Capacitor charge/discharge time calculation

Before entering the subject, let's review the formula for calculating the charge and discharge time of the capacitor. Assume that the power supply vu is charging the capacitor C through the resistance R, and the v0 is the initial voltage value on the capacitor, VU is the voltage value after the capacitor is fully charged. If VT is the voltage value on the capacitor at any time t, the following formula can be obtained:

Vt = V0 + (VU-V0) * [1-exp (-T/RC)]

If the initial voltage on the capacitor is 0, the formula can be simplified:

Vt = VU * [1-exp (-T/RC)]

According to the above formula, because the exponent value may only be infinitely close to 0, but never equal to 0, it takes an infinite amount of time to fully fill the capacitor power.

When T = RC, VT = 0.63vu;

When T = 2rc, VT = 0.86vu;

When T = 3rc, VT = 0.95vu;

When T = 4rc, VT = 0.98vu;

When T = 5rc, VT = 0.99vu;

Visible, after 3 ~ After five RC instances, the charging process basically ends.

When the capacitor is fully charged, the power vu is short-circuited, And the capacitor C is discharged through R. T at any time, the voltage on the capacitor is:

Vt = VU * exp (-T/RC)

For a simple series circuit, the time constant is equal to the product of the resistance R and the capacitor C. However, in the actual circuit, the time constant RC is not so easy to calculate, for example ().

For (A), it would be difficult to calculate the time constant from the charging point of view. We may consider it from another point of view. We know that the time constant is only related to the resistance and capacitance, it has nothing to do with the power supply. For a circuit that is simply connected by a resistor R and a capacitor C, the charging and discharging time parameters are the same, all of which are RC, we can short-circuit the power supply to discharge the capacitor C1, as shown in (B), so that we can easily obtain the time constant:
T = rc = (R1 // R2) * C

Using the same method, the (a) circuit can be equivalent to the (B) discharge circuit form to obtain the time constant of the circuit:

T = rc = R1 * (C1 + C2)

Using the same method, the (a) circuit can be equivalent to the (B) discharge circuit form to obtain the time constant of the circuit:

T = rc = (R1 // R3 // R4) + R2) * C1

The RC calculation of the circuit time constant can be summarized as follows:

1) if the power supply in the RC Circuit is in the form of a voltage source, first "short-circuit" the power supply and keep its series internal resistance;

2) The circuit removed from the power supply is simplified into an RC discharge circuit in series of equivalent resistance R and equivalent capacitor C. The product of equivalent resistance R and equivalent capacitor C is the time constant of the circuit;

3) if the current source is used in the circuit, open the current source and keep its parallel internal resistance, and then find the time constant by simplifying the circuit;

4 ). when calculating the time constant, pay attention to the unit of each parameter. When the unit of resistance is "ohm" and the unit of capacitance is "Farah", the unit of the obtained time constant is "second ".

Due to the influence of parasitic parameters, it is difficult to calculate the time constant RC Based on the nominal values of each component in the RC Circuit under high frequency operation, we can use the curve Calculation Method Based on the charging and discharging characteristics of the capacitor. We have already introduced that when the capacitor is charged with a time constant RC, the voltage on the capacitor is equal to 0.63 times of the voltage of the charging power supply. When the discharge goes through a time constant RC, the voltage on the capacitor drops to 0.37 times of the power supply voltage.

As shown in, as shown in the experiment, the charging and discharging curve of the capacitor is drawn, and a charging and discharging tangent is made at the starting point. The intersection of the tangent and the horizontal axis is the time constant RC.