Circuit filtering principle

The filter capacitor typically has a high capacitance, so electrolytic capacitors are commonly used. When wiring, always pay attention to the polarity of the electrolytic capacitor. The capacitor filter circuit leverages the charging and discharging properties of the capacitor to smooth out the output voltage.

★ During the positive half-cycle of u2, when the value exceeds the voltage uC across the capacitor, diodes D1 and D3 turn on, while D2 and D4 turn off. The current flows through the load resistor RL, and the capacitor C charges through the other path. When uC > u2, D1 and D3 are reverse-biased and shut off, causing the capacitor to discharge through the load resistor RL, resulting in a slow exponential decline of uC.

★ During the negative half-cycle of u2, when the amplitude approaches uC, D2 and D4 become conductive due to the forward voltage, allowing u2 to recharge C. The voltage uC rises to the peak of u2 before starting to fall; once it drops to a certain value, D2 and D4 cut off, causing C to discharge through RL, leading to an exponential decrease in uC. When the discharge reaches a specific point, D1 and D3 become conductive, restarting the aforementioned process.

Influence of RL and C on Charge and Discharge:

The charging time constant of the capacitor is rDC. Since the rD of the diode is minimal, the charging time constant is small, resulting in a fast charging speed;

RLC represents the discharge time constant. Given that RL is large, the discharge time constant is significantly longer than the charging time constant. Thus, the filtering effect relies heavily on the discharge time constant.

The larger the capacitance C, the larger the load resistance RL, the smoother the filtered output voltage becomes, and the larger the average value, as illustrated in the figure below.

The function of the filter capacitor is simply to convert the output voltage after filtering into a stable DC voltage. Its working principle involves charging the capacitor when the rectified voltage surpasses the capacitor voltage and discharging the capacitor when the rectified voltage falls below the capacitor voltage, ensuring the output voltage remains relatively stable.

The filter capacitor has a large capacity, hence electrolytic capacitors are usually employed. When wiring, ensure you correctly identify the positive and negative terminals of the electrolytic capacitor. The capacitor filter circuit uses the charging and discharging characteristics of the capacitor to make the output voltage more stable.

★ During the positive half-cycle of u2, when the value exceeds the voltage uC across the capacitor, diodes D1 and D3 turn on, while D2 and D4 turn off. The current flows through the load resistor RL, and the capacitor C charges through the other path. When uC > u2, D1 and D3 are reverse-biased and shut off, causing the capacitor to discharge through the load resistor RL, resulting in a slow exponential decline of uC.

★ During the negative half-cycle of u2, when the amplitude approaches uC, D2 and D4 become conductive due to the forward voltage, allowing u2 to recharge C. The voltage uC rises to the peak of u2 before starting to fall; once it drops to a certain value, D2 and D4 cut off, causing C to discharge through RL, leading to an exponential decrease in uC. When the discharge reaches a specific point, D1 and D3 become conductive, restarting the aforementioned process.

Influence of RL and C on Charge and Discharge:

The charging time constant of the capacitor is rDC. Since the rD of the diode is minimal, the charging time constant is small, resulting in a fast charging speed;

RLC represents the discharge time constant. Given that RL is large, the discharge time constant is significantly longer than the charging time constant. Thus, the filtering effect relies heavily on the discharge time constant.

The larger the capacitance C, the larger the load resistance RL, the smoother the filtered output voltage becomes, and the larger the average value, as illustrated in the figure below.

The rectifying circuit transforms alternating current into direct current, yet the pulsating component of the direct current output is substantial. The ripple coefficient of the DC power required by most electronic equipment is less than 0.01. Consequently, measures must be taken to minimize the ripple component in the output voltage while preserving the DC component to make the output voltage resemble an ideal DC power source. Such a circuit is referred to as a filter circuit in a DC power supply.

Commonly used filter circuits include passive filtering and active filtering. Passive filtering primarily consists of capacitive filtering, inductive filtering, and complex filtering (such as L-type, LC filtering, LCÏ€-type filtering, and RCÏ€-type filtering). Active filtering mainly involves active RC filtering, also known as electronic filtering.

The magnitude of the pulsating component in the direct current is indicated by the ripple coefficient. The higher the value, the poorer the filtering effect of the filter.

Ripple Coefficient (S) = Maximum AC Component of Output Voltage / DC Component of Output Voltage

The ripple coefficient of the half-wave rectified output voltage is S=1.57, while the ripple coefficient of the output voltage for full-wave and bridge rectification is approximately S=0.67. For full-wave and bridge rectifiers, a C-type filter circuit is used, with a ripple coefficient of S=1/(4(RLC/T-1)). (T is the period of the DC ripple voltage of the rectified output.)

The RC-Ï€ type filter circuit is essentially composed of a RC filter circuit based on capacitor filtering, as shown in Figure 1.

The box represents the added primary RC filter circuit. If S' is used to denote the ripple coefficient of the voltage across C1, the ripple coefficient S at both ends of the output voltage is given by S=(1/ωC2R')S'.

From the analysis, we can see that the larger the R and the larger the C2, the smaller the ripple coefficient, meaning the better the filtering effect. However, increasing the R value leads to a greater DC voltage drop across the resistor, increasing the internal loss of the DC power supply. Increasing the C2 capacitance increases the size and weight of the capacitor, making practical implementation difficult.

To address this contradiction, an active filter circuit, also known as an electronic filter, is often used. The circuit is shown in Figure 2. It is formed by connecting a π-type RC filter circuit consisting of C1, R, and C2 with an active device - a transistor T. As seen in Figure 2, the current flowing through R is IR = IE / (1 + β) = IRL / (1 + β). The current through resistor R is only 1/(1+β) of the load current. Hence, a larger R can be used, paired with C2, to achieve better filtering results, reducing the pulsating component of the voltage across C2. The output voltage is nearly equal to the voltage across C2, thereby reducing the ripple component of the output voltage.

From the perspective of the RL load resistor, the filter components R and C2 of the base circuit are folded into the emitter circuit, which is equivalent to a decrease of (1+β) times and an increase in C2 by (1+β) times. The required capacitance C2 is only 1/β of the capacitance needed for a typical RCπ-type filter. For instance, if the DC amplification factor of the transistor β=50 and a general RCπ-type filter requires a capacitance of 1000 μF, using an electronic filter would only require a capacitor of 20μF. This circuit allows for the use of larger resistors and smaller capacitors to achieve the same filtering effect, making it widely used in the power supplies of some small electronic devices.