Lab8
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EE 97 Spring 2023
Tuesday 3:00-5:45 PM
Lab #8: Frequency Response
Huy Nguyen
Partner: Edward Nguyen
Submission Date: 04/21/2023
Lab #8: Frequency Response
Learning Objectives
After completing this lab, students should be able to
• Explain the definition of the frequency response of a circuit.
• Experimentally determine a circuit’s frequency response
• Present a circuit’s frequency response data using a Bode plot.
Experiment 1:
In this experiment, we will determine the voltage gain of this amplifier and its maximum output power to the speaker.
1.
First, we connected the output of the function generator to the input of the R-CH amplifier. The red wire is the input to the R-CH amplifier.
2. Then, connect scope probe 1 to the input of the amplifier and probe 2 to the output of the amplifier.
Figure 1 Amplifier setup.
2.
Turn the volume control of the amplifier to the maximum. Set the function generator frequency to 1kHz and the peak-to-peak output amplitude to100mV.
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Figure 2 The function generator setup.
4. Determine the voltage gain of the amplifier by dividing the output amplitude by the input amplitude. V
out
÷V
in
.
𝑇ℎ? ??????? ??𝑖? =
?
???
?
𝑖?
=
5.480 ?
0.80 ?
= 6.85
5. We gradually increased the function generator output amplitude until the output waveform is just 'clipped' (as shown in Figure 4) and recorded the peak-to-peak saturation level. ?
?𝑒𝑎𝑘−??−?𝑒𝑎𝑘
= 5.480 ? ?
?𝑒𝑎𝑘
= 2.74? ?
?𝑀?
= 0.707 × 2.74 ? = 1.94 ?
Figure 3 Measuring Vpeak-to-peak value.
6. Finally, we used the formula Power=V
rms
2
/Z to determine the output power to the speaker at this level of output. Z in this equation represents the impedance of the speaker and its value is 4Ω.
𝑃???? =
?
?𝑀?
2
?
=
(1.94 ?)
2
4 Ω
= 0.94 ?
Explanation: I can't entirely agree with the claim. The actual power calculated based on the obtained data is only 0.94W, which indicates that the amplifier may not be able to deliver the claimed maximum power.
Experiment 2 (Frequency Response):
In this experiment, we will determine the frequency response of the amplifier. The scope and function generator connections remain the same as in Experiment 1 above.
1.
First, set the function generator frequency to 1kHz and peak-to-peak amplitude to 100mV. Adjust the scope so that both input and output signals are stable, and the gain and the phase shift can be read out from the scope screen as shown in Figure 1.
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Figure 4 The output waveform.
2.
To measure phase shift, first, we measured the time difference ∆T between the two signals where they cross the reference line and are either both rising or both falling (see Figure 5). Next measure the cycle time of the signal, T.
𝑇ℎ? ?ℎ??? ????? 𝜑 ??? ?? ?????????? ?? 𝜑 = 360 ×
∆𝑇
𝑇
= 360 ×
13.5??
50.0??
= 97.2 ??????? 3.
We repeated the above step with several input frequencies ranging from 20Hz to 300kHz and recorded the gain and the phase shift in a data table.
Low Frequency Data table:
Low Frequency Delta T (mS) T (mS) Phase V
out
(V) Gain 20 13.8ms 50.0ms 99.4 o 0.27V 2.7 40 5.4ms 25.0ms 77.8 o
0.48V 4.8 60 3.2ms 16.5ms 69.8 o
0.62V 6.2 80 2.1ms 12.5ms 60.5 o
0.74V 7.4 100 1.6ms 10.0ms 57.6 o
0.88V 8.8 120 1.2ms 8.3ms 53.7 o
1.06V 10.6 140 900us 7.2ms 45.0 o
1.12V 11.2 160 760us 6.3ms 43.4 o
1.19V 11.9 180 600us 5.6ms 38.6 o
1.21V 12.1 200 500us 5.0ms 36.0 o
1.28V 12.8 High Frequency Data table:
High Frequency Delta T (
𝝁𝒔
) T (
𝝁𝒔
) Phase V
out
(V) Gain 20k 1.00 50.0 -7.2 o
1.21 12.1 40k 1.18 28.0 -15.2 o
1.09 10.9 60k 1.21 17.9 -24.3 o
0.90 9.00
80k 1.24 13.4 -33.3 o
0.87 8.70 100k 1.29 10.9 -42.6 o
0.85 8.50 120k 1.16 9.3 -44.9 o
0.81 8.10 140k 1.10 8.2 -48.3 o
0.75 7.50 160k 0.90 7.4 -43.8 o
0.72 7.20 180k 0.79 6.3 -45.1 o
0.69 6.90 200k 0.74 5.5 -48.4 o
0.64 6.40 220k 0.65 5.1 -45.9 o
0.60 6.0 240k 0.68 4.8 -51.0 o
0.56 5.60 260k 0.70 4.7 -53.6 o
0.53 5.30 280k 0.68 3.5 -69.9 o
0.49 4.90 300k 0.65 2.9 -80.7 o
0.46 4.60 4.
The "Bandwidth" of an amplifier is defined as the range of frequency es in which the gain is within 70.7% of the nominal gain (the gain at 1kHz for this amplifier) as shown in Figure 𝑇ℎ? ???????? ???𝑖??? ??𝑖? = 12.8
70.7% ?? ?ℎ? ???𝑖??? ??𝑖? = 12.8 × 70.7% = 9.1
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Comparing the data from the table, we can see that the bandwidth of this amplifier starts from 120Hz to 40kHz. Based on the data, I disagree with the manufacturer of this amplifier claims that this amplifier's bandwidth is from 60Hz to 20kHz.
5.
Sketch the bode plot.
Experiment 3
1.
First, we set the function generator's output amplitude to 100mV and set the function generator's sweep function parameters to the following values:
Starting frequency = 10Hz Stop frequency = 1MHz.
Sweep time = 1 second. Sweep Mode = Log.
Figure 5 Set up the Function Generator.
2.
The amplifier output waveform on the scope (only this channel) and use the SYNC output from the function generator for triggering through the Aux-In connector in the trigger group.
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Figure 6 The amplifier output waveform on the scope.
3.
Label the frequencies at the bandwidth limits.
?
?𝑒𝑎𝑘
= 940??
?
?𝑀?
= 940?? × 0.707 = 664.6??
𝑇ℎ? ?????𝑖??ℎ ?𝑖?𝑖? 𝑖? ???? 100𝐻𝑧 ?? 80?𝐻𝑧.
Figure 7 The bandwidth limit is from 100Hz to 80kHz.
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