I. Capacitors
The simplest capacitor consists of two plates and an insulating dielectric (including air) in between. When current flows through it, the plates become charged, creating a voltage (potential difference). However, due to the insulating material, the capacitor as a whole is not conductive. This is under the condition that the capacitor's critical voltage (breakdown voltage) is not exceeded. We know that all materials are relatively insulators. When the voltage across a material increases to a certain level, the material can conduct electricity; this voltage is called the breakdown voltage. Capacitors are no exception; once a capacitor breaks down, it is no longer an insulator. However, in high school, such a voltage is not encountered in circuits, so they operate below the breakdown voltage and can be considered insulators.
However, in an AC circuit, the direction of the current changes as a function of time. The charging and discharging process of a capacitor takes time, during which a changing electric field is formed between the plates, and this electric field also changes as a function of time. In reality, the current flows through the capacitor in the form of this electric field.
II. Why do capacitors allow high frequencies to pass while blocking low frequencies?
Explanation 1:
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. In this case, 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 this 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 larger than 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 limits 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.
