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 theLCRcircuit 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 small

For large : .

For the corner frequency: .

For ,

.

For ,

Figure 3.11 is a sketch of the transfer functions.

Figure 3.11:Sketch of the transfer functions for the above circuit.

Example:

- 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?
For large

For small

- 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.

Tue Jul 13 16:55:15 EDT 1999