What is a filter capacitor and the calculation formula and selection of filter capacitor size

一、 What is a filter capacitor

An energy storage device installed at both ends of the rectifier circuit to reduce the ripple coefficient of the ac pulsation and improve the smooth dc output. This device is usually called the filter capacitor. Because the filter circuit requires the energy storage capacitor to have a large capacitance. Therefore, most filter circuits use electrolytic capacitors. Electrolytic capacitors get their name from the fact that they use an electrolyte as the electrode (negative pole).One end of the electrolytic capacitor is the positive pole and the other end is the negative pole, which cannot be reversed. The positive terminal is connected to the positive terminal of the rectified output circuit, and the negative terminal is connected to the negative terminal of the circuit. In all circuits that need to convert alternating current to direct current, setting filter capacitors will make the performance of electronic circuits more stable, and at the same time reduce the interference of alternating pulsation ripples on electronic circuits. The symbol of the filter capacitor in the circuit is generally represented by "C", and the capacitance should be determined according to the load resistance and the output current. When the filter capacitor reaches a certain capacity, increasing the capacitor capacity will have harmful effects on other indicators.

二、 The characteristics of the filter capacitor

1. Low temperature rise

The harmonic filter circuit is composed of capacitors in series with reactors, which form a very low impedance at a certain harmonic order to absorb a large amount of harmonic current. The quality of the capacitor will affect the stable absorption effect of the harmonic filter.The service life of the capacitor has a great relationship with the temperature. The higher the temperature, the lower the service time. The filter full-film capacitor has features such as low temperature rise, which can ensure its service life.

2. Low loss

Tangent value of dielectric loss angle（tgδ）：≤0.0003

3. Security

Conforming to GB and IEC standards, the internal single capacitors are equipped with protection devices; when the line or single capacitors are abnormal, the protection device will act immediately and automatically cut off the power supply to prevent secondary disasters. A discharge resistor is attached to ensure the safety of power consumption and maintenance. The shell is made of steel stamping, and the inside and outside are painted with high-temperature baking paint with good weather resistance and high safety.

4. Convenience

Small size and light weight, very convenient to carry and install

三、 The role of the filter capacitor

Filter capacitors are used in power rectification circuits to filter out ac components. Make the output dc smoother. Moreover, for precision circuits, the combination of parallel capacitor circuits [1] is often used at this time to improve the working efficiency of filter capacitors.

The low-frequency filter capacitor is mainly used for mains filtering or filtering after transformer rectification, and its working frequency is 50Hz consistent with the mains;The high-frequency filter capacitor mainly works in the filter after the switching power supply is rectified, and its working frequency is from several thousand Hz to tens of thousands of Hz. Filter capacitors play a very important role in switching power supplies. How to correctly select filter capacitors, especially the selection of output filter capacitors, is a matter of great concern to every engineer.

Ordinary electrolytic capacitors used in 50 Hz power frequency circuits have a pulsating voltage frequency of only 100 Hz, and the charging and discharging time is on the order of milliseconds.In order to obtain a smaller pulsation coefficient, the required capacitance is as high as hundreds of thousands of microfarads. Therefore, the goal of ordinary low-frequency aluminum electrolytic capacitors is to increase the capacitance.Capacitance, loss tangent and leakage current of capacitors are the main parameters to identify its advantages and disadvantages.The output filter electrolytic capacitor in the switching power supply has a sawtooth wave voltage frequency as high as tens of thousands of hertz, or even tens of megahertz. At this time, capacitance is not the main indicator, and the standard for measuring the quality of high-frequency aluminum electrolytic capacitors is the "impedance-frequency" characteristic. It is required to have a lower equivalent impedance within the operating frequency of the switching power supply, and at the same time have a good filtering effect on the high-frequency spike signals generated when the semiconductor device is working.

Ordinary low-frequency electrolytic capacitors begin to show inductance at about 10,000 Hz, which cannot meet the requirements of switching power supplies. The high-frequency aluminum electrolytic capacitor dedicated to the switching power supply has four terminals. The two ends of the positive aluminum sheet are respectively drawn out as the positive electrode of the capacitor, and the two ends of the negative aluminum sheet are also respectively drawn out as the negative electrode. The current flows in from one positive terminal of the four-terminal capacitor, passes through the capacitor, and then flows from the other positive terminal to the load; the current returning from the load also flows in from one negative terminal of the capacitor, and then flows from the other negative terminal to the negative terminal of the power supply.

四、 Selection principle of filter capacitor

In power supply design, the selection principle of filter capacitor is:

C≥2.5T/R

Among them: C is the filter capacitor, the unit is F;

T is the period, the unit is S, T=1/f

f is the AC power frequency, the unit is Hz

R is the load resistance, the unit is Ω

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

Since the four-terminal capacitor has good high-frequency characteristics, it provides an extremely favorable means for reducing the pulsating component of the voltage and suppressing the switching spike noise. High-frequency aluminum electrolytic capacitors also have a multi-core form, that is, the aluminum foil is divided into several shorter sections, and multiple leads are connected in parallel to reduce the impedance component in the capacitive reactance. And the use of low-resistivity materials as lead-out terminals improves the ability of the capacitor to withstand large currents.

五、 Filter capacitor size calculation formula

In the engineering design, the value of the filter capacitor of the bridge rectifier circuit is generally calculated by two entry points.

One is determined based on the cycle of charging the capacitor from the rectified power supply and discharging the load resistor, and then multiplying it by a coefficient. The other entry point is calculated based on the ripple coefficient of the power filter output.No matter which cut-in point is used to calculate the filter capacitor, it needs to be based on the two values of the MAX output voltage and current of the bridge rectifier. Usually, the filter capacitor is calculated according to the formula of power supply filter output ripple coefficient.

C》0.289/{f×(U/I)×ACv}

C, is the filter capacitor, the unit is F.

0.289 is a constant deduced from the ripple coefficient of the half-wave resistive load rectifier circuit.

 f, is the pulse frequency of the rectification circuit, such as 50Hz AC power input, the pulse frequency of the half-wave rectification circuit is 50Hz, and the pulse frequency of the full-wave rectification circuit is 100Hz. The unit is Hz.

U is the MAX output voltage of the rectifier circuit, and the unit is V.

 I, is the MAX output current of the rectifier circuit, and the unit is A.

ACv is the corrugation coefficient, and the unit is %.

For example, for a bridge rectifier circuit, the output is 12V, the current is 300mA, the ripple coefficient is 8%, and the filter capacitor is:

 C》0.289/{100Hz×(12V/0.3A)×0.08}

The filter capacitor is approximately equal to 0.0009F, and a capacitor of 1000uF can meet the basic requirements.

六、 Selection of the size of the filter capacitor

When there are contactors, relays, buttons and other components in the printed board. When operating them, a large spark discharge will be generated, and an RC absorption circuit must be used to absorb the discharge current.Generally, R takes 1~2kΩ, and C takes 2.2~4.7μF. Generally, a capacitor of about 10PF is used to filter out high-frequency interference signals.About 0.1UF is used to filter out low-frequency ripple interference, and can also play a role in stabilizing voltage.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, and choose according to the 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 useless for the time being, you can not post it first, and then choose the capacity according to the actual debugging situation.If the main operating frequency on your PCB is relatively low, just add two capacitors, one for ripple removal and one for 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, that is, the large capacitance and small capacitance you mentioned are decoupling and bypass.

I won’t talk about the principle, but it’s more practical. Generally, digital circuits can be decoupled by 0.1uF, which is used for less than 10M; for more than 20M, use 1 to 10 uF, which is better for removing high-frequency noise, and it is probably C=1/f.The bypass is generally relatively small, generally 0.1 or 0.01uF according to the resonance frequency. When it comes to capacitors, various names will make people dizzy, bypass capacitors, decoupling capacitors, filter capacitors, etc., In fact, no matter how it is called, its principle is the same, that is, to use the characteristic of low impedance to AC signals, which can be seen through the equivalent impedance formula of capacitance: Xcap=1/2лfC, the higher the operating frequency, the capacitance value The larger the value, the smaller the impedance of the capacitor.

In the circuit, if the main function of the capacitor is to provide a low-impedance path for the AC signal, it is called a bypass capacitor; if it is mainly 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 bypass capacitor. It is a decoupling capacitor; if it is used in a filter circuit, it can also be called a filter capacitor; in addition, for DC voltage, the capacitor can also be used as a circuit energy storage, and the charge and discharge can be used to play the role of a battery. In actual situations, the role of capacitance is often multifaceted, and we don't need to spend too much thought on how to define it.In this article, we collectively refer to these capacitors used in high-speed PCB design as 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 lead wire and PCB layout, the capacitor is actually a parallel circuit of the inductor and the capacitor (there is also the resistance of the capacitor itself, which cannot be ignored sometimes). This introduces the concept of resonant frequency: ω=1/(LC) 1/ 2 The capacitance below the resonant frequency is capacitive, and the capacitor above the resonant frequency 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 the STM package with the same capacitance is higher than that of the DIP package. As for how much capacitance to use, this is a reference.

Capacitor resonance frequency

Capacitance DIP (MHz) STM (MHz)

1.0μF2.55

　　0.1μF816

　　0.01μF2550

　　1000pF80160

　　100pF250500

　　10pF8001.6（GHz）

But it's just a reference, in the words of an old engineer-mainly by experience. A more reliable approach is to connect two capacitors, one large and one small, in parallel, generally requiring a difference of 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 capacitor value is inversely proportional to the square of the frequency you want to filter out. The selection of specific capacitors can use the formula C=4Pi*Pi/(R*f*f) how to select the power supply filter capacitor, and it is not difficult to master its essence and method.

1) In theory, the impedance of an ideal capacitor decreases with the increase of 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, and 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 filters the ground, when the frequency exceeds the FSR, the suppression of interference will be greatly reduced, so a smaller capacitor is required to be connected in parallel to the ground , can you think about why?The reason is that the small capacitor and the large SFR value provide a path to the ground for high-frequency signals, so we often understand it in power filter circuits: large capacitors consider low frequencies, and small capacitors consider high frequencies. The root cause is SFR (self-resonance Frequency) values are different, of course, you can also think about why? If you think about it from this perspective, you can understand why the capacitance to the ground pin in the power filter should be as close as possible to the ground.

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 capacitor values with different SFR values? Is to choose a capacitor or two capacitors?

The SFR value of the capacitor is related to the capacitance value and the pin inductance of the capacitor, so the SFR value of 0402, 0603, or in-line capacitors with the same capacitance value will not be the same. Of course, there are two ways to obtain the SFR value.1) Device Datasheet, such as the SFR value of 22pf0402 capacitor is about 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, to choose one or two circuits depending on whether the working frequency band of your power supply circuit has sufficient noise rejection ratio. After the simulation, it is the actual circuit test. For example, when debugging the receiving sensitivity of a mobile phone, the power filter of the LNA is the key. A good power filter can often improve several dB.