Capacitors have a charging and discharging time. During the positive half-cycle of the alternating current, when the capacitor is charging, current flows through the circuit, making it a closed circuit. Once the capacitor is fully charged, no current flows through the circuit, making it an open circuit. When the negative half-cycle of the alternating current arrives, current is generated again, first canceling out the opposite charge that was originally on the capacitor, and then continuing to charge it until it is fully charged.
Now, assuming the charging time t required for the capacitor is constant, when the positive half-cycle of a high-frequency alternating current ends, and assuming the capacitor has a large enough capacitance, it will not be fully charged before the negative half-cycle begins. In this case, the circuit will continue to flow current, which means that the capacitor is a closed circuit for this high-frequency alternating current.
If the frequency of this alternating current is low, after the positive half-cycle has fully charged the capacitor, the negative half-cycle has not yet arrived, and the current will be interrupted midway. Therefore, the capacitor is not a complete circuit for this low-frequency alternating current.
If the charging time is a significant proportion of the half-cycle of the AC current, then the capacitor is not completely disconnected from the AC current of that frequency; it only has a certain impedance.
If the charging time is extremely short relative to half a cycle of the alternating current at that frequency, then the capacitor can be considered completely open-circuited, with no current flowing through it.
Explanation 2:
According to the formula for capacitive reactance, Xc = 1/(ωC) = 1/(2πfC), the higher the frequency f, the lower the capacitive reactance, and therefore the easier it is to pass through.
Similarly, the lower the frequency, the greater the capacitive reactance, and therefore the less likely it is to pass through.
Why do small capacitors pass high frequencies while large capacitors pass low frequencies?
Explanation 1:
Large capacitors require a large dielectric area, and the electrodes and dielectric are rolled or stacked together. To achieve a large area, there must be a lot of rolling or stacking, which will increase the distributed inductance. The larger the distributed inductance, the more difficult it is for high frequencies to pass through.
Theoretically (assuming the capacitor is purely capacitive), a larger capacitance results in lower impedance and allows for higher frequencies to pass through. However, in practice, most capacitors exceeding 1µF are electrolytic capacitors, which have a significant inductive component. Therefore, at higher frequencies, their impedance can actually be quite high. Sometimes, you'll see a large capacitor connected in parallel with a smaller capacitor. In this case, the larger capacitor passes low frequencies, and the smaller capacitor passes high frequencies. The function of a capacitor is to pass high frequencies and block low frequencies. The larger the capacitor, the easier it is for low frequencies to pass through; the smaller the capacitor, the easier it is for high frequencies to pass through. Specifically, in filtering, a large capacitor filters low frequencies, and a small capacitor filters high frequencies.
Explanation 2:
Theoretically, the larger the capacitance, the smaller the impedance, and the higher the frequency, the easier it is to pass through; the theory is correct.
Low frequencies cannot pass through small capacitors: It's not that they absolutely cannot pass through, but the impedance is too high and they are not easy to pass through.
High frequencies cannot pass through large capacitors: Theoretically, large capacitors allow high frequencies to pass through more easily. However, due to the limitations of the manufacturing process of large capacitors, they are generally wound. The distributed inductance of large capacitors is much larger than that of small capacitors. Since inductive reactance is inversely proportional to high-frequency impedance, it restricts the passage of high-frequency signals. Generally, manufacturers responsible for power supply filtering circuits will install a small ceramic capacitor next to the large capacitor to filter out high-frequency interference signals.
Theoretically, small capacitors are better at filtering high-frequency signals, while large capacitors are better at filtering low-frequency signals. This phenomenon stems from the impedance characteristics of a capacitor to AC signals, known as capacitive reactance (X_C). Capacitive reactance is a measure of how much a capacitor impedes AC signals, and its value is closely related to the frequency f of the AC signal and the capacitance C of the capacitor. Specifically, the formula for calculating capacitive reactance X_C is: X_C = 1/2πf C. From the formula, it can be seen that when the capacitance is fixed, the higher the frequency, the smaller the capacitive reactance; conversely, when the frequency remains constant, the larger the capacitance, the smaller the capacitive reactance. In particular, for DC signals (frequency 0), the capacitive reactance tends to infinity, equivalent to an open circuit.
I've always had a question: Capacitor reactance is 1/jwC. A large capacitor has a large C, and at high frequencies, w is also large, so the impedance should be very small. Wouldn't that be more suitable for filtering high-frequency signals?
However, the truth is that large capacitors filter out low-frequency signals.
The answer I found today is as follows:
Generally, capacitors around 10pF are used to filter out high-frequency interference signals, while those around 0.1uF are used to filter out low-frequency ripple interference and can also act as voltage regulators. The specific capacitance value of the filter capacitor depends on the main operating frequency of your PCB and the harmonic frequencies that may affect the system. You can check the capacitor datasheets of relevant manufacturers or refer to the manufacturer's database software to select according to your specific needs. The number of capacitors is not fixed; it depends on your specific needs. Adding one or two more is fine. You can leave unused capacitors out for now and choose the capacitance value based on actual debugging results. If the main operating frequency of your PCB is relatively low, adding two capacitors is sufficient: one to filter ripple and one to filter high-frequency signals. If there are large instantaneous currents, it is recommended to add a larger tantalum capacitor.
In fact, filtering also includes two aspects, namely, large capacitance and small capacitance, which are decoupling and bypass, as you mentioned. I won't go into the principles, but for practical purposes, 0.1uF is generally sufficient for decoupling in digital circuits below 10MHz; for above 20MHz, 1 to 10uF is used to better remove high-frequency noise, roughly according to C=1/f. Bypass capacitors are generally smaller, usually 0.1 or 0.01uF depending on the resonant frequency. Speaking of capacitors, the various names can be confusing: bypass capacitors, decoupling capacitors, filter capacitors, etc. In fact, no matter what they are called, their principle is the same, which is to utilize the characteristic of presenting low impedance to AC signals. This can be seen from the equivalent impedance formula of a capacitor:
Xcap = 1/2лfC,
The higher the operating frequency and the larger the capacitance value, the lower the impedance of the capacitor.
In circuits, if a capacitor's primary function is to provide a low-impedance path for AC signals, it's called a bypass capacitor; if its main purpose is to increase AC coupling between power and ground, reducing the impact of AC signals on the power supply, it can be called a decoupling capacitor; if used in a filtering circuit, it can be called a filter capacitor; in addition, for DC voltage, capacitors can also act as energy storage devices, functioning like batteries through charging and discharging. In reality, capacitors often serve multiple purposes, so we don't need to spend too much time defining them. In this article, we will uniformly refer to all capacitors used in high-speed PCB design as bypass capacitors.
The essence of a capacitor is to pass alternating current (AC) and block direct current (DC). Theoretically, the larger the capacitor used for power supply filtering, the better. However, due to lead wires and PCB layout, a capacitor is actually a parallel circuit of an inductor and another capacitor (and the capacitor's own resistance is sometimes also significant).
This introduces the concept of resonant frequency: ω = 1/(LC)¹/²
Below the resonant frequency, a capacitor behaves capacitively, while above the resonant frequency, it behaves inductively. Therefore, large capacitors generally filter low-frequency waves, while small capacitors filter high-frequency waves.
This also explains why STM-packaged capacitors of the same capacitance value have a higher filtering frequency than DIP-packaged capacitors. As for the appropriate capacitor size, this is a reference capacitor resonant frequency.
However, this is just for reference; as the veteran engineer would say, it mainly relies on experience.
A more reliable approach is to connect two capacitors, one large and one small, in parallel, generally with a capacitance difference of at least two orders of magnitude, to achieve a wider filtering frequency range. Generally, the large capacitor filters out low-frequency waves, and the small capacitor filters out high-frequency waves. The capacitance value is inversely proportional to the square of the frequency you want to filter.
The specific capacitor selection can be done using the formula C = 4Pi * Pi / (R * f * f )
Selecting power supply filter capacitors is not difficult if you grasp the essence and methods.
1) Theoretically, the impedance of an ideal capacitor decreases with increasing frequency (1/jwc). However, due to the inductive effect of the capacitor's leads, the capacitor should be considered as an LC series resonant circuit. The self-resonant frequency is the FSR parameter of the device. This means that when the frequency is greater than the FSR value, the capacitor becomes an inductor. If the capacitor is used for filtering to ground, the suppression of interference is greatly reduced when the frequency exceeds the FSR. Therefore, a smaller capacitor is needed in parallel with ground. Why? The reason is that a small capacitor has a large SFR value, providing a path to ground for high-frequency signals. Therefore, in power supply filtering circuits, we often understand it this way: large capacitors filter low frequencies, and small capacitors filter high frequencies. The fundamental reason is the difference in SFR (self-resonant frequency) values. Of course, why? If you think about it from this perspective, you can understand why the capacitor's ground pin in power supply filtering should be as close to ground as possible.
2) In actual design, we often have questions: How do I know the SFR (Sound Rejection Ratio) of a capacitor? Even if I know the SFR value, how do I choose capacitors with different SFR values? Should I choose one capacitor or two? The SFR value of a capacitor is related to its capacitance value and the lead inductance. Therefore, the SFR values of 0402, 0603, or through-hole capacitors with the same capacitance value will not be the same. Of course, there are two ways to obtain the SFR value: 1) the device datasheet, such as the SFR value of a 22pF 0402 capacitor being around 2GHz; 2) directly measuring its self-resonant frequency using a network analyzer. Think about how to measure it? S21? After knowing the SFR value of the capacitor, use software simulation, such as RFsim99. Choosing one or two circuits depends on whether the operating frequency band of your power supply circuit has sufficient noise suppression ratio. After the simulation, it's time for actual circuit testing. For example, when debugging the sensitivity of a mobile phone receiver, the power supply filtering of the LNA is crucial; good power supply filtering can often improve the signal by several dB.
To put it simply, think of a capacitor as a leaking tank, and the arrival of AC peaks as adding water to the tank. If the amount of water leaking is the same, then if the frequency of adding water is high, you need to use a smaller tank to ensure a high water level. Conversely, if the frequency of adding water is low, and the tank is too small, the water level will drop significantly before the second water arrives. Therefore, you need to use a larger tank to mitigate the drop in water level caused by leakage.
In electronic circuits, capacitors are fundamental components with multiple functions such as filtering and energy storage. However, there's a saying about capacitor usage: "Large capacitors filter low frequencies, small capacitors filter high frequencies." Is this true?
Before exploring this issue, let's understand the principle of capacitor filtering. The basic principle of capacitor filtering is to smooth the input signal through the charging and discharging characteristics of the capacitor. When the input signal is an AC signal, the capacitor will charge and discharge according to the frequency of the input signal.
For high-frequency signals, the charging/discharging time of a capacitor is short, so the high-frequency signal is attenuated when it passes through the capacitor. However, for low-frequency signals, the charging/discharging time of a capacitor is long, so the low-frequency signal can also pass through the capacitor.
The frequency response of a capacitor refers to the degree to which it attenuates signals of different frequencies. Generally speaking, capacitors attenuate high-frequency signals more and low-frequency signals less. However, it should be noted that this attenuation is not simply proportional to the size of the capacitor. In fact, the frequency response of a capacitor is affected by a variety of factors, such as the capacitance, equivalent series resistance (ESR), and equivalent series inductance (ESL).
Therefore, it is incorrect to assume that the statement "large capacitors filter low frequencies and small capacitors filter high frequencies" is correct. In fact, the frequency response of a capacitor is a relatively complex issue that requires comprehensive consideration of multiple factors.
