# 15.5: Procedure

## 15.5.1: Low Q Circuit

1. Using Figure 15.4.1 with R = 470 $$\Omega$$, L = 10 mH, and C = 10 nF, determine the theoretical resonance frequency and Q, and record the results in Table 15.6.1. Based on these values determine the upper and lower frequencies defining the bandwidth, $$f_1$$ and $$f_2$$, and record them in Table 15.6.1.

2. Build the circuit of Figure 15.4.1 using R = 470 $$\Omega$$, L = 10 mH and C = 10 nF. Place a probe across the resistor. Set the output of the generator to a 1 V p-p sine wave. Set the frequency to the theoretical resonance frequency of Table 15.6.1. 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.

3. Adjust the frequency in small amounts, up and down, until the maximum voltage is found. This is the experimental resonance frequency. Record it in Table 15.6.1. Note the amplitude (it should be approximately equal to the source voltage of 1 V p-p). Sweep the frequency above and below the resonance frequency until the experimental $$f_1$$ and $$f_2$$ are found. These will occur at a voltage amplitude of approximately 0.707 times the resonant voltage (i.e., the half-power points). Record these frequencies in Table 15.6.1. Also, determine and record the experimental Q based on the experimental $$f_0$$, $$f_1$$, and $$f_2$$.

4. Transcribe the experimental frequencies of Table 15.6.1 to the top three entries of Table 15.6.2. For all of the frequencies in Table 15.6.2, measure and record the voltage across the resistor. Also measure and record the inductor and capacitor voltages. Note that the inductor and capacitor will have to be swapped with the resistor position in order to maintain proper ground reference with the oscilloscope.

5. Based on the data from Table 15.6.2, plot $$V_R$$, $$V_C$$, and $$V_L$$ as a function of frequency.

6. Change R to 47$$\Omega$$ and repeat steps 1 through 5 but using Tables 15.6.3 and 15.6.4 for high Q.

## 15.5.2: Computer Simulation

7. Build the circuit of Figure 15.4.1 in a simulator. Using AC Analysis, plot the voltage across the resistor from 1 kHz to 100 kHz for both the high and low Q cases and compare them to the plots derived from Tables 15.6.2 and 15.6.4. Be sure to include the 50 $$\Omega$$ source resistance and coil resistance in the simulation.