How to calculate the delay time of an RC filter circuit with a combination of resistors and capacitors?

The calculation of the delay time of the RC filter circuit composed of resistors and capacitors mainly depends on the RC time constant (τ). The RC time constant is the product of resistance (R) and capacitance (C), i.e., τ=R × C. This time constant is of great significance in analyzing the transient response of RC circuits, including the charging and discharging processes of capacitors.
Calculation of RC delay time
In RC circuits, the delay time is usually closely related to the RC time constant. However, it should be noted that the specific calculation of delay time is not simply equal to the RC time constant, but depends on the specific configuration of the circuit and the characteristics of the signal.

Charging process: When the capacitor starts charging, its voltage will gradually increase over time until it reaches the power supply voltage. The time constant of the charging process is the RC time constant (τ=R × C). But this does not mean that it takes such a long time for the capacitor to be fully charged. In fact, the time required for the capacitor voltage to reach 63.2% of the power supply voltage (i.e. 1-1/e, where e is the base of the natural logarithm) is approximately equal to the RC time constant. To reach 95% of the power supply voltage (i.e. 1-1/e ²), approximately 4 RC time constants are required.
Discharge process: Similar to the charging process, the time required for a capacitor to discharge to 36.8% of its initial voltage (i.e. 1/e) is approximately equal to the RC time constant. To achieve complete discharge (i.e. voltage drops to 0V), theoretically it takes an infinite amount of time, but in practical applications, when the voltage drops to a negligible level without timing, it can be considered that the capacitor has discharged completely.

The practical application of delay time
In RC filtering circuits, delay time is crucial for understanding the transient response of the circuit and the way signals are processed. For example, when designing a low-pass filter, it is necessary to know the response speed of the circuit to signals of different frequencies in order to determine whether the circuit can meet specific filtering requirements. Similarly, when designing circuits that require precise control of signal delay, such as timing circuits, flip flops, etc., a deep understanding of the delay characteristics of RC circuits is also necessary.
matters needing attention

When calculating the RC delay time, it is important to ensure the accuracy of the resistance and capacitance values used, and to pay attention to the consistency of units (resistance in ohms Ω and capacitance in Farads F).
The RC delay time is an approximate value that provides a basic understanding of the transient response of a circuit. In practical applications, it may also be necessary to consider the impact of other factors (such as other components in the circuit, signal characteristics, etc.) on the delay time.
For complex RC circuits or circuits that require high-precision delay control, it may be necessary to use more complex circuit models or simulation tools for accurate analysis and design.

In summary, the delay time of the RC filter circuit can be approximately estimated by calculating the RC time constant, but attention should be paid to the actual meaning and influencing factors of the delay time. In practical applications, precise calculations and designs should be carried out according to specific needs.