12.5: Procedure

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1. Typical function generators have a 50 \(\Omega\) internal impedance. These are not shown in the circuit of Figure 12.4.1. To test the Superposition Theorem, sources \(E1\) and \(E2\) will be examined separately and then together.

12.5.1: Source One Only

2. Consider the circuit of Figure 12.4.1 with C = 100 nF, L = 10 mH, R = 1 k\(\Omega\), using only source \(E1\) = 2 V p-p at 1 kHz and with source \(E2\) replaced by its internal impedance of 50 \(\Omega\). Using standard series-parallel techniques, calculate the voltages across \(E1\), R, and \(E2\). Remember to include the 50 \(\Omega\) internal impedances in the calculations. Record the results in Table 12.6.1.

3. Build the circuit of Figure 12.4.1 using C = 100 nF, L = 10 mH, and R = 1 k\(\Omega\). Replace \(E2\) with a 50 \(\Omega\) resistor to represent its internal impedance. Set \(E1\) to 2 V p-p at 1 kHz, unloaded. Make sure that the Bandwidth Limit of the oscilloscope is engaged for both channels. This will reduce the signal noise and make for more accurate readings. Place probe one across \(E1\) and probe two across R. Measure the voltages across \(E1\) and R, and record in Table 12.6.1. Record a copy of the scope image. Move probe two across \(E2\) (the 50 \(\Omega\)), measure and record this voltage in Table 12.6.1.

12.5.2: Source Two Only

4. Consider the circuit of Figure 12.4.1 using only source \(E2\) = 2 V p-p at 10 kHz and with source \(E1\) replaced by its internal impedance of 50 \(\Omega\). Using standard series-parallel techniques, calculate the voltages across \(E1\), R, and \(E2\). Remember to include the 50 \(\Omega\) internal impedances in the calculations. Record the results in Table 12.6.2.

5. Replace the 50 \(\Omega\) with source \(E2\) and set it to 2 V p-p at 10 kHz, unloaded. Replace \(E1\) with a 50 \(\Omega\) resistor to represent its internal impedance. Place probe one across \(E2\) and probe two across R. Measure the voltages across \(E2\) and R, and record in Table 12.6.2. Record a copy of the scope image. Move probe two across \(E1\) (the 50 \(\Omega\)), measure and record this voltage in Table 12.6.2.

12.5.3: Sources One and Two

6. Consider the circuit of Figure 12.4.1 using both sources, \(E1\) = 2 V p-p at 1 kHz and \(E2\) = 2 V p-p at 10 kHz. Add the calculated voltages across \(E1\), R, and \(E2\) from Tables 12.6.1 and 12.6.2. Record the results in Table 12.6.3. Make a note of the expected maxima and minima of these waves and sketch how the combination should appear on the scope

7. Replace the 50 \(\Omega\) with source \(E1\) and set it to 2 V p-p at 1 kHz, unloaded. Both sources should now be active. Place probe one across \(E1\) and probe two across R. Measure the voltages across \(E1\) and R, and record in Table 12.6.3. Record a copy of the scope image. Move probe two across \(E2\), measure and record this voltage in Table 12.6.3.

12.5.4: Computer Simulation

8. Build the circuit of Figure 12.4.1 in a simulator. Using Transient Analysis, determine the voltage across the resistor and compare it to the theoretical and measured values recorded in Table 12.6.3. Be sure to include the 50 \(\Omega\) source resistances in the simulation.