Fig. 4.6 shows a passive twin T notch filter. You will create an AC sweep and plot the frequency response of the circuit.

1. Draw the circuit of the notch filter in Fig. 4.6. The V_AC source can be found in the source library.

2. Create a PSpice simulation profile to perform a logarithmic sweep from 1 Hz to 100 kHz in steps of 100 points per decade (Fig. 4.7).

3. Place a V_dB voltage marker on the output node, “out.” This will automatically calculate the output voltage in dB: PSpice > Markers > Advanced > dB Magnitude of Voltage (Fig. 4.8).

4. Run the simulation and you should see the notch filter response (Fig. 4.9). What we need to do now is to determine the frequency at the deepest part of the notch.

5. Turn on the cursor, Trace > Cursor > Display and place the cursor at the bottom of the notch. For a more accurate reading, zoom in towards the bottom of the trace, View > Zoom > Area or use the icons
Alternatively, you can use one of the cursor functions, Trace > Cursor > Min or .
The Probe Cursor box will display a notch frequency 53.703 Hz with an attenuation of −59.348 dB as seen in Fig. 4.10, depending on which software version you are using. In both software versions, the Probe Cursor box can be positioned anywhere in the Probe screen.

6. Restore the Probe display to its original size, View > Zoom > Fit
Select the trace name at the bottom of the display and press delete on the keyboard or select Trace > Delete all Traces. Now we are going to manually add the trace for the output voltage V(out).

7. Select Trace > Add Trace and the Add Traces window will appear as shown in Fig. 4.11.

8. The Add Traces window displays all the data for all the nodes and devices in the circuit. Uncheck the boxes for Currents and Power and in the list of Simulation Output Variables, scroll down and select the V(out) variable.
Click on OK.

9. The V(out) trace will be displayed in the Probe trace window. However, what we want is the voltage in dB. Select the trace name V(out) and press the delete key to remove the trace.

10. Select Trace > Add Trace and in the right-hand side of Add Traces under Analog Operators and Functions, select DB().
Then, as before, select V(out) from the list of Simulation Output Variables. At the bottom of the window in the Trace Expression box, you should see DB(V(out)). The DB function automatically calculates the DB of V(out). See Fig. 4.12.
Click on OK and you should see the trace shown in Fig. 4.13.

11. Repeat Step 5 to determine the depth of notch attenuation in dB.

4.3.1 Twin T notch filter

Fig. 4.14 shows the implementation of a notch filter which has a notch frequency given by

$f_{\mathrm{o}}=\frac{1}{2\pi \mathrm{RC}}$

Using only one value of resistor and one value of capacitor, the circuit in Fig. 4.14 can be implemented as shown in Fig. 4.15.

The parallel combination of the two capacitors is given by:

${\mathrm{C}}_{\mathrm{p}}=\mathrm{C}+\mathrm{C}=2\mathrm{C}$

The parallel combination of the resistors is given by:

${\mathrm{R}}_{\mathrm{p}}=\frac{\mathrm{R}\times \mathrm{R}}{\mathrm{R}+\mathrm{R}}=\frac{\mathrm{R}}{2}$

which conforms to the circuit implementation shown in Fig. 4.14.

For the notch filter in Fig. 4.6, R = 27 kΩ and C = 110n. Therefore, using Eq. (4.1), the notch frequency is given by:

$\begin{array}{l}{f}_{\mathrm{o}}=\frac{1}{2\pi \mathrm{RC}}\hfill \\ f_{\mathrm{o}}=\frac{1}{2\pi \times 27\times {10}^3\times 110\times {10}^{-9}}=53.6\mathrm{Hz}\hfill \end{array}$