Consider the RCL circuits as shown in figure 3.9. Each has a low-frequency and high-frequency approximation. Considering the band-reject filter (figure 3.6d) we obtain for the transfer function
Figure 3.9: LCR filters: a) low-pass, b) high-pass, c) band-pass and d) band-reject.
The approximations are:
We notice a zero in the transfer function at . In the low-medium frequency range
for high-medium frequencies
Solving for the corner frequencies we have
Example: Sketch for the LCR circuit shown in figure 3.10 for the two conditions and . In each case, determine the values of at , , and , and label these points on the sketches.
Figure 3.10: LCR circuit with two components across the output.
The transfer function is
For large : .
For the corner frequency: .
Figure 3.11 is a sketch of the transfer functions.
Figure 3.11: Sketch of the transfer functions for the above circuit.
- Write an expression for the transfer function of the circuit shown in figure 3.12.
Figure 3.12: Circuit with components in parallel at the output.
- What phase shift is introduced by this filter at very small and very large frequencies?
- On a log-log scale, sketch and the phase shift as a function of .
For the corner frequency .
Figure 3.13: Transfer function and phase shift for the above circuit.