How to choose capacitors

In electronic circuits, especially various Hi-Fi related circuits including HFI FAF, the frequency of use of capacitors is roughly second only to resistors. Although resistors are used in large numbers, their types of functional characteristics are far simpler than those of capacitors. Because on a circuit diagram, we can often see the description of the resistor specifications is that carbon film 1/2 watt is used unless otherwise specified, while capacitors are not so convenient.

Because the specifications of capacitors, in addition to voltage capacity, also have various differences in shape and characteristics due to different structures. If the wrong one is selected, not only will the circuit not work, but it may even cause danger, including damage to other parts and human body. This article intends to describe the common sense of selecting general capacitors for amateurs. Due to limited space, the more practical ones are given priority.

A capacitor in an electronic circuit

The basic function of a capacitor is charging and discharging, but many circuit phenomena derived from this basic charging and discharging function give capacitors a variety of different uses. For example, in electric motors, we use it to produce phase shifts. In photographic flash, we use it to produce high-energy instantaneous discharges, and in electronic circuits, capacitors of different properties have many uses. Although these many different uses are also quite different, because their functions all come from charging and discharging, there are inevitably commonalities between different uses. For example, a bypass capacitor can actually be called a smoothing filter capacitor, depending on the perspective from which it is explained.

The following is a classification based on commonly used names to explain the functions and basic requirements of capacitors in different circuits.

1.1 DC charging and discharging capacitors

The basic function of a capacitor is charging and discharging, so directly utilizing this charging and discharging function is one of the main uses of a capacitor.

The capacitor used in this application functions like a battery and a flywheel. When the energy supplied is higher than the demand, it absorbs and stores it. When the energy supplied is lower than the demand or there is no energy supplied, the stored energy is released. The charging and discharging function of a capacitor is different from that of a battery. Whether a battery is charging or discharging, the required action time is longer. Therefore, it cannot absorb a large amount of electrical energy in an instant, nor can it release a large amount of electrical energy in an instant.

Figure 1-1 is a common rectifier circuit. The diode in the figure only conducts the current in the lower half cycle, and stores electrical energy in the capacitor during the conduction period. In the negative half cycle, the diode does not conduct electricity. At this time, the electrical energy required by the load is only supplied by the capacitor.

In this circuit, you may wonder whether the energy charged by the capacitor in the positive half cycle is enough to last until the negative half cycle. There are three factors to determine this issue: 1. Whether the AC power can fully supply the required energy in the positive half cycle; 2. Whether the capacitor can store sufficient energy during the charging period of the positive half cycle; 3. What is the average power required by the load.

Among the above three factors, if the numbers of 1.2. are very large, and the demand for 3. is very small, pure DC cannot be obtained even in theory, because the capacitor is not charged during the entire positive half-cycle, but only when the voltage of the positive half-cycle is higher than the existing voltage of the capacitor, it is charged. When the capacitor is not connected to a load, the leakage current is not counted, and the charging time is only when the voltage rises in the first quarter of the positive half-cycle and until the voltage rises to the peak value, it will no longer charge in the second positive half-cycle. When the capacitor is connected to a negative load, it begins to discharge. During the non-charging time, the amount of electrical energy released is equal to the amount of electrical energy that can be recovered during charging. Because of this, the ripple cannot be equal to zero.

Conventional rectification charging and discharging circuits charge in a very short time when the AC is close to the peak value, and then discharge in a stable manner such as a pre-amplifier or unstable such as a Class B amplifier, and the amount of discharge is only a very small part of the total capacitance. However, there are also a few circuits in which the capacitors are charged slowly for a long time and then discharged in large quantities in an instant. Such circuits, such as the flash circuit used in photography and the discharge circuit in a spot welding machine, have capacitors with characteristics that are different from those of general rectification capacitors.

1.2 Power smoothing and filtering and anti-cross-coupling capacitors

The charging and discharging capacitors in the aforementioned power rectifier circuit have different charging and discharging times, so there will inevitably be ripples. In order to reduce the ripple rate as much as possible, a capacitor C2 can be added as shown in Figure 1-2A. This capacitor is purely used to smooth the ripple. In the figure, A uses inductor L as a cross-connection, and B uses resistor cross-connection. When L is used as a cross-connection, it has higher efficiency and has excellent smoothing and filtering effects when the design is appropriate. In Figure 1-2, if the load after rectification is stable, such as a light bulb or a battery, then the only function of C2 is smoothing and filtering. However, if this power supply If the load of the input device is not stable, then the voltage across C2, in addition to the ripple of the AC power supply, may also fluctuate due to load changes. The amplitude of the fluctuation varies with the amplitude of the load change. At this time, if the same power supply is used to supply two different loads, and one of the loads is extremely sensitive to voltage, then the current change of the first load may affect the operation of the second load, such as crosstalk between the two channels of stereo, and ultra-low frequency oscillation that may be caused when the front and rear stages share the power supply and the operation phase is restored to the same phase. In order to prevent similar cross-linking effects from the power supply, a capacitor can be added before each load separately, which is called an anti-cross-linking capacitor, as shown in C2 and C3 in Figure 1-2C.

1.3 High-pass, low-pass and bandpass and classification

When a voltage with constant polarity is applied across the two ends of a capacitor, the capacitor will be charged. Although the polarity of this voltage does not change, the voltage changes at any time. The two ends of the capacitor will maintain the highest voltage value. We have described this phenomenon in the previous section. In this section, what we want to discuss is, what happens when a voltage with a changing polarity is applied across the two ends of a capacitor?

Please see Figure 1-3A. When the voltage at point a in the figure is positive relative to point b, the capacitor is charged for the first time. The charging direction is positive near end a and negative near end b. During the entire charging process, since there was no electrical energy inside the capacitor and it must now store electrical energy, there must be electrical energy consumption. Although this consumption is stored in a capacitor that acts like a reservoir, there is undoubtedly current flowing in the circuit. Since there is current flowing, the capacitor can be regarded as conductive.

Then, when the voltage at point a reaches the highest positive value relative to point b, it begins to decrease again. At this time, since there is no unidirectional conductive diode like in Figure 1-2 in the circuit of Figure 1-3A, when the voltage at point a relative to point b is lower than the voltage across the capacitor, the capacitor begins to discharge. The direction of discharge is of course opposite to that of charging. Since there is a discharge phenomenon, there is current. With current, we can regard the capacitor as conductive.

The voltage at point a keeps decreasing until it becomes the same as that at point b, and then continues to decrease. At this time, the voltage at point a is lower than that at point b, or we can say that point a becomes negative with respect to point b. As a result, the capacitor changes from discharging to reverse charging, and this continues until a reaches the maximum negative value with respect to b. During this entire process, although a has undergone a change from positive to negative with respect to b, its effect on the capacitor is only from high to low with respect to b, and the direction does not change. Therefore, the capacitor maintains the same current direction from positive discharge to negative charging. Of course, it is also conductive, and the conductive effect in this direction continues until a exceeds the highest negative value with respect to b, causing the capacitor to discharge negatively.

In this whole change of situation, we need to pay attention to three phenomena. The performance of capacitors in the whole process of voltage change is that although they can conduct electricity, is the amount of their conductivity the maximum amount that the power supply can provide? This is not necessarily the case. For example, if the capacity of the capacitor is very small, it can only charge a small amount of electricity when charging, and when discharging, it will discharge all the charged energy. Therefore, it can be imagined that the larger the capacitance, the greater the conductivity. Second, it takes time to charge the capacitor. When the capacitance is very small compared to the energy supplied by the power supply, the voltage across the capacitor can closely follow the changes in the power supply voltage. The current seems to change 90 degrees ahead of the voltage. Therefore, when a changes from negative to positive, the current is in one direction, and from the positive maximum value to the negative maximum value is in another direction. The voltage changes from negative to positive and then back to zero in one direction, and changes to the other direction after crossing the zero axis. The third phenomenon is also the main phenomenon described in this section. That is, when the capacitance is fixed, we speed up or slow down the frequency of the power supply change, and the resulting situation will be the same as the change in capacitance. That is, when the frequency is high, it is equivalent to an increase in capacity, so the amount of conductivity is also greater. Conversely, when the power supply frequency is low, it is equivalent to a decrease in capacity and a smaller amount of conductivity.

Since the amount of conductivity can be large or small, it has a function similar to that of a resistor, but it is somewhat different from the conductive properties of a resistor. The difference is that the conductivity of a resistor is only related to its own resistance value, while a capacitor, in addition to being related to capacity, must also be an alternating current, and is related to the frequency of the alternating current. After combining the similarities and differences, we call this conductive characteristic of a capacitor capacitive reactance. The concept of capacitive reactance is established through comparison with the resistance value, so the unit of measurement is the resistance value unit, Ohm, or Ω for short.

The formula for capacitive reactance is

Xc=1/2πfc

Where Xc is the capacitive reactance in ohms, f is the applied AC frequency, and C is the capacitance in farads.

From the above formula, we can calculate the capacitive reactance of a fixed-capacity capacitor as it changes with frequency and plot it into a curve. Figure 1-3B is the capacitive reactance curve of a 0.1 microfarad capacitor. We can find that 1. The capacitive reactance is inversely proportional to the frequency 2. When the frequency is zero DC, the capacitive reactance is infinite and does not conduct electricity.

By utilizing the capacitive reactance characteristic of the capacitor and connecting it in series in the circuit, the high frequency can be allowed to pass more and the low frequency can pass less. Conversely, if it is connected in parallel in the circuit, the high frequency will be weakened because of the short circuit, and the low frequency will be weakened less. The effects of series and parallel connection on the circuit can be said to be exactly the opposite.

However, it must be noted that although a simple capacitor has capacitive reactance, it has no performance. In order to make it have a clear performance, other components different from capacitors must be added. For example, resistors are one of the commonly added components.

Let's look at Figure 1-3C. If the internal resistance of the AC power supply is very small and much smaller than the capacitive reactance of the capacitor at the AC frequency, then the voltage of the AC power supply will appear completely across the capacitor. But if the internal resistance of the AC power supply is quite large and much larger than the capacitive reactance of the capacitor at the AC frequency, there will not be enough time for the capacitor to charge and discharge, so the AC voltage presented is almost zero. From the above two extreme phenomena, we find that the internal resistance of the power supply will determine the attenuation of a capacitor of a given capacity at a certain frequency. In actual use, since the internal resistance of the power supply or signal source is not a controllable factor, the source resistance must be set very low during design, and then the frequency control function is achieved by combining external resistors and capacitors.

Figure 1-3D shows the simplest RC type high-pass or low-pass network. If you look closely at the two figures, you will find that their basic structures are the same. The only difference is the voltage extraction point. When the voltage is extracted from both ends of the capacitor, the higher the frequency, the more it is attenuated. But when the voltage is extracted from both ends of the resistor, the higher the frequency, the less it is attenuated. This is a low-pass or high-pass network. The mixed composition of high-pass and low-pass networks can be designed to allow a specific frequency range to pass through the network, which is called a bandpass network. The frequency division network uses the principles of high-pass, low-pass and bandpass to extract different frequencies of high, medium and low.

1.4 Roadside

If we want to remove signals above a certain frequency or all AC components in a circuit, we can use filter capacitors. However, in custom, we call a small part of the capacitor filtering function a bypass capacitor. For example, we call the capacitor in parallel with the emitter resistor of a transistor or the cathode resistor of a vacuum tube a bypass capacitor because the AC signal passes through it and enters the ground. In the power supply circuit, in addition to smoothing filters or anti-cross-coupling capacitors of thousands of microfarads, high-frequency dedicated capacitors of a few tenths of a microfarad are often used to bypass the high frequency. In fact, this high-frequency bypass capacitor can also be regarded as a high-frequency filter and anti-cross-coupling capacitor.

In Section 1.3, we mentioned that the conductivity of a capacitor occurs before charging or discharging is completed, so current is generated before voltage. In electronic circuits, there is another component, the inductor, whose characteristics are just opposite to those of the capacitor, that is, voltage is generated before current. If these two components with opposite characteristics are connected in series or parallel, then at a certain frequency, the current of the capacitor leads and the current of the inductor lags behind, so that the two overlap and the current becomes maximum, which is called current resonance. Conversely, the current of the capacitor leads and the current of the inductor lags behind, so that the two cancel each other out due to a difference of 180 degrees, and the current becomes minimum. This is called series resonance.

Series or parallel resonance is often used in extremely efficient bandpass or filtering networks.

1.6 Oscillation

When a capacitor conducts alternating current, there is a phase difference between the current and voltage, so it is easy to produce oscillation in a circuit with gain.

Figure 1-6A is a phase-shift oscillator. The capacitors in the figure create gain between the FET drain and the drain, so the repetitive action generates oscillation.

In addition, using a series RC connected to a Nihon discharge tube can also induce sawtooth wave oscillation. The action process is 1. The power supply voltage charges to C through R 2. The voltage of C gradually increases 3. When the voltage of the Nihon discharge tube reaches the discharge voltage, it starts to discharge 4. Continue to discharge until the discharge stops 5. Start charging again. The conditions for the above actions to occur are 1. The start discharge voltage of the Nihon tube is higher than the stop discharge voltage 2. The continuous current that R can provide is less than the discharge current of the Nihon tube.

1.7 Voltage Division

Capacitors will produce capacitive reactance for an alternating current of a specific frequency, and the nature of capacitive reactance is similar to that of resistance. Therefore, when two capacitive reactances are connected in series, they will also produce a voltage-dividing effect, just like connecting resistors in series. Because of the relationship between capacitive reactance and capacitance, the attenuator in the high-frequency attenuator (Figure 1-7) is an oscilloscope or high-frequency voltmeter input circuit. Basically, the attenuator uses resistance as the basis for voltage-dividing attenuation. However, in order to reduce the effect of potential capacitance on input impedance, each voltage-dividing resistor is connected with a capacitor. The simple way to determine the capacitance is to make all R*C values ​​equal.

1.8 Standard Capacitance

Like standard resistors, special capacitors are used to compare other capacitors. Their capacity is precise and their quality is extremely stable, but their price is also very high.

Characteristics of two capacitors

2.1 Capacitor Structure

Capacitors have various uses and functions as described in the previous chapter, so what is their structure and how is their capacity formed?

Please see Figure 2-1A. There are two metal sheets close to each other but not connected. When voltage is applied to the two metal sheets, positive and negative charges attract each other, so when the applied voltage is removed, the two metal sheets still maintain their original charges. This is the capacitive effect. In this simple example, we can imagine that if the relative area of ​​the metal sheets is larger, the area that can accommodate charges will be larger, and the smaller the distance between the metal sheets, the stronger the charge interaction will be. Therefore, the above two factors can determine the size of the capacitance.

2.2 Dielectric and polarization

The capacitance formed when two metal sheets are placed close to each other described in the previous section assumes that there is no other substance in the gap between the two metal sheets, that is, a vacuum is assumed.

In actual construction, the vacuum structure is naturally difficult, especially when a certain gap must be maintained in a vacuum, so we usually add non-conductive materials in between. For example, when the air is not pumped out, the middle is separated by air, or most capacitors use mica oil paper or plastic film as insulation.

When insulating material is added between the two poles, will the charges still attract each other? The answer is that they can still attract each other, but the direct attraction becomes indirect attraction. The indirect attraction comes from the polarization inside the insulating material. Although the insulating material is not conductive, there are equal amounts of negative electrons and positive electrons inside its molecules. Originally, these positive and negative electrons are arranged in a disorderly manner to form a balanced situation. When this insulating material is placed between the two poles, the charge of the poles attracts these electrons to form a regular arrangement in the same direction, just like the case of iron molecules being magnetized. Therefore, the charge on the poles reaches the other side through these neatly arranged electrons, making the insulating material a medium for static charge. Therefore, this insulating material is called a medium.

When a dielectric is added between two metal sheets that are close to each other, its capacity is not only affected by the relative area distance, but also by the type of dielectric. For example, if the standard for air vacuum is 1, the influence of different dielectrics on capacity is called the dielectric coefficient. For example, glass is 4 to 7, paraffin is 2, mica is 6 to 8, kerosene is 2, and pure water is 81, etc. Therefore, when we want to obtain or manufacture a capacitor with a large capacity, we must start from three aspects. First, increase the relative area, but the volume will be very large. Second, reducing the gap will cause poor insulation. Third, using a material with a larger dielectric coefficient as the medium also requires consideration of physical and insulation properties.

2.3 Polarization time and applicable frequency

The polarization of the medium does not occur immediately with the generation of the electrostatic field. In other words, when the voltage is applied to the diode, it must wait for a period of time for the polarization to complete. The polarization time is of course very short. However, if the capacitor is to work at a high frequency, the time required for the polarization is a very important factor.

The polarization time required for different substances to serve as media is not the same. Generally speaking, the polarization time of highly polar compounds is faster because its molecules are already bipolarized before polarization. Nonpolar substances need to be induced into bipolar molecules before polarization. Not only is the time slower, the dielectric constant is also low, so they are not suitable as media that require containers.

2.4 Capacitance

In Section 2.1, we mentioned that the larger the relative area of ​​the two metal sheets or the smaller the distance between them, the greater the force will be. In addition, the dielectric effect can be enhanced by selecting an appropriate medium, as shown in the formula:

In the formula, the dielectric coefficient is the various dielectric constants calculated based on the dielectric constant in vacuum. A is the relative area unit, which is square meters. d is the distance unit, which is meters. C is the capacitance unit, which is Farad, abbreviated as F. Because the quantity of this basic unit is too large in electronic circuits, microfarad, Nino Farad or pico Farad is often used.

One farad of capacity refers to the capacity of the capacitor when it can store one coulomb of charge when a voltage of one volt is applied to it.

2.5 Capacitor Withstand Voltage

If the voltage applied across a capacitor increases, its charge will also increase. However, in reality, this voltage cannot be increased arbitrarily because the distance between the capacitor's electrodes is very small. When the voltage increases, electric sparks (corona, or spark discharge) may occur, which may damage the capacitor. Therefore, in addition to the capacity, the operating voltage of each capacitor is also a very important usage data.

2.6 Series and Parallel Connection of Capacitors

If two metal sheets of unit area form a fixed capacitance C, then if the area of ​​the metal sheet is increased by two units, the capacitance is also 2C. The two unit areas of the metal sheet are not necessarily a whole large area. The units are connected to each other by conductors. This is called the parallel connection of capacitors.

After the capacitors are connected in parallel, their total capacitance is the sum of the capacitances of each capacitor in parallel, that is:

In some special cases, capacitors can also be used in series. When capacitors are used in series, the reciprocal of the series capacity is the sum of the reciprocals of each capacity, that is:

C = C1 + C2 + C3 …+ Cn

In certain specific cases, capacitors are used in series. When capacitors are connected in series, the reciprocal of the series capacity is the sum of the reciprocals of the individual capacities, that is:

1/C = 1/ C1 + 1/ C2 + 1/C3 …+ 1/Cn

When capacitors are connected in series, a voltage divider effect will be produced, and the voltage divider ratio is the inverse ratio of the capacitance. Therefore, even if a DC voltage is applied, unless the capacitance of all series capacitors is the same, the total withstand voltage value after series connection is not the sum of the withstand voltage values ​​of each capacitor.

2.7 Equivalent Circuit of a Capacitor

The above descriptions are all about an ideal capacitor, that is, only the capacitance is taken into account without considering other factors.

In fact, due to manufacturing technology or requirements, capacitors have not only capacity but also parallel, series or series internal resistance and series inductance. Figure 2-7A is its equivalent circuit.

The g in the circuit is the leakage resistance, which is caused by the inverse of the conductivity and insulation resistance of the medium or packaging material. To put it more clearly, the medium or packaging material is not absolutely insulating. Since it is not absolutely insulating, there will be leakage. Therefore, the leakage current is caused by the leakage resistance. The leakage current will consume electrical energy and is not what we need. However, different media and structures will have different leakage currents, so it should be selected according to actual requirements when using.

Rs in the figure is the series resistance. The series resistance value mainly comes from the effective resistance of the electrode sheet and the lead. If this resistance cannot be ignored, the capacitor will consume a part of the electric energy during the charging and discharging process and become mature. Not only will the power be wasted, but the capacitor itself may also be easily damaged due to maturity.

The effect of series resistance is often measured as the power factor or the reciprocal of the dissipation factor. However, when the capacity is small and not used for power purposes, it is expressed as Q, which is the reciprocal of the dissipation factor.

Ls in the figure is the reason for the series inductance. It is mainly because the internal structure of some capacitors is composed of two long strips of metal foil wound with a dielectric. The inductance will produce inductive reactance to the alternating current. Its phase shift characteristic is just opposite to that of the capacitive reactance. Therefore, special attention should be paid to the existence of series inductance when working at high frequencies.