A (momentary) and 0.14A (delay) at DC220V.5) Delay repeat error: ≤9%.6) Hot-state pull-in voltage: no more than 85% of the rated voltage of the relay. When the voltage drops from the rated value to 10% of the rated value in cold-state, it can be reliably released. And it can reliably release after reaching 110% of the rated voltage.7) The mechanical life is not less than 1 million times, and the electrical life is 1 million times (the DC life of the delay contacts assembly is 500,000 times). 1.5 Four-type Time Relay ContactsFigure 2. Time Relay SymbolsNOTC (normally-open, timed-closed): When the coil is not energized, the NOTC contact is normally open. It is closed by energizing the relay coil, but only within a specified time after the coil is continuously energized. The moving direction of the contact (close or open) is the same as that of a standard normally open contact. Since the delay occurs in the direction in which the coil is energized, this type of contact is normally open and on-delay. NOTO (normally-open, timed-open): Unlike the NOTC contact, the timed action occurs when the coil is de-energized. Since the delay occurs when the coil is de-energized, this type of contact is normally open and off-delay. NCTO (normally-closed, timed-open): When the coil is not powered on, the NCTO contact is normally closed. By energizing the relay coil, the contact is opened, but only within a specified time after the coil is continuously energized. The movement direction of the contact (closed or opened) is the same as the standard normally closed contact, but there is a delay in the opening direction. NCTC (normally-closed, timed-closed): The NCTC contact is similar to NCTO contact, because when the coil is normally closed when in de-energized and opened by energizing the coil. Ⅱ Understanding Time Delay in Relay CircuitSet delay time of a relay. Generally speaking, the delay performance of the time relay can be adjusted within the range of design, so as to facilitate the adjustment of its delay time in circuit. Time Delay Relay Circuit (Power-Off)If you are using an on delay relay, the delay will start immediately after the input signal is obtained. After the delay is completed, the executive part will output the signal to the control circuit. When the input signal disappears, the relay will immediately return to the pre-action status. It is opposite to an off delay relay. When the input signal is obtained, the execution part immediately has an output signal. After the input signal disappears, the relay needs a certain time to restore to the state before the action.Figure 3. Timer Relay StructureⅢ Time Relay Classifications3.1 According to Working PrincipleAccording to different working principles, time relays can be divided into air damping time relays, electric time relays, electromagnetic time relays, electronic time relays, etc. (1) Air damping time relayThe type is obtained by using the principle of damping when air passes through the small hole. Its structure is composed of three parts: electromagnetic system, delay mechanism and contact. The electromagnetic mechanism is a double-port direct-acting type, the contact system is a micro switch, and the delay mechanism adopts an airbag damper. (2) Electronic time relayUtilize the principle that the capacitor voltage in the RC circuit can't jump, and can only change gradually according to the exponential law, that is, the delay is obtained by electrical damping characteristics.Features: Wide delay range, high precision (generally about 5%), small size, shock resistance and easy adjustment. (3) Electric time relayUse the miniature synchronous motor to drive the reduction gear train to obtain the time delay.Features: The delay range is wide, up to 72 hours, and the delay accuracy can reach 1%. At the same time, the delay value is not affected by voltage fluctuations and environmental temperature.Its delay range and accuracy are unmatched by other time relays. Its disadvantages are complex structure, large size, short life, high price, and accuracy is affected by the power frequency. (4) Electromagnetic time relayUse the principle of slow attenuation of the magnetic flux after the electromagnetic coil is cut off to delay the release of the armature of the magnetic system to obtain the delay action of contacts. It is characterized by a large contact capacity, so the control capacity is large. However, the delay time range is small, and the accuracy is slightly worse. So it is mainly used in the control of DC circuits. 3.2 According to the Delay ModesBased on it, time relays can be divided into two types: on-delay type and off-delay type.(1) The on delay type time relay starts to delay immediately after receiving the input signal. After the delay is completed, its execution part outputs the signal to manipulate the control circuit. When the input signal disappears, the relay immediately returns to the state before the action.(2) The off delay type time relay is just the opposite. When the input signal is obtained, the execution part immediately has an output signal. After the input signal disappears, the relay needs a certain delay to restore to the state before the action. Ⅳ How to Wire Time Relay?The time relay is a very important component in the electrical control system. There are power-on delay types and power-off delay types. Based on the action type, there are electronic type and electric type, etc. Between them, the electronic type uses the principle of capacitor charging and discharging combined with electronic components to achieve delay action. There are many electric styles by using air bags and springs.Figure 4. Time Relay Wiring Schematics Time Relay Wiring:1) Control wiring: Consider it as a DC relay.2) Work control: Although the control voltage is connected, whether it plays a control role is determined by the timer on the panel.3) Function understanding: It is a switch,single-pole double-throw, with an active point, just like the active arm of a common knife switch.4) Load wiring: Connect the neutral wire of the power supply or the negative terminal.5) Working principle: When the timer is invalid, it is equivalent to the normal light in the switch-off state. When timing, the relay will act and the electrical appliances will be energized to work, which is equivalent to the normal light in the switch-on state.Take the power-on delay time relay as an example:Figure 5. On Delay Relay Contacts Wiring Ⅴ Time Relay ApplicationsIn Flash ControlTwo-time relays cooperate with each other to provide constant frequency on/off pulses of the contacts, sending intermittent power to the light.  In Furnace Safety Purge ControlBefore the combustion furnace can be safely ignited, the fan must run for a certain period of time to clean out any flammable or explosive steam in the furnace chamber. The time relay provides the required time parts for the furnace control work.In Electric Soft-start Delay ControlIt is not necessary to start a large electric engine by switching full power from a completely stopped state, and can reduce voltage softly start with less inrush current.In Conveyor Belt Sequence DelayWhen multiple conveyor belts are arranged to transport materials, the conveyor belts must be started in the reverse order (the last one is first, the first one is last) to prevent materials from accumulating on the moving conveyor which may be stop or move slowly. Ⅵ Time Relay SelectionThe selection of time relay is mainly due to delay mode and parameter coordination. The following aspects should be considered when selecting.(1) Delay mode selectionIt should be selected according to the requirements of the control circuit. The reset time after the action is longer than the inherent action time, so as to avoid misoperation or even no delay. This is especially important in the occasions of repeating delay circuits and frequent operations. (2) Type selectionFor occasions where the delay accuracy is not high, cheaper electromagnetic or air damping time relays are always used. On the contrary, for occasions where the delay accuracy is high, electronic time relays can be used. (3) Coil voltage selectionAccording to the voltage of the control circuit, the voltage at which the relay attracts the coil is selected. (4) Selection of power supply parametersIn the occasions where the power supply voltage fluctuates greatly, it is better to use air damping or electric time relays than the transistor type. And in the occasions where the power frequency fluctuates, electric time relays should not be used. In addition, when the temperature changes greatly, air damping type should not be used. When selecting a time relay, pay attention to the current type and voltage level of its coil (or power supply), and other factors, such as delay mode, contact form, delay accuracy and installation method according to the control requirements.Ⅶ Timer Relay Using Instructions7.1 General Ideas1) Keep the time relay clean, otherwise, the error will increase.2) Before use, check whether the power supply voltage and frequency are consistent with the voltage and frequency of the time relay.3) Choose the control time of the time relay according to user requirements. Regardless of the type of time relay, as long as the timing time is equal to the set time, its output contacts will act to achieve the purpose of the timing control circuit.4) For DC products, pay attention to wiring according to the circuit diagram and pay attention to the polarity of the power supply.5) After the time relay is out of working state, it should be reset immediately for the next use. If the repeated use interval is less than the preset time, the control circuit will be abnormal. What’s more, the power-on delay type is automatically reset after power off; and the power-off delay type is automatically reset after power on.6) Try to avoid using it in places with obvious vibration, direct sunlight, humidity and soil contact. 7.2 Two Points for Attention in Using Time RelaysThree Key Points1) Starting point of timingOn one hand, when selecting the timing point of the power-on delay time relay, you should choose to supply power to the time relay when the timing signal is sent by the control circuit that needs to perform timing. On the other hand, when selecting the timing point of the power-off delay type time relay, you should choose to cut off the power supply of the time relay when the control circuit that needs to send out the timing signal, so that the timing can be performed.2) Ending point of timingThe timing endpoint has two meanings: one refers to the point at which the set time is equal to the timing time; the other refers to the point at which the contract operates.3) Reset point of timingThe reset of the time relay is to clear the last timing content for the next use. If it is not reset, an abnormality will occur the next time it is used. Special attention should be paid to: the interval between two uses should be greater than the reset time, which is particularly important in electric time relays. The relationship between the starting point, ending point and reset point of timing1) After the time relay is used, there is a reset problem. Therefore, most of the control circuits are in the next level circuit by the time relay output. After the timing completion signal is accurately obtained, it is used to cut off the power supply of the time relay (power-on delay type), or power the time relay (power-off delay type).2) In the upper and lower control circuits of the time relay, there are components that cannot work at the same time. If the time relay cannot accurately operate the upper and lower control circuits at these points, it will cause the device to operate abnormally. Ⅷ Case Study: Time Relay Switch in Light CircuitControl requirements: Light 1 and light 2 are on at the same time, and light 2 is off in 30 seconds after light 1 is off. When light 1 is on, light 2 can be off at any time.According to the control requirements, explain through the following circuit diagram.Figure 6. Time Relay Switch in Light Circuit1) Press SB2, the contactor KM is energized and self-locked, and at the same time KT is also energized, and KT closes.2) After KT is turned on, the intermediate relay KA is also energized to work.3) At the same time, contact KM and contact KA are also closed at the same time, light 1 and light 2 are on.4) When the stop button SB1 is pressed, the contactor KM powers off, the contact KM opens, and the light 1 is off at the same time. Because of the existence of the power-off delay relay, KT is still on as well as the light 2. It goes out after the timing set by the time relay.5) When light 1 is on, and contact KA1 is turned on at any time, the time relay resets. KT disconnects and the light off.This is the typical application of an off delay relay. However, in the actual circuit, the control logic may be more complicated than this, so we must deeply understand the working principle and application of the time relay. Ⅸ Frequently Asked Questions about Time Delay Relay Basics1. What is time-delay relay?Time-delay, or time-release relays, allow necessary actions to happen at specific times in an electrical apparatus because they, in essence, act as a timer. 2. How does a time delay relay work?Time delay relays control the flow of electrical power and can be used to control power to many different types of electrical loads. Combining electromechanical output relay capability with control circuitry, these relays are pre-engineered to perform up to eleven time delay functions. 3. What is time delay relay circuit?Time Delay Relays. Time-Delay Relay. Relays are switches that are controlled by a circuit. Relays, in essence, send messages that tell something to start. When a car is started, the ignition only indirectly interacts with the battery of the car because a relay is sending the signal that tells the car to start. 4. How does a time delay relay work?Upon application of input voltage, the time delay relay is ready to accept trigger signals. Upon application of the trigger signal, the relay is energized and the preset time begins. ... Continuous cycling of the trigger signal at a rate faster than the preset time will cause the relay to remain energized. 5. How do you make a time delay relay?These relays provide a “Time Delay” between the energizing or de-energizing of the coil and movement of the armature. Such relays are called Time Delay Relays. A Time Delay Relay consists of a normal electromechanical relay along with a control circuit to control the relay operation and timing. 6. What is off delay relay?Abbreviated “NOTO”, these relays close immediately upon coil energization and open after the coil has been de-energized for the time duration period. Also called normally-open, off delay relays. 3: Normally-closed, timed-open. 7. How does an off delay timer relay work?Operation of Off Delay FunctionUpon application of input voltage, the time delay relay is ready to accept a trigger. When the trigger is applied, the output is energized. Upon removal of the trigger, the time delay (t) begins. At the end of the time delay (t), the output is de-energized. 8. What is the difference between off delay and on delay timer?As for Timer ON Delay, Timer starts by turning ON the timer trigger bit, and the timer output bit turns ON when the setup time has passed. As for Timer OFF Delay, the timer output bit turns OFF when the setup time has passed after the timer input bit had turned OFF. 9. How do you test a timer relay?Burden TestAdjust the timer with high time delay for example: 2 minutes.Energize the relay with 125V and measure the dc current.Note down the current before timer operates.After 2 minutes relay will pick up. Note down the current after operation.Calculate the relay power (W) = 125v x measured current. 10. What is the function of an time delay relay?Typical time delay functions include on-delay, repeat cycle (starting off), interval, off-delay, retriggerable one shot, repeat cycle (starting on), pulse generator, one shot, on / off delay, and memory latch.

IntroductionPCB exists in every electronic device. A fully functional PCB is mainly used to create connections between components, such as resistors, capacitors, inductors, diodes, transistors, integrated chips, etc. It is the carrier of the entire logic circuit. Sound PCB design can save production costs, and achieve good circuit performance and heat dissipation effect. PCB designs vary in complexity according to product needs. This article mainly talks about wiring, one of the basics of PCB design.PCB Design: From Idea to Schematic to PCBCatalogIntroductionⅠ PCB Basics: Wiring RulesⅡ Three PCB Wiring MethodsⅢ PCB Design: Wire InspectionⅣ Complete PCB Design Projects Inspection4.1 General PCB Design Inspection Projects4.2 PCB Electrical Characteristics Checking Projects4.3 PCB Physical Characteristics Checking Projects4.4 PCB Mechanical Design Factors4.5 PCB Installation Requirements4.6 PCB Pull-out Requirements4.7 PCB Mechanical Considerations4.8 PCB Electrical Considerations4.9 Electronics Inspection Before Into A PCBⅤ ConclusionⅠ PCB Basics: Wiring Rules1. The area within 1mm from the edge of the PCB board and within 1mm around the mounting hole will not take wiring.2. The power line width should not be less than 18mil; the signal line width should not be less than 12mil; the cpu input and output lines should not be less than 10mil (or 8mil); the line spacing should not be less than 10mil.3. It is necessary noted that the power line and the ground line should be as radial as possible, and the signal line must not be looped.4. Ground circuit rulesThe loop area formed by the signal line should be as small as possible. The smaller the loop area, the less external radiation and the less interference from the outside. An example is shown in the figure below:5. Crosstalk controlHere crosstalk refers to the mutual interference caused by long parallel wiring between different networks on the PCB, which caused by the distributed capacitance and inductance between the parallel lines. The main measures to overcome it are:a. Increase the spacing of parallel wiring and follow the 3W rule. To ensure that the distance between the lines is large enough, when the distance between the line and the center of the line is not less than 3 times the line width (as shown in the figure below). If the line center distance is not less than 3 times the line width, 70% of the line electric fields will not interfere with each other, which is called 3W rule.b. Insert a grounded isolation wire between the parallel wires. Reduce the distance between the wiring layer and the ground plane.6. The direction control rules of routing:The routing directions of adjacent layers are orthogonal. Different signal lines in the same direction on adjacent layers should be avoided to reduce unnecessary interlayer crosstalk. When the signal rate is high, use a ground plane to isolate each wiring layer, in other words, isolate each signal line with ground line. The neighbouring wires used in the input and output end of the circuit shouldn’t be parallel to prevent the feedback, and it is best to add a ground wire between these wires.7. Open loop inspection rules for wiring:Generally, it is not allowed to have a floating wiring at one end, because of the "antenna effect" and unnecessary interference radiation and reception, which may bring unpredictable results.8. Impedance matching inspection rulesThe wiring width of the same network should be kept the same. Line width variations will bring uneven line characteristic impedance, and reflection will occur when the transmission speed is high. This situation should be avoided in the design. Under certain conditions, such as the lead wires of the connector and the similar structure of the lead wires of the BGA package, the change of the line width may not be avoided, so that the length of the middle inconsistent part should be minimized.9. Wiring closed loop inspection rules:Prevent signal lines from forming self-loops between different layers. Such problems are prone to occur in multilayer board design, and it will cause radiation interference. As shown below:10. The branch length control rule of wiring:Try to control the length of branches, and the general requirement is Tdelay≤Trise/20.11. Resonance rules of wiring:For high-frequency signal design, the wiring length must not be an integer multiple of its wavelength to avoid resonance.12. Line length control rules:In fact, it refers to the short-circuit rule. When designing, you should keep the wiring length as short as possible to reduce interference problems caused by unnecessary lines. Especially for some important signal lines, such as clock lines, be sure to place oscillators close to the device. In the case of driving multiple devices, the network topology should be decided according to the specific situation.13. Parallel input and output wires on the PCB board should be avoided as far as possible to avoid parallel. It is best to place a ground wire between the two wires to avoid circuit feedback coupling.14. Digital ground and analog ground should be separated. For low-frequency circuits, single-point parallel grounding should be used. High-frequency circuits should be grounded in series with multiple points. For digital circuits, the ground wire should be closed into a loop to improve anti-noise capability.15. The wiring and via distribution of the whole circuit board should be uniformity. When the outer signal of the circuit board has a large blank area, auxiliary lines should be added to make the lines distribution on the board basically balanced.16. The low-frequency circuit can be grounded at a single point in parallel, and the actual wiring can be connected in series and then grounded in parallel. The high-frequency circuit can be grounded in series with multiple points. The ground wire should be short and thick. For high-frequency components, a large area ground foil can be used. The ground wire should be as thick as possible. If the ground wire is a very thin, the ground potential will change with the current, which reduces the noise resistance.17. Multilayer boards should be as symmetrical as possible when designing the laminated structure, as well as the wiring density and copper layout of each layer to reduce warpage and reduce EMI during soldering.18. The signal line should not cross the power supply and ground. The signal reference plane should be as complete as possible.19. Impedance controlThe signal lines that need impedance control must be wired in strict accordance with the calculated data, in addition, it is necessary to tell manufacturers it. For signal lines that do not require it, the impedance should be calculated to prevent unnecessary interference.20. Grid copper should be used less in low frequency circuits. Although it can effectively reduce the problem of large area copper skin blistering. When using grid copper, you need to consider the electrical length of the grid line and the working frequency of the circuit board. If using grid copper, the power supply should also be coated with solid copper as much as possible.21. A group of buses with the same attribute should be wired side by side as much as possible, and the length should be as equal as possible. Ⅱ Three PCB Wiring MethodsThe wires should take the shortest route between components according to the specified wiring rules. Limit the coupling between parallel wires as much as possible. Good PCB design requires the minimum number of wiring layers, and also requires fair use of the widest wire and the largest pad size corresponding to packaging density. For example, rounded corners and smooth inner corners design may avoid some electrical and mechanical problems, therefore, sharp corners and sharp corners in the wire should be avoided. Here introduces three main PCB routing methods; right-angle wiring, differential wiring, and serpentine wiring to illustrate PCB layout:A. The influence of right-angle wiring on the signal is mainly reflected in three aspects:1. The corner can be equivalent to the capacitive load on the transmission line to slow down the rise time.2. Discontinuous impedance will cause signal reflection.3. The EMI generated by the right-angle tip reaches the RF field above 10GHz. Such a right-angle is likely to develop into the source of high-speed problems. B. To figure out what is differential wiring, you must first understand what is differential signal. In a word, the driving end sends two equal and inverted signals, and the receiving end judges the logic state "0" or "1" by comparing the difference between the two voltages. The pair of traces carrying differential signals is called differential traces. Compared with ordinary single-ended signal traces, differential signals have the most obvious advantages in the following three aspects:1. Have Strong anti-interference ability. Because the coupling between the two differential traces occurs, when there is noise interference from the outside, they are almost coupled to the two lines at the same time. However, the receiving end only cares about the difference between the two signals. Therefore, the external common mode noise can be completely canceled.2. It can effectively suppress EMI. Due to the opposite polarity of the two signals, the electromagnetic fields radiated by them can cancel each other out. What’s more, the tighter the coupling, the less the electromagnetic energy leaked to the outside world.3. The timing positioning is accurate. Because the switch change of the differential signal is located at the intersection of the two signals. Unlike ordinary single-ended signals, which rely on the high and low threshold voltages to judge. Timing positioning is less affected by the process and temperature, and also more suitable for circuits with low amplitude signals. The current popular LVDS (low voltage differential signaling) refers to this small amplitude differential signaling technology. C. Serpentine line is a type of wiring method often used in PCB layout. Its main purpose is to adjust the delay to meet the system timing design requirements. The two most critical parameters are the parallel coupling length (Lp) and the coupling distance (S). Obviously, when a signal is transmitted on a serpentine trace, the parallel line segments will be coupled in a differential mode. The smaller the S, the greater the Lp, the greater the coupling. It may cause the transmission delay to be reduced, also the signal quality is greatly reduced due to crosstalk. The mechanism can refer to the analysis of common mode and differential mode crosstalk. The following are some suggestions when dealing with serpentine wring:1. Try to increase the distance (S) of parallel lines, at least more than 3H(H refers to the distance from the signal trace to the reference plane). As long as S is large enough, the mutual coupling effect can be almost completely avoided.2. Reduce the coupling length Lp. When the double Lp delay approaches or exceeds the signal rise time, the crosstalk generated will reach saturation.3. The signal transmission delay caused by the strip-line or embedded micro-strip line is less than that of the micro-strip. Theoretically, the strip-line will not affect the transmission rate due to differential mode crosstalk.4. For signal lines with high-speed and strict timing requirements, try not to take serpentine lines, especially in a small area.5. You can often use s-shaped routing at any angle, which can effectively reduce the mutual coupling.6. In high speed, the serpentine line has no ability so-called filtering or anti-interference, and can only reduce the signal quality, so it is better to use for timing matching.7. Sometimes you can consider the spiral routing method for winding. Simulation shows that its effect is better than normal serpentine routing.Ⅲ PCB Design: Wire Inspection1.Wire SpacingThe minimum spacing of wires must be determined to eliminate voltage breakdown or arcing between adjacent wires. The spacing is variable, it mainly depends on the following factors:1) Peak voltage between adjacent wires2) Atmospheric pressure (maximum working altitude)3) Coating layer4) Capacitive coupling parametersComponents with critical impedance or high-frequency components should be placed very close to reduce the critical stage delay. There is something need to pay attention to. Transformers and inductive components should be isolated to prevent coupling. Inductive signal wires should be laid orthogonally at right angles. Components that generate any electrical noise due to magnetic field movement should be isolated or rigidly installed to prevent excessive vibration.2. Whether the wire is short and straight without sacrificing function.3. Whether the restrictions on the wire width are complied with.4. There must be a minimum distance between wires, wires and mounting holes, wires and pads.5. Whether to avoid all the wires (including component leads) closer to parallel wiring.6. Whether sharp corners (≤90℃) are avoided in the wire pattern. Ⅳ Complete PCB Design Projects Inspection4.1 General PCB Design Inspection Projects1) Has the circuit been analyzed? Is the circuit divided into basic units to smooth the signal?2) Does the circuit allow short or isolated key leads?3) Where must be shielded, are they effectively shielded?4) Have you made full use of the basic grid graphics?5) Is the best size of the printed circuit board?6) Do you use the available wire width and spacing as much as possible?7) Has the preferred pad size and hole size been used?8) Are the base plate and the sketch consistent?9) Is less cross-wiring used? Do cross wires pass through components and accessories?10) Are the letters visible after assembly? Are their size and model correct?11) In order to prevent blistering, is there any window on the large area of copper foil?12) Are there tool positioning holes?4.2 PCB Electrical Characteristics Checking Projects1) Have you analyzed the influence of wire resistance, inductance, and capacitance, as well as the critical voltage drop on the ground?2) Does the wire spacing and shape meet the insulation requirements?3) Has the insulation resistance value been controlled and specified in key areas?4) Is the polarity fully recognized?5) According to geometric view, has the effect of wire spacing on leakage resistance and voltage been measured?6) Has the medium for changing the surface coating been identified?4.3 PCB Physical Characteristics Checking Projects1) Are all pads and their positions suitable for final assembly?2) Can the assembled PCB meet the shock and vibration conditions?3) What is the required spacing of standard components?4) Are the components that are not firmly installed or the heavier parts fixed?5) Is the heating element heat dissipation and cooling normally? Or is it isolated from the printed circuit board and other heat-sensitive elements?6) Are the voltage divider and other multi-lead components placed correctly?7) Is the arrangement and orientation of components easy to check?8) Has it eliminated all possible interference on the printed circuit board?9) Is the size of the positioning hole correct?10) Are the tolerances complete and reasonable?11) Have you controlled and signed the physical properties of all coatings?12) Is the ratio of via hole and lead diameter within an acceptable range?4.4 PCB Mechanical Design FactorsThe printed circuit board adopts mechanical methods to support the components, however, it cannot be used as an unique structural part of the entire device. On the edge of the printing plate, at least every 5 inches for a certain support. The factors that must be considered when selecting and designing printed circuit boards are as follows:1) The size and shape of the printed circuit board.2) The type of mechanical accessories and plug (seat) required.3) The environmental adaptability of circuits.4) According to some factors, such as heat and dust, install the printed circuit board vertically or horizontally.5) Some environmental factors that require special attention, such as heat dissipation, ventilation, shock, vibration, and humidity, dust, and radiation, etc.6) Physical support7) Install and fix.8) Disassemble4.5 PCB Installation RequirementsAccording to practical experience, the distance between the supporting points of a printed circuit board with a thickness of 0.031-0.062 inches should be at least 4 inches. For a printed circuit board with a thickness greater than 0.093 inches, the distance between the supporting points should be at least 5 inches. Taking this measure can improve the rigidity of the printed circuit board and avoid possible resonance. The following factors should be considered before deciding which mounting technology they use.1) PCB structure.2) Input and output terminals.3) Available equipment space.4) Convenience of loading and unloading.5) Type of attachments.6) Required heat dissipation.7) Required shieldability.8) The type of circuit and its relationship with other circuits.4.6 PCB Pull-out Requirements1) The influence of plugging tools on the installation distance between two printed circuit boards.2) When the plug-in tool used in the equipment, its size should be considered.3) A plug-in device is required, which is usually fixed to the printed circuit board assembly with rivets.4) As for the mounting frame of the printed circuit board, special design such as load bearing flange is required.5) The adaptability of the plug-in tool used and the size, shape and thickness of the printed circuit board.4.7 PCB Mechanical ConsiderationsThe characteristics of the board substrate that have an important influence on the printed circuit assembly are: water absorption, thermal expansion coefficient, heat resistance, flexural strength, impact strength, tensile strength, shear strength and hardness. All these characteristics affect the function and the production efficiency of the printed circuit board structure. For most applications, the dielectric substrate materials of the printed circuit board are as following:1) Phenolic impregnated paper2) Acrylic-polyester impregnated randomly arranged glass mat3) Epoxy impregnated paper4) Epoxy impregnated glass clothEach substrate can be flame retardant or combustible. The first 3 types mentioned above can be processed. The most common used material for printed circuit boards with metalized holes is epoxy-glass cloth. Its dimensional stability is suitable for high-density circuits and can minimize the occurrence of cracks in the metalized holes. One disadvantage of epoxy-glass cloth laminate is that it is difficult to punch in the usual thickness range of printed circuit boards. For this, all holes are usually drilled and copied and milled to form a print shape of the circuit board.4.8 PCB Electrical ConsiderationsIn DC or low-frequency AC applications, the most important electrical characteristics of insulating substrates are: insulation resistance, anti-isolation, printed wire resistance, and breakdown strength. In high frequency and microwave applications, include: dielectric constant, capacitance, and dissipation factors. In all applications, the current carrying capacity of printed wires is important.4.9 Electronics Inspection Before Into A PCB1) Check the rationality and correctness of the schematic diagram.2) Check the correctness of the component packaging of the schematic.3) The distance between strong and weak current lines, and the distance between isolation areas.4) Check the schematic diagram and PCB diagram to prevent the loss of the network table.5) Whether the package of the component matches the physical object.6) Whether the placement of the components is appropriate.7) Whether the components are easy to install and disassemble.8) Whether the temperature sensitive element is too close to the heating element.9) Whether the distance and direction of the mutual inductance components are appropriate.10) Whether the placement between the connectors is smooth.11) Easy to plug in and plug out12) Input and output13) Strong current and weak current14) digital and analog should be interlaced.15) Arrangement of elements on the upside and downside16) Check whether the directional component has been wrong flipped instead of rotated.17) Check whether the mounting holes of the component pins are suitable and whether it is easy to insert.18) Check whether the empty pin of each component is normal and whether it is a missing line.19) Check whether there are vias between the upper and lower wiring of the same net table. And the pads are connected through the holes, to prevent disconnection and ensure the integrity of the circuit.20) Silk screen printing should be clear, so that the operation of welding or maintenance can be easy.21) The arrangement of power and signal lines in the socket should ensure signal integrity and anti-interference.22) Pay attention to the proper ratio of pads and solder holes.23) Each plug should be placed on the edge of the PCB board as much as possible and easy to operate.24) Whether the size and distribution of the mounting holes on the PCB are appropriate to reduce the PCB bending stress.25) Pay attention to the height distribution of the components on the PCB to ensure easy assembly.Ⅴ ConclusionBased on the above mentioned rules, drawing the PCB schematics you need becomes easier. Decide what PCB you want to and install a PCB design software. PCB software is really helpful and powerful. Also a software can check your design to make sure the design does not contain errors such as traces that incorrectly touch, traces too skinny, or drill holes that are too small. For example, run the Electrical Rules Checker (ERC) to see if you’ve made any typical errors. There is less thing stopping you from making your first PCB, right? Frequently Asked Questions about PCB Design Diagram1. Which side of PCB is correct for soldering?The bottom side of the PCB is usually the side without components and the side that touches the solder wave during assembly. That is why sometimes it is also called SOLDER side. However more often, PCB are populated on both sides and the assembly process does not require wave soldering. 2. Which soldering method is suitable for soldering printed circuit board?Soldering Iron – Used to melt solder and connect component pins to board pads. A cheap soldering pencil may be sufficient, but a temperature-controlled solder station is best for high performance boards. Solder – An alloy of tin and lead with a low melting point. 3. What is PCB diagram?A PCB schematic is a simple two-dimensional circuit design showing the functionality and connectivity between different components. ... Once the blueprint has been completed, the PCB design comes next. The design is the layout, or physical representation of the PCB schematic and includes the copper track and hole layout. 4. Why we use PCB in soldering?PCB soldering is another term for the process of soldering electrical circuit boards. ... As the soldering iron melts this metal, it is then used a bit like glue to stick to pieces together. As the solder metal cools, it will re-harden into one large shape that connects the two parts. 5. How do you read a PCB board?Start with an easy analog circuit, such as a guitar distortion pedal, and work your way up to more complicated versions. Make a drawing of the top of the circuit board. Show the positions of the capacitors, integrated circuits, resistors, transistors and other components. Review it to make sure everything is included.

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.