RC Problem Example

The fall time of the RC circuit below is measured to be 2.6 ms. What is the value of C? What is the maximum digital frequency of this system?

We know:

$$\begin{array}{rl}{t}_f& =2.6=2.2\tau \\ \tau & =RC\\ tf& =2.2RC\\ C& =\frac{t_f}{2.2R}=\frac{2.6m}{2.2\times 10K}\\ & \\ C& =118\text{ nF}\end{array}$$

The maximum digital frequency would be charging from 0 to 1 to 0 to 1, etc.

We assume that we need at least one rise time and one fall time per cycle as the minimum. Any faster than that and there isn’t enough charging/discharging to detect the values as 0s and 1s. Thus, one period is:

$$T=t_f+t_r=4.4\tau$$

Thus:

$$f_{max}=\frac{1}{T}=\frac{1}{4.4\tau }=\frac{1}{4.4\times 2.6(m)}=192\text{ Hz}$$