Detailed analysis of the selection and calculation of power supply filter capacitors

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Detailed analysis of the selection and calculation of power supply filter capacitors [Copy link]

The impedance of an inductor is proportional to the frequency, and the impedance of a capacitor is inversely proportional to the frequency. Therefore, an inductor can block high frequencies, and a capacitor can block low frequencies. The proper combination of the two can filter various frequency signals. For example, in a rectifier circuit, connecting a capacitor to a load or connecting an inductor to a load in series can filter out AC ripple. Capacitor filtering is a voltage filter, which directly stores the pulsating voltage to smooth the output voltage. The output voltage is high and close to the peak value of the AC voltage. It is suitable for small currents. The smaller the current, the better the filtering effect.

Inductor filtering is a current filter, which relies on electromagnetic induction generated by the current to smooth the output current. The output voltage is low and lower than the effective value of the AC voltage. It is suitable for large currents. The larger the current, the better the filtering effect. Many characteristics of capacitors and inductors are exactly the opposite.

In general, the function of electrolytic capacitors is to filter out low-frequency signals in the current, but even for low-frequency signals, the frequency is divided into several orders of magnitude. Therefore, in order to be suitable for use at different frequencies, electrolytic capacitors are also divided into high-frequency capacitors and low-frequency capacitors (the high frequency here is relative).

Low-frequency filter capacitors are mainly used for mains filtering or filtering after transformer rectification, and their operating frequency is consistent with the mains, which is 50Hz; while high-frequency filter capacitors mainly work in filtering after switching power supply rectification, and their operating frequency is from several thousand Hz to tens of thousands Hz. When we use low-frequency filter capacitors in high-frequency circuits, due to the poor high-frequency characteristics of low-frequency filter capacitors, it has a large internal resistance and a high equivalent inductance during high-frequency charging and discharging. Therefore, during use, a large amount of heat will be generated due to the frequent polarization of the electrolyte. Higher temperatures will vaporize the electrolyte inside the capacitor, increasing the pressure inside the capacitor and eventually causing the capacitor to bulge and burst.

The size of the power filter capacitor. Usually, when designing, the front stage uses 4.7uF to filter low frequencies, and the second stage uses 0.1uF to filter high frequencies. The function of the 4.7uF capacitor is to reduce output pulsation and low-frequency interference, and the 0.1uF capacitor should be to reduce the high-frequency interference caused by the instantaneous change of the load current. Generally, the larger the former, the better, and the difference between the two capacitance values is about 100 times. For power filtering and switching power supply, it depends on how large your ESR (equivalent series resistance of the capacitor) is, and the choice of high-frequency capacitor is best at its self-resonant frequency. Large capacitors prevent surges, and the mechanism is just like a large reservoir with stronger flood control capabilities; small capacitors filter high-frequency interference. Any device can be equivalent to a series-parallel circuit of resistors, inductors, and capacitors, and there is self-resonance. Only at this self-resonant frequency is the equivalent resistance the smallest, so the filtering is the best!

The equivalent model of a capacitor is a series connection of an inductor L, a resistor R and a capacitor C.

The inductor L is where the capacitor leads to, the resistor R represents the active power loss of the capacitor, and the capacitor C.

Therefore, it can be equivalent to a series LC circuit to find its resonant frequency. The condition for series resonance is WL=1/WC, W=2*PI*f, thus obtaining this formula f = 1/(2pi* LC). At the center frequency of the series LC circuit, the reactance is the smallest and it behaves as a pure resistor, so it has a filtering effect at the center frequency. The size of the lead inductance varies depending on its thickness, length and width. The inductance of the grounding capacitor is generally around 10nH for 1MM, depending on the frequency that needs to be grounded.

Parameters that need to be considered when using capacitor filtering design:

ESR

ESL

Withstand voltage

Resonant frequency

[p=30, null, So how to select the power supply filter capacitor?

How to select power supply filter capacitors and master their essence and methods is actually not difficult

1) In theory, the impedance of an ideal capacitor decreases with increasing frequency (1/jwc), but due to the inductance effect of the pins at both ends of the capacitor, the capacitor should be regarded as an LC series resonant circuit at this time. The self-resonant frequency is the FSR parameter of the device, which means that when the frequency is greater than the FSR value, the capacitor becomes an inductor. If the capacitor is filtered to ground, when the frequency exceeds the FSR, the suppression of interference is greatly reduced, so a smaller capacitor is needed in parallel to the ground. The reason is that a small capacitor has a large SFR value and provides a ground path for high-frequency signals.

So in the power supply filter circuit, we often understand it this way: large capacitors filter low frequencies, small capacitors filter high frequencies. The fundamental reason is that the SFR (self-resonant frequency) values are different. Think about why? If you think from this perspective, you can understand why the capacitor ground pin in the power supply filter should be as close to the ground as possible.

2) Then in the actual design, we often have questions, how do I know the SFR of the capacitor? Even if I know the SFR value,

How do I choose capacitors with different SFR values? Should I choose one capacitor or two capacitors?

34)] The SFR value of a capacitor is related to its capacitance value and the pin inductance of the capacitor. Therefore, the SFR values of 0402, 0603, or plug-in capacitors with the same capacitance value will not be the same. Of course, there are two ways to obtain the SFR value: 1) Device Data Sheet, such as the SFR value of a 22pf0402 capacitor is around 2G, 2) Directly measure its self-resonant frequency through a network analyzer. Think about how to measure S21?

After knowing the SFR value of the capacitor, use software simulation, such as RFsim99, to select one or two circuits to see if the operating frequency band of the circuit you are powering has enough noise suppression ratio. After the simulation, it is the actual circuit test. For example, when debugging the receiving sensitivity of a mobile phone, the power supply filtering of the LNA is the key. Good power supply filtering can often improve it by several dB. The essence of capacitors is to pass AC and block DC. In theory, the larger the capacitor used for power supply filtering, the better. However, due to the lead and PCB wiring reasons, the capacitor is actually a parallel circuit of inductance and capacitance (there is also the resistance of the capacitor itself, which is sometimes not negligible). This introduces the concept of resonant frequency: ω=1/(LC)1/2

Below the resonant frequency, the capacitor is capacitive, and above the resonant frequency, the capacitor is inductive. Therefore, generally large capacitors filter low-frequency waves, and small capacitors filter high-frequency waves. This can also explain why the capacitor filtering frequency of STM package with the same capacitance is higher than that of DIP package. As for how large the capacitor should be, this is a reference capacitor resonant frequency. Capacitance Value DIP (MHz) STM (MHz) 1.0μF 2.5 5 left] 0.1μF 8 16

0.01μF 25 50

1000pF 80 160

100 pF 250 500

10 pF 800 1.6(GHz)

But it's just a reference. Old engineers say it depends mainly on experience.

A more reliable approach is to connect two capacitors, one large and one small, in parallel.

Generally, the difference between them is required to be more than two orders of magnitude in order to obtain a larger filtering frequency band.

Article source: http://blog.sina.com.cn/s/blog_545edca401000ax6.html

I read this article and would like to make a rough summary:

1. Capacitor-to-ground filtering requires a smaller capacitor in parallel to the ground, which provides a ground path for high-frequency signals.

2. The capacitor pin in the power supply filter should be as close to the ground as possible.

3. In theory, the larger the capacitor used for power supply filtering, the better. Generally, large capacitors filter low-frequency waves, and small capacitors filter high-frequency waves.

4. The reliable method is to connect two capacitors, one large and one small, in parallel. Generally, the difference is required to be more than two orders of magnitude to obtain a larger filtering frequency band.

Principles for selecting filter capacitors

The current after passing through the rectifier bridge is pulsating DC with a large fluctuation range. Generally, two capacitors of different sizes are used later; the large capacitor is used to stabilize the output. As we all know, the voltage across the capacitor cannot change suddenly, so the output can be smoothed; the small capacitor is used to filter out high-frequency interference to make the output voltage pure; the smaller the capacitance, the higher the resonant frequency, and the higher the interference frequency that can be filtered out;Capacitance selection: (1) Large capacitor: the heavier the load, the stronger the ability to absorb current, the larger the capacity of this large capacitor should be. (2) Small capacitor: based on experience, 104 is usually enough. 2. Other people's experience (from the Internet) 1. Capacitor-to-ground filtering requires a smaller capacitor to be connected in parallel to the ground, providing a path to the ground for high-frequency signals.

2. The capacitor-to-ground pin in power supply filtering should be as close to the ground as possible.

3. In theory, the larger the capacitor used for power supply filtering, the better. Generally, large capacitors filter low-frequency waves, and small capacitors filter high-frequency waves.

4. A reliable approach is to connect two capacitors, one large and one small, in parallel. Generally, the difference is required to be more than two orders of magnitude to obtain a larger filtering frequency band.

Specific example: After AC220-9V passes through full-bridge rectification, how big is the filter capacitor that needs to be added? How big is the capacitor that needs to be added after passing through 78LM05?

The former capacitor's withstand voltage should be greater than 15V, and the capacitor's capacity should be greater than 2000 microfarads. The latter capacitor's withstand voltage should be greater than 9V, and the capacity should be greater than 220 microfarads. 2. There is a single-phase bridge rectifier circuit with a capacitor filter. The output voltage is 24V and the current is 500mA. The requirements are: (1) Select the rectifier diode; (2) Select the filter capacitor; (3) In addition: Does capacitor filtering reduce or increase the voltage?

(1) Because the bridge type is full-wave, the current of each diode only needs to reach half of the load current, so the maximum current of the diode must be greater than 250mA; the output voltage of the capacitor filter bridge rectifier is equal to 1.2 times the effective value of the input AC voltage, so the effective value of the AC voltage input to your circuit should be 20V, and the maximum reverse voltage that the diode can withstand is twice the square root of this voltage, so the diode withstand voltage should be greater than 28.2V.

(2) Select the filter capacitor: 1. The voltage is greater than 28.2V; 2. Find the value of C: The formula RC ≥ (3--5) × 0.1 seconds, in this question R = 24V/0.5A = 48 ohms

So it can be concluded that C ≥ (0.00625--0.0104) F, that is, the value of C should be greater than 6250μF.

(3) Capacitor filtering is to increase the voltage.

Principles for selecting filter capacitors

In power supply design, the principle for selecting filter capacitors is: C≥2.5T/R

Wherein: C is the filter capacitor, the unit is UF;

T is the frequency, the unit is Hz

R is the load resistance, in Ω

Of course, this is just a general selection principle. In actual applications, if conditions (space and cost) permit, C≥5T/R is selected.

3. Selection of filter capacitor size

PCB plate capacitor selection

When there are contactors, relays, buttons and other components in the printed circuit board. When operating them, large spark discharges will be generated, and an RC absorption circuit must be used to absorb the discharge current. Generally, R is 1~2kΩ and C is 2.2~4.7μF.

The general capacitor of about 10PF is used to filter out high-frequency interference signals, 0.About 1UF is used to filter out low-frequency ripple interference and can also play a role in voltage stabilization. The specific value of the filter capacitor depends on the main operating frequency on your PCB and the harmonic frequency that may affect the system. You can check the capacitor information of the relevant manufacturer or refer to the database software provided by the manufacturer to select according to specific needs. As for the number, it is not certain. It depends on your specific needs. It is also good to add one or two more. If it is not used for the time being, you can leave it unattached and choose the capacitance value according to the actual debugging situation. If the main operating frequency on your PCB is relatively low, you can add two capacitors, one to filter out ripples and the other to filter out high-frequency signals. If there will be a relatively large instantaneous current, it is recommended to add a relatively large tantalum capacitor.

In fact, filtering should also include two aspects, which are what you call large capacitance and small capacitance, that is, decoupling and bypassing. I won't talk about the principle. For practical purposes, 0.1uF is enough for decoupling of general digital circuits, which is used below 10M; 1 to 10uF is used for more than 20M to remove high-frequency noise, roughly according to C=1/f. The bypass is generally smaller, generally 0.1 or 0.01uF according to the resonant frequency.

When it comes to capacitors, the various names will make people dizzy, such as bypass capacitors, decoupling capacitors, filter capacitors, etc. In fact, no matter how it is called, the principle is the same, that is, it uses the characteristic of low impedance to AC signals. This can be seen from the equivalent impedance formula of capacitors: Xcap=1/2лfC. The higher the operating frequency, the larger the capacitance value, and the smaller the impedance of the capacitor.

In a circuit, if the main function of a capacitor is to provide a low-impedance path for an AC signal, it is called a bypass capacitor; if it is mainly used to increase the AC coupling between the power supply and the ground and reduce the impact of the AC signal on the power supply, it can be called a decoupling capacitor; if it is used in a filter circuit, it can be called a filter capacitor; in addition, for DC voltage, capacitors can also be used as circuit energy storage, using charge and discharge to play the role of a battery. In actual situations, the role of capacitors is often multifaceted, and we don't have to spend too much time considering how to define it. In this article, we uniformly call these capacitors used in high-speed PCB design bypass capacitors.

The essence of a capacitor is to pass AC and block DC. In theory, the larger the capacitor used for power filtering, the better.

However, due to the leads and PCB wiring reasons, the capacitor is actually a parallel circuit of inductance and capacitance (there is also the resistance of the capacitor itself, which is sometimes not negligible)

This introduces the concept of resonant frequency: ω=1/(LC)1/2

Below the resonant frequency, the capacitor is capacitive, and above the resonant frequency, the capacitor is inductive.

Therefore, generally large capacitors filter low-frequency waves, and small capacitors filter high-frequency waves. This can also explain why the capacitor filtering frequency of STM package with the same capacitance is higher than that of DIP package. As for how large a capacitor should be used, this is a reference.

Capacitor Resonance Frequency

Capacitor Value DIP (MHz) STM (MHz)

1.0μF 2.5 5

0.1μF 8 16

0.01μF 25 50

1000pF 80 160

100 pF 250 500

10 pF 800 1.6(GHz)

But it's just a reference. In the words of an old engineer, it mainly depends on experience. A more reliable approach is to connect two capacitors, one large and one small, in parallel. Generally, they should differ by more than two orders of magnitude to obtain a larger filtering frequency band. Generally speaking, large capacitors filter out low-frequency waves, and small capacitors filter out high-frequency waves. The capacitance value is inversely proportional to the square of the frequency you want to filter out. The specific capacitor selection can be calculated using the formula C=4Pi*Pi /(R * f * f )

34)] How to select power supply filter capacitors and master their essence and methods is actually not difficult.

1) In theory, the impedance of an ideal capacitor decreases with increasing frequency (1/jwc), but due to the inductance effect of the pins at both ends of the capacitor, the capacitor should be regarded as an LC series resonant circuit at this time. The self-resonant frequency is the FSR parameter of the device, which means that when the frequency is greater than the FSR value, the capacitor becomes an inductor. If the capacitor is filtered to the ground, when the frequency exceeds the FSR, the suppression of interference will be greatly reduced, so a smaller capacitor is needed in parallel to the ground. Can you think about why?

The reason is that small capacitors have large SFR values, which provide a path to the ground for high-frequency signals. Therefore, in power supply filter circuits, we often understand that large capacitors consider low frequencies, and small capacitors consider high frequencies. The fundamental reason is that the SFR (self-resonant frequency) values are different. Of course, you can also think about why? If you think from this perspective, you can also understand why the capacitor ground pin in power supply filtering should be as close to the ground as possible.

2) Then in actual design, we often have questions, how do I know the SFR of the capacitor? Even if I know the SFR value, how do I choose capacitor values with different SFR values? Should I choose one capacitor or two capacitors? The SFR value of a capacitor is related to the capacitance value and the pin inductance of the capacitor. Therefore, the SFR values of 0402, 0603, or through-hole capacitors with the same capacitance value will be different. Of course, there are two ways to obtain the SFR value: 1) device data sheet, such as the SFR value of a 22pf0402 capacitor is around 2G, 2) directly measure its self-resonant frequency through a network analyzer. Think about how to measure it? S21?

After knowing the SFR value of the capacitor, use software simulation, such as RFsim99, and choose one or two circuits to see if the working frequency band of the circuit you are powering has enough noise suppression ratio. After the simulation, it is the actual circuit test. For example, when debugging the receiving sensitivity of a mobile phone, the power supply filtering of the LNA is the key. Good power supply filtering can often improve it by several dB.

Selection and calculation of filter capacitors

From the Internet, there are two commonly used calculation methods in engineering: (for reference, it seems to make some sense)

[p=30, null, 1. If the requirement is not very precise, you can calculate it based on the load, 2uf per mA. 2. It can be estimated based on the RC time constant which is approximately equal to 3~5 times the half cycle of the power supply. Here is an example: Load condition: DC 1A, 12V. Its equivalent load resistance is 12 ohms. Bridge rectifier: RC = 3 (T/2) C = 3 (T/2) / R = 3 x (0.02 / 2 ) / 12 = 2500 (μF) In engineering, 2200 μF can be used because there is no specification of 2500 μF. If you want a smaller ripple, multiply it by 5. Here, T is the period of the power supply. At 50HZ, T = 0.02 seconds.

The result of full-wave rectification is the same, but the time constant is doubled for half-wave rectification.

According to the full-wave rectifier waveform, it can be seen that the smoothness of the output voltage is related to the capacitor charging and discharging time and the frequency of the signal. When the frequency of the signal increases, the fluctuation of the output voltage becomes larger. The size of the filter capacitor can be changed to change the charging and discharging time to reduce the fluctuation. This also reflects the calculation relationship of the above filter capacitor. In theory, the larger the filter capacitor, the better the filtering effect and the smoother the output voltage. However, at the moment the circuit is connected, the impact current factor generated in the circuit cannot be ignored. This is because almost all electronic components have a maximum current value that can pass through them. Therefore, when selecting electronic components, the maximum value of the instantaneous current flowing through the relevant components caused by the impact current must be considered. The larger the impact current, the higher the requirements for electronic components, and the cost of the circuit will increase.

34)] 2) In actual design, we often have questions, how do I know the SFR of a capacitor? Even if I know the SFR value, how do I select capacitors with different SFR values? Should I select one capacitor or two capacitors? The SFR value of a capacitor is related to the capacitance value and the pin inductance of the capacitor, so the SFR values of 0402, 0603, or plug-in capacitors with the same capacitance value will not be the same. Of course, there are two ways to obtain the SFR value: 1) Device Data Sheet, such as the SFR value of a 22pf0402 capacitor is around 2G, 2) Directly measure its self-resonant frequency through a network analyzer. Think about how to measure it? S21?

After knowing the SFR value of the capacitor, use software simulation, such as RFsim99, and choose one or two circuits to see if the operating frequency band of the circuit you are powering has enough noise suppression ratio. After the simulation, it is the actual circuit test. For example, when debugging the receiving sensitivity of a mobile phone, the power supply filtering of the LNA is the key. Good power supply filtering can often improve it by several dB.

Selection and calculation of filter capacitor

From the Internet, there are two commonly used calculation methods in engineering: (for reference, it seems to make some sense)

First, if the requirements are not very precise, you can calculate based on the load, 2uf per mA. Second, estimate based on the RC time constant, which is approximately equal to 3 to 5 times the power supply half cycle. Here is an example: Load condition: DC 1A, 12V. Its equivalent load resistance is 12 ohms. Bridge rectifier: RC = 3 (T/2) C = 3 (T/2) / R = 3 x (0.02 / 2 ) / 12 = 2500 (μF)

In engineering, 2200 μF can be used because there is no specification of 2500 μF. If you want a smaller ripple, multiply it by 5. Here, T is the period of the power supply. At 50HZ, T = 0.02 seconds.

The result of full-wave rectification is the same, but the time constant is doubled for half-wave rectification.

According to the full-wave rectifier waveform, it can be seen that the smoothness of the output voltage is related to the capacitor charging and discharging time and the frequency of the signal. When the frequency of the signal increases, the fluctuation of the output voltage becomes larger. The size of the filter capacitor can be changed to change the charging and discharging time to reduce the fluctuation. This also reflects the calculation relationship of the above filter capacitor. In theory, the larger the filter capacitor, the better the filtering effect and the smoother the output voltage. However, at the moment the circuit is connected, the impact current factor generated in the circuit cannot be ignored. This is because almost all electronic components have their maximum current value that can pass through. Therefore, when selecting electronic components, the maximum value of the instantaneous current flowing through the relevant components caused by the impact current must be considered. The larger the impact current, the higher the requirements for electronic components, and the cost of the circuit will increase.

34)] 2) In actual design, we often have questions, how do I know the SFR of a capacitor? Even if I know the SFR value, how do I select capacitors with different SFR values? Should I select one capacitor or two capacitors? The SFR value of a capacitor is related to the capacitance value and the pin inductance of the capacitor, so the SFR values of 0402, 0603, or plug-in capacitors with the same capacitance value will not be the same. Of course, there are two ways to obtain the SFR value: 1) Device Data Sheet, such as the SFR value of a 22pf0402 capacitor is around 2G, 2) Directly measure its self-resonant frequency through a network analyzer. Think about how to measure it? S21?

After knowing the SFR value of the capacitor, use software simulation, such as RFsim99, and choose one or two circuits to see if the operating frequency band of the circuit you are powering has enough noise suppression ratio. After the simulation, it is the actual circuit test. For example, when debugging the receiving sensitivity of a mobile phone, the power supply filtering of the LNA is the key. Good power supply filtering can often improve it by several dB.

Selection and calculation of filter capacitor

From the Internet, there are two commonly used calculation methods in engineering: (for reference, it seems to make some sense)

First, if the requirements are not very precise, you can calculate based on the load, 2uf per mA. Second, estimate based on the RC time constant, which is approximately equal to 3 to 5 times the power supply half cycle. Here is an example: Load condition: DC 1A, 12V. Its equivalent load resistance is 12 ohms. Bridge rectifier: RC = 3 (T/2) C = 3 (T/2) / R = 3 x (0.02 / 2 ) / 12 = 2500 (μF)

In engineering, 2200 μF can be used because there is no specification of 2500 μF. If you want a smaller ripple, multiply it by 5. Here, T is the period of the power supply. At 50HZ, T = 0.02 seconds.

The result of full-wave rectification is the same, but the time constant is doubled for half-wave rectification.

According to the full-wave rectifier waveform, it can be seen that the smoothness of the output voltage is related to the capacitor charging and discharging time and the frequency of the signal. When the frequency of the signal increases, the fluctuation of the output voltage becomes larger. The size of the filter capacitor can be changed to change the charging and discharging time to reduce the fluctuation. This also reflects the calculation relationship of the above filter capacitor. In theory, the larger the filter capacitor, the better the filtering effect and the smoother the output voltage. However, at the moment the circuit is connected, the impact current factor generated in the circuit cannot be ignored. This is because almost all electronic components have their maximum current value that can pass through. Therefore, when selecting electronic components, the maximum value of the instantaneous current flowing through the relevant components caused by the impact current must be considered. The larger the impact current, the higher the requirements for electronic components, and the cost of the circuit will increase.

34)] In the project, 2200 μF can be used because there is no specification of 2500 μF. If you want a smaller ripple, take 5 times. Here, T is the period of the power supply. At 50HZ, T = 0.02 seconds.

The result of full-wave rectification is the same, but in half-wave rectification, the time constant is doubled.

According to the full-wave rectifier waveform, it can be seen that the smoothness of the output voltage is related to the capacitor charging and discharging time and the frequency of the signal. When the frequency of the signal increases, the fluctuation of the output voltage becomes larger. The size of the filter capacitor can be changed to change the charging and discharging time to reduce the fluctuation. This also reflects the calculation relationship of the above filter capacitor. In theory, the larger the filter capacitor, the better the filtering effect and the smoother the output voltage. However, at the moment the circuit is connected, the impact current factor generated in the circuit cannot be ignored. This is because almost all electronic components have their maximum current value that can pass through. Therefore, when selecting electronic components, the maximum value of the instantaneous current flowing through the relevant components caused by the impact current must be considered. The larger the impact current, the higher the requirements for electronic components, and the cost of the circuit will increase.

34)] In the project, 2200 μF can be used because there is no specification of 2500 μF. If you want a smaller ripple, take 5 times. Here, T is the period of the power supply. At 50HZ, T = 0.02 seconds.

The result of full-wave rectification is the same, but in half-wave rectification, the time constant is doubled.

According to the full-wave rectifier waveform, it can be seen that the smoothness of the output voltage is related to the capacitor charging and discharging time and the frequency of the signal. When the frequency of the signal increases, the fluctuation of the output voltage becomes larger. The size of the filter capacitor can be changed to change the charging and discharging time to reduce the fluctuation. This also reflects the calculation relationship of the above filter capacitor. In theory, the larger the filter capacitor, the better the filtering effect and the smoother the output voltage. However, at the moment the circuit is connected, the impact current factor generated in the circuit cannot be ignored. This is because almost all electronic components have their maximum current value that can pass through. Therefore, when selecting electronic components, the maximum value of the instantaneous current flowing through the relevant components caused by the impact current must be considered. The larger the impact current, the higher the requirements for electronic components, and the cost of the circuit will increase.