Charging and discharging process of capacitance and its application

first, charge and discharge principle

1. The charging and discharging process of RC series circuit

In a DC series circuit composed of resistors R and C, the transient process is the charge and discharge process of the capacitor (Figure 1), and when the switch k hits position 1 o'clock, the power supply charges the capacitor C until the voltage on both ends is equal to the power supply E. The specific mathematical description of this transient change is Q=CUC, and I =dq/dt, so

The above means that the charging voltage at both ends of the capacitor is an exponential growth curve, the steady-state capacitor at both ends of the voltage is equal to the supply voltage E, as shown in Figure 2 (a). The rc=t with time dimension, called the time constant of the circuit, is an important physical quantity to characterize the speed of the transient process (the smaller the T, the faster the charge and discharge), the higher the voltage UC rises to the 0.63e,1/e≈0.37, and the corresponding time is T.

When the switch K1 to position 2 o'clock, capacitance C through the Resistance r discharge, the mathematical description of the discharge process is

This indicates that the discharge voltage at both ends of the capacitor is attenuated to zero, and t can be determined by the time at which the curve decays to 0.37E. The charge-discharge curve is shown in Figure 2.

2. Half-Life T1/2

Another characteristic value that is more easily measured in the experiment than the time constant tau, called the Half-life T1/2, which is the time required when UC (T) drops to the initial value (or up to the end), also reflects how quickly the transient process is, and the relationship to T is: t1/2 =ΤLN2 = 0.693τ (or τ= 1.443T1/2)

3. Rectangular pulse response of RC circuit.

If the rectangular pulse sequence signal is added to the RC series circuit with zero voltage initial value, the transient process of the circuit occurs periodically. Obviously, the impulse response of the RC circuit is a continuous capacitor charge and discharge process. As shown in Figure 3.

If the amplitude of the rectangular pulse is u, the pulse width is TP. The voltage on the capacitor can be expressed as:

Second, the application of RC circuit