Approximate Differentiator

A high-pass filter acts as an approximate differentiator at low frequencies. Consider

and differentiate to obtain

We define

Again the filter attenuates the signal by 1/(RC).

Example: Write the transfer function for the network in figure 3.4 and from it find:

1. the corner frequency,

   Treating the circuit like a voltage divider, the transfer function is

   

   For .

   For large .

   For the corner frequency .

   Therefore

   

    
   Figure 3.4:  Four-terminal network without resistance.
   

2. the value of at the corner frequency.

   At the corner frequency

   

3. How many degrees of phase shift are introduced by this network just below and just above the corner frequency?

   Since is always real there is no phase shift.