Analyses of Series and Parallel Resonant Filters

I. Objectives:

After completing this lab experiment using, you should be able to:

1. Build and test series resonant band-pass filters.

2. Build and test parallel resonant band-stop filters.

3. Calculate and measure the center frequency and bandwidth of series resonant band-pass filters

4. Calculate and measure the minimum output voltage for parallel resonant band-stop filters.

5. Use the Bode analyzer to observe and measure the frequency response of the filters.

II. Parts List:

1. Resistor 8 Ω, 10 Ω, 18 Ω, 100 Ω, 560 Ω, 1 kΩ.

2. Inductor 5 µH, 1.0 mH.

3. Capacitor 2.2nF (0.0022 µF), 150 pF

4. Voltage Power Source 10 VRMS.

5. Bode Plotter

III. Procedures:

Series Resonant Band-Pass Filter

Part I. Series Resonant Band-Pass Filter

1. Review the solution to Example 18-8 on pages 849-850 in your textbook.

2. Construct the circuit in Figure 1 in Multisim.

Diagram, schematic Description automatically generated

Figure 1. Series Resonant Band Pass Filter

3. Verify the following calculations for bandwidth from Example 18-8.

Calculate the resonant or center frequency, f0:

Calculate the inductive reactance, XL, at the center frequency f0:

Calculate the total circuit resistance:

Calculate the Q factor:

Finally, calculate the bandwidth, BW:

4. Measure the center frequency of the Series Resonant Band-Pass filter using the Bode plotter as shown in Figure 2.

Diagram Description automatically generated with medium confidence

Figure 2. Bode Plotter showing the Center or Resonant frequency

( Note: Connect the Bode Plotter as shown. Set the parameter as shown in the figure as well. Use Set… to set the resolution to 1000. Run the simulation. Use the cursor to find the maximum gain. This point of maximum gain is your center or resonant frequency (f0=107.4 kHz). Also note the gain at the center frequency (-0.828 dB). To find the bandwidth you will find the upper and lower critical frequencies where the gain is -3dB from the maximum. In this case we will record the frequencies where the gain is -0.828 dB – 3 dB = -3.828 dB.)

5. Measure the upper critical frequency as shown in Figure 3.

Graphical user interface, diagram Description automatically generated

Figure 3. Upper critical frequency, f1=116.39 kHz

6. Measure the lower critical frequency as shown in Figure 4.

Diagram, schematic Description automatically generated

Figure 4. Lower critical frequency, f2 = 98.924 Hz

7. Subtract the lower critical frequency from the upper critical frequency to find the bandwidth.

8. Record your findings in Table 1. (The first row is completed for you.)

9. Repeat steps 2-8 using a winding resistance of Rw = 18 Ω

RW

Calculated f0

Calculated BW

Measured f0

Upper Critical Frequency f1

Lower Critical Frequency f2

Measured BW f1-f2

10 Ω

107.3 kHz

17.5 kHz

107.4 kHz

116.39 kHz

98.824 kHz

17.47 kHz

18 Ω

107.3 kHz

18.76 kHz

107.399kHz

117.079kHz

98.342kHz

18.737kHz

Table 1. Resonant Frequency and Bandwidth for Band-pass filter

Parallel Resonant Band-Stop Filter

Part II. Parallel Resonant Band-Stop Filter

1. Review the solution to Example 18-12 on pages 855-856 in your textbook.

2. Construct the circuit in Figure 5 below in Multisim.

Diagram, schematic Description automatically generated

Figure 5. Parallel Resonant Band-Pass Filter

3. Verify the following calculations for bandwidth and minimum output voltage for the example below. The center frequency is:

At the center or resonant frequency:

Use voltage-divider to find the minimum output voltage (magnitude only).

4. Measure the output gain in dB at the center or resonant frequency using the Bode Plotter as shown in Figure 6.

Diagram Description automatically generated

Figure 6. Gain at Resonant Frequency

5. Calculate the minimum output voltage from the definition of voltage gain in decibels (VdB).

6. Record your results in Table 2. The first row is completed for you.

RL

Calculated Center Frequency

Measured Center Frequency

Calculated Vout(min)

Measured Vout(min)

560 Ω

5.81 MHz

5.808 MHz

1.18 V

1.18 V

1.0 kΩ

5.81 MHz

5.808 MHz

1.92V

1.94 V

Table 2. Calculated and Measured Minimum Output Voltage

7. Repeat steps 1-6 using RL = 1.0 kΩ.

IV. References:

Floyd, T. L., & Buchla, D. M. (2019). Principles of Electric Circuits (10th Edition). Pearson Education (US). https://bookshelf.vitalsource.com/books/9780134880068

National Instruments. (2019, April 3). Multisim Education Edition Version (14.2.0).

10