“If the rectangular pulse train signal is applied to the RC series circuit with the initial value of voltage zero, the transient process of the circuit will occur periodically. Obviously, the impulse response of the RC circuit is the continuous process of charging and discharging the capacitor.

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1. Rectangular Impulse Response of RC Circuit

If the rectangular pulse train signal is applied to the RC series circuit with the initial value of voltage zero, the transient process of the circuit will occur periodically. Obviously, the impulse response of the RC circuit is the continuous process of charging and discharging the capacitor. as the picture shows.

If the amplitude of the rectangular pulse is U, the pulse width is tp. The voltage across the capacitor can be expressed as:

The voltage across the resistor can be expressed as:

That is, when 0 to t1, the capacitor is charged; when t1 to t2, the capacitor is discharged through the resistor R.

(It can also be explained in this way: the voltage across the capacitor cannot mutate, but the current can, so it is reflected in the figure that the voltage across the resistor has mutated.)

2. RC Differential Circuit

Take the two ends of the resistor in the RC series circuit as the output terminal, and select the appropriate circuit parameters to make the time constant τ << tp (the pulse width of the rectangular pulse). Since the charging and discharging of the capacitor proceeds quickly, the voltage uc

The above formula shows that the output voltage uo

3. RC integrating circuit

If the two ends of the capacitor of the RC circuit are used as the output end, and the circuit parameters satisfy the condition of τ > > > tp (the pulse width of the rectangular pulse), it becomes an integrating circuit. Since this circuit capacitor charges and discharges very slowly, the voltage ur

The above formula shows that the output voltage uo

The integrator is essentially a low-pass filter, and the longer the integration time, the lower the cutoff frequency.

4.time constant

In RC circuit, time constant=R*C;

In the RL circuit, the time constant = L/R.

In RC circuit:

Integrating circuit, the output of the circuit is both ends of the capacitor, and the time constant is large;

Differential circuit, the output of the circuit is both ends of the resistor, and the time constant is small.

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