A high-pass filter acts as an approximate differentiator at low frequencies. Consider
and differentiate to obtain
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:
- the corner frequency,
Treating the circuit like a voltage divider, the transfer function is
For large .
For the corner frequency .
Figure 3.4: Four-terminal network without resistance.
- the value of at the corner frequency.
At the corner frequency
- 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.