EET222 Worksheet #1: Frequency Response and Gain
Help for this worksheet may be found in Chapter 14 of the textbook. This is not the only place to find
help. Don’t be afraid to explore.
Educational Objectives
• Calculate Gain as a ratio and in Decibel for Amplifiers
• Explain how cascading amplifiers affects gain as a ratio and in Decibel
• Interpret and describe what information is provided by frequency response graphs.
• Sketch Bode Plots
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If you want additional practice you should try these problems from the book
Gain: 4-14
Bode: 21-25,40,41
Risetime: 30-32,42,43,44
Discussion answers: All Job Interview Questions
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Questions
Question 1
What does it mean to speak of the gain of a circuit? This term is very commonly used when describing
amplifier circuits, but it may also be used to describe circuits containing nothing but passive components,
and are thus incapable of amplifying.
What letter is used to symbolize gain in mathematical equations?
Kuphaldt file 00672
Question 2
Calculate the voltage gain of this circuit, if R1 has a resistance of 8.1 kΩ and R2 has a resistance of
1.75 kΩ:
Vin
R1
R2
Vout
Kuphaldt file 00673
Question 3
Suppose an AC signal amplifier circuit has a voltage gain (ratio) of 5. That is, Vout is five times as large
as Vin :
Power source
Amplifier
Vin
Vout
Vout = 5(Vin)
Translate this voltage gain ratio into a decibel figure. Explain why the conversion from voltage gain
ratio to decibels is not the same as conversion of a power gain ratio to decibels.
Kuphaldt file 00828
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Question 4
Convert the following amplifier gains (either power, voltage, or current gain ratios) into gains expressed
in the unit of decibels (dB):
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AP = 25 ; AP (dB) =
AV = 10 ; AV (dB) =
AI = 37 ; AI(dB) =
AP = 150 ; AP (dB) =
AI = 41 ; AI(dB) =
AV = 3.4 ; AV (dB) =
AP = 18 ; AP (dB) =
AV = 100 ; AV (dB) =
Kuphaldt file 02447
Question 5
Convert the following amplifier gains between decibels and (unitless) ratios as necessary:
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AV = 14.1 dB ; AV (ratio) =
AI = 202 ; AI(dB) =
AP = 15 dB ; AP (ratio) =
AI = 33 ; AI(dB) =
AP = 49 dB ; AP (ratio) =
AV = 57 ; AV (dB) =
AP = 8.8 dB ; AP (ratio) =
AV = 30 ; AV (dB) =
Kuphaldt file 02449
Question 6
Calculate the overall voltage gain of this cascaded amplifier circuit, where the output of one voltage
amplifier feeds into the input of another:
Power source
Power source
Amplifier
Amplifier
Vin
Vout
AV = 12
AV = 2
Also, convert the voltage gains of each amplifier into units of decibels, then convert the overall voltage
gain ratio into units of decibels as well.
What do you notice about the overall gain of this circuit in relation to the individual amplifier gains,
compared as ratios versus compared as decibel figures?
Kuphaldt file 02535c
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Question 7
In this circuit, one amplifier feeds into an attenuator circuit, which then feeds into a second amplifier
stage. Calculate the ”gain” of the attenuator, and then calculate the overall voltage gain of this three-stage
circuit:
Power source
Power source
Attenuator
1 kΩ
Amplifier
Amplifier
Vin
Vout
1 kΩ
AV = 5
AV = 4
AV = ???
Also, convert the voltage gains of each stage into units of decibels, then convert the overall voltage gain
ratio into units of decibels as well.
What do you notice about the overall gain of this circuit in relation to the individual amplifier gains,
compared as ratios versus compared as decibel figures?
Kuphaldt file 02536
Question 8
Calculate the necessary gain of the second-stage amplifier to give the whole circuit a voltage gain of 25
decibels, then translate all decibel figures into gain ratios:
Power source
Power source
Amplifier
Amplifier
Vin
Vout
AV = 18 dB
AV = ???
AV (overall) = 25 dB
Kuphaldt file 02537
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Question 9
Most of the simple amplifiers you will be initially studying tend to lose gain as the frequency of the
amplified signal increases. This loss of gain is sometimes quantified in terms of rolloff, usually expressed in
units of decibels per octave (dB/octave) or decibels per decade (dB/decade).
What, exactly, is ”rolloff?” What is an ”octave,” in the context of the units of measurement used to
specify rolloff? What is a ”decade” in the context of the units of measurement used to specify rolloff? Why
would rolloff be important to a technician or engineer?
Kuphaldt file 01247 ch16007
Question 10
An important performance parameter for amplifier circuits is bandwidth. Explain what ”bandwidth”
means, and what factor(s) limit the bandwidth for electronic amplifiers.
Kuphaldt file 02562
Question 11
Draw the ideal bode plot of a LT1115 operational amplifier. This is a DC amplifier with a maximum
gain of 20x106 . If has a cutoff frequency of 3.5Hz and rolls-off at 20dB per decade. (Make sure you draw
this on Semilog Paper)
What is the ordinary gain at 400Hz?
file ch16002
Question 12
For the circuit shown below create a bode plot. Make sure you create this on semilog paper.
4.7kΩ
+
+
Vin
-
22pF
Vout
-
Additional Discussion
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What is the cutoff frequency of this circuit?
How does the cutoff frequency compare to the half power or 3dB frequency?
What does it mean if the current frequency is at the half power or 3dB frequency?
What is the advantage of using semi-log paper?
Should I use semi-log paper if I wanted to plot normal gain instead of dB?
ch16006
Question 13
You wish to experimentally determine the bandwidth of a dc amplifier in the EET lab. You have access
to the dc amplifier and all of the standard bench equipment that we have in the lab. Describe how you
would find the bandwidth for this amplifier.
What makes an amplifier a DC amplifier?
file ch16001
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Question 14
A Bode plot of an unknown amplifier system is shown below:
ch16004 Magnitude Bode Response
40
20
Mag (dB)
0
-20
-40
-60
-80
1e+0
1e+1
1e+2
1e+3
Frequency (Hz)
1e+4
1e+5
1e+6
From this graph answer the following questions about the system:
a What is the normal or ratio gain of this system at DC?
b What is the dB gain at 2kHz?
c What is the rolloff at 2kHz?
d What is the ratio gain at 30kHz?
e What is the rolloff at 30kHz?
f What frequency has a gain of 1?
g According to this graph what would you say the cutoff frequency is?
h At the cutoff frequency, what gain does the graph show, in dB?
i At the cutoff frequency what is the actual gain in dB and normal ratio?
j This graph is made by cascading two amplifiers. What is the gain of each amplifier and the cutoff
frequency of each amplifier? Sketch a block diagram of this system.
file ch16004
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Question 15
The data sheet for the LM741A lists a rise time of .25us, while the LM741C lists a rise time of .3us.
Which version of the LM741 has a larger bandwidth?
Additional Discussion
• The typical Bandwidth for a LM741A is listed as 1.5MHz. Does this conflict with the stated rise time?
file ch16003
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Answers
Answer 1
”Gain” (A) refers to the ratio of output signal compared to input signal.
Answer 2
AV = 0.178
Follow-up question: how does this gain figure (AV ) relate to the ”voltage divider formula”?
ER = Etotal
R Rtotal
Answer 3
AV = 13.98 dB
Answer 4
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AP = 25 ; AP (dB) = 13.98 dB
AV = 10 ; AV (dB) = 20 dB
AI = 37 ; AI(dB) = 31.36 dB
AP = 150 ; AP (dB) = 21.76 dB
AI = 41 ; AI(dB) = 32.26 dB
AV = 3.4 ; AV (dB) = 10.63 dB
AP = 18 ; AP (dB) = 12.55 dB
AV = 100 ; AV (dB) = 40 dB
Answer 5
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AV = 14.1 dB ; AV (ratio) = 5.07
AI = 202 ; AI(dB) = 46.1 dB
AP = 15 dB ; AP (ratio) = 31.62
AI = 33 ; AI(dB) = 30.37 dB
AP = 49 dB ; AP (ratio) = 79,432
AV = 57 ; AV (dB) = 35.12 dB
AP = 8.8 dB ; AP (ratio) = 7.59
AV = 30 ; AV (dB) = 29.54 dB
Answer 6
Cascaded voltage gains expressed as ratios:
AV = 12 × 2 = 24
Cascaded voltage gains expressed a decibel figures:
AV = 21.58 dB + 6.02 dB = 27.6 dB
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Answer 7
Cascaded voltage gains expressed as ratios:
AV = 5 ×
1
× 4 = 10
2
Cascaded voltage gains expressed a decibel figures:
AV = 13.98 dB + (−6.02 dB) + 12.04 = 20 dB
Answer 8
• Stage 1 gain = 18 dB = 7.94
• Stage 2 gain = 7 dB = 2.24
• Overall gain = 25 dB = 17.8
Answer 9
Most amplifiers’ frequency responses resemble that of low-pass filters. ”Rolloff” is the term used to
denote the steepness of the amplifier’s Bode plot as it attenuates the amplified signal at ever-increasing
frequencies.
An ”octave” denotes a doubling of signal frequency. This unit applies well to logarithmic-scale Bode
plots. A ”decade” denotes a 10x change in frequency.
Answer 10
Bandwidth is the measure of the signal frequency range that an amplifier can effectively handle while
maintaining usable gain:
Bandwidth
Amplifier
gain
Signal frequency
Rolloff at the high-frequency end is largely due to the Miller effect, while rolloff at the low-frequency
end is usually due to coupling capacitors in the circuit.
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Answer 11
ch16002 Magnitude Bode Response
160
140
Mag (dB)
120
100
80
60
1e+0
1e+1
1e+2
Frequency (Hz)
1e+3
1e+4
At 400Hz the gain is 105dB or 178V/V.
Answer 12
ch16006 Magnitude Bode Response
0
-10
Mag (dB)
-20
-30
-40
-50
-60
1e+4
1e+5
1e+6
1e+7
1e+8
1e+9
Frequency (Hz)
As far as additional discussion: The cutoff frequency is 1.54MHz. This is the same as the 3dB frequency
or half power frequency. For discussion in class be prepared to explain what all of these terms mean. For
plotting normal gain use log-log paper. Why do you think this is?
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Answer 13
There are multiple ways to approach this problem. I am looking for what equipment you will use, how
you will set it up, and what measurement you will take. Bandwidth is determined by when the gain is -3dB
from max gain. Remember that gain is the ratio of output to input.
DC amplifiers amplify AC and DC signals. They can operate all the way to down to 0Hz input frequency.
Answer 14
a 40dB=100
b @2kHz AvdB ≈ 15dB and rolloff is -20dB/decade
d @30kHz AvdB ≈ −13dB, Av=.223, rolloff is -40dB/decade
f Av=1 when f=10kHz
g fc=100Hz
h 40dB
i Actual gain is 37dB or 70.7.
j No answer given, this is for discussion. Lots of possible answers.
Answer 15
Bandwidth LM741A = 1.40MHz while the Bandwidth for the LM741C=1.17MHz.
Kuphaldt, Tony. ”Socratic Electronics.” Socratic Electronics. Ibiblio.org, n.d. Web. 28 Dec. 2014.
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