Prelab 7: Frequency Response
Name:
Lab Section:
i(t)
C
v1 (t)
v2 (t)
A
Figure 1: Amplifier with a “Miller” capacitor
The Miller effect plays an important role in determining the poles of an amplifier. If there is gain, A,
across the capacitor, C, as shown in Figure 1, then the current across C can be written as:
d
d
(v1 (t) − v2 (t)) = C dt
(v1 (t) − Av1 (t))
i(t) = C dt
By distributing the derivative, this simplifies to:
d
i(t) = C(1 − A) dt
v1 (t)
Therefore, the equivalent capacitance looking into v1 (t) is the capacitance C multiplied by (1 − A). If the
gain, A, is large enough, this Miller effect can make the capacitor dominate over other capacitances and
thus, contribute to the dominantpole of the amplifier. Similarly, the equivalent capacitance looking into
1
v2 (t) can be derived as C 1 − A
.
1. For the common emitter amplifier shown in Figure 2, derive/state expressions for the two poles of
vout /vin in terms of Cµ , Cπ , gm , RS , rπ , and/or ro . (Remember to use the Miller approximation.)
Fill in your answers in the designated boxes. Keep in mind that these expressions will later help you
predict and understand the results of the lab experiment.
1
2
VCC = 5 V
RC
0.25 mA
vOUT
−
VBIAS
+
−
vin
+
RS
Figure 2: Common emitter amplifier. Note that this amplifier has negative gain.
ωp1 =
ωp2 =
2. If RS = 51 Ω, RC = 10 kΩ, Cµ = 11 pF, Cπ = 25 pF, gm = 3 mS, rπ = 10 kΩ, and ro = 100 kΩ, what
are the poles of this amplifier? Please provide numerical answers.
ωp1 =
ωp2 =
3. What will happen to the poles if a capacitor CM is added across the base collector junction?
3
4. SPICE
• Construct the common emitter amplifier circuit shown in Figure 2 in SPICE. Use VBIAS = 0.58 V,
RS = 51 Ω, and RC = 10 kΩ.
• Use the 2N4401 SPICE model provided on the course website.
• Perform an AC analysis of the circuit from 100 Hz to 10 GHz in HSPICE.
• Also perform a poles/zeros analysis using the .pz command. The results of this command should
appear in the output text file. No need to print out the whole output file, just write down the
values below. Note: If necessary, refer to the appendix of the HSPICE Tutorial for instructions
on how to use poles/zeros analysis.
• Use Awaves to generate Bode plots (both magnitude and phase) for vout /vin . Attach the Bode
plots to this prelab worksheet. Do the results agree with your hand calculations (check the pole
frequencies)?
c
University
of California, Berkeley 2008
Reproduced with Permission
Courtesy of the University of California, Berkeley and of Agilent Technologies, Inc.
This experiment has been submitted by the Contributor for posting on Agilents Educators Corner. Agilent has not tested it. All who offer or perform this experiment do so solely at their own risk. The Contributor
and Agilent are providing this experiment solely as an informational facility and without review.
NEITHER AGILENT NOR CONTRIBUTOR MAKES ANY WARRANTY OF ANY KIND WITH
REGARD TO THIS EXPERIMENT, AND NEITHER SHALL BE LIABLE FOR ANY DIRECT, INDIRECT, GENERAL, INCIDENTAL, SPECIAL OR CONSEQUENTIAL DAMAGES IN CONNECTION
WITH THE USE OF THIS EXPERIMENT.
Experiment 7: Frequency Response
1
Objective
You have already seen the performance of several BJT amplifiers. Even though they were each designed to
operate well at certain small-signal frequencies, there is a frequency limit imposed on each of them by the
innate parasitic capacitances of the BJTs. In this lab, you will observe how an amplifier responds to different
frequencies as well as the effects of external capacitative loads and innate parasitic capacitances.
2
Materials
The items listed in table 1 will be needed. Note: Be sure to answer the questions on the report as you proceed
through this lab. The report questions are labeled according to the sections in the experiment. CAUTION:
FOR THIS EXPERIMENT, THE TRANSISTORS CAN BECOME EXTREMELY HOT!!!
Component
2N4401 NPN BJT
10 kΩ resistor
1 kΩ resistor
51 Ω resistor
1 nF Capacitor
Quantity
1
1
1
1
1
Table 1: Components used in this lab
3
Procedure
The two following subsections are instructions on how to use the oscilloscope to make Bode magnitude and
phase measurements. Please use them as references.
3.1
Technique for Measuring Magnitude using the Oscilloscope
The following instructions assume you have an amplifier already built and that it has one input, vin , and
one output, vout . In addition, the input, vin , must be controlled by the function generator.
1. Use the function generator to create a sine wave with the frequency of your choice; this shall be the
vin for your circuit.
2. Also connect vin and vout to their respective channels on the oscilloscope. The following steps will
assume that vin is on Channel 2 and vout is on Channel 1.
3. Press the “Quick Measure” button in the MEASURE section. Next, select Channel 1 as the source and
P eak − P eak as the measurement. Now, press the third menu button that corresponds to Measure.
1
3
2
PROCEDURE
4. Repeat the previous step for Channel 2.
5. At the bottom of the screen, each peak-to-peak voltage will be displayed. Calculate
value should be the magnitude of the frequency response at the chosen frequency.
P k−P k(1)
P k−P k(2) ;
this
k−P k(1)
6. To obtain the magnitude in decibels, simply scale the logarithm of the magnitude by 20 (i.e. 20 log P
P k−P k(2) ).
7. Record this value on paper or in Windows Excel.
8. Repeat the same procedures again for a different frequency by simply changing the frequency setting
on the function generator.
9. When the desired frequency range has been swept, simply plot the values to acquire the magnitude
Bode plot.
3.2
Technique for Measuring Phase using the Oscilloscope
The following instructions assume you have an amplifier already built and that it has one input, vin , and
one output, vout . In addition, the input, vin , must be controlled by the function generator.
1. Use the function generator to create a sine wave with the frequency of your choice; this shall be the
vin for your circuit.
2. Also connect vin and vout to their own respective channels on the oscilloscope. The following steps will
assume that vin is on Channel 2 and vout is on Channel 1.
3. Press the “Quick Measure” button in the MEASURE section. Next, select Channel 1 as the source
and P hase as the measurement.
4. Adjust the “Settings” - this option opens up a new menu and is only availabe when P hase or Delay is
selected. Use this option to select the order of comparison (i.e. the phase of Source 1 relative to Source
2 or vice versa). For this example, set Channel 1 for the first source and Channel 2 for the second.
5. When finished making adjusts, go back to the previous menu and press the third menu button that
corresponds to Measure.
6. At the bottom of the screen, the phase difference should be displayed. This value is the phase of the
frequency response at the chosen frequency.
7. Record this value on paper or in Windows Excel.
8. Repeat the same procedures again for a different frequency by simply changing the frequency setting
on the function generator.
9. When the desired frequency range has been swept, simply plot the values to acquire the phase Bode
plot.
3.3
IMPORTANT FACTS
1. Since the oscillscope can simultaneously display multiple measurements, you can easily conduct the
Bode magnitude and phase measurements in one experiment run. All you have to do is setup the equipment as mentioned above to measure both magnitude and phase. Then, simply record the magnitude
and phase values while sweeping through the frequency range using the function generator.
2. Also, autoscale does not work very well at high frequencies. For such cases, you must manually scale
the vertical and horizontal axes as well as use the averaging feature. For a review of how to do so,
please see the oscilloscope tutorial.
3. As a reminder, the output impedance of the function generator is mismatched from the input impedances
of the amplifiers in this lab. Thus, the actual delivered voltage is doubled the amount displayed on
function generator. FOR THIS LAB, ALL LISTED VOLTAGES ARE THE ACTUAL DELIVERED
VOLTAGES (NOT THE ONE DISPLAYED ON THE FUNCTION GENERATOR).
3
3
PROCEDURE
3.4
Frequency Response of a Common Emitter Amplifier
VCC
RC
IBIAS
vOUT
−
VBIAS
+
−
vin
+
RS
Figure 1: Common emitter amplifier test setup
1. Construct the common emitter amplifier as shown in Figure 1. Use a RC = 10 kΩ, RS = 51 Ω, and
VCC = 5 V.
2. For the input signal, use a 25 mV peak-to-peak sine wave with a DC offset of 580 mV. This signal is
both VBIAS and vin combined, and will be referred to as vIN . Note: You may notice some nonlinear
effects on the output waveform. This is due to the high input signal amplitude that we are using. We
chose this amplitude to avoid noise from the oscilloscope interfering with the Bode plot measurements.
3. What are the respective values of IBIAS and VOUT (the DC voltage at the output)?
4. Using the oscilloscope, plot vIN on Channel 2 and vOUT on Channel 1. Make sure to transfer the
waveforms over to the lab report.
5. At 1 kHz, what are the magnitude and phase of vout /vin as measured from the oscilloscope?
6. Using the techniques mentioned above, create the Bode magnitude and phase plots. To save time,
sweep the frequency in decades first (i.e. increment by factors of 10) and do not exceed 2 MHz for this
circuit. Then, take more measurements in frequency ranges where the poles are located.
7. Find the frequency where the gain decreases from its DC value by 3 dB; this frequency is called the
dominant pole of the amplifier. What is the phase at this frequency? Is the phase consistent with the
magnitude? (Recall that at the −3 dB point, the phase should drop from its DC value by 45 degrees.)
3.5
Miller Effect
1. Let us evaluate the impact of the Miller effect by adding a 1 nF capacitor, CM , as shown in Figure 2.
2. Create the Bode magnitude and phase plots. Do not exceed 500 kHz. Attach the plots to the lab
report.
3. How does the dominant pole of this amplifier compare to the dominant pole of the previous amplifier?
Is this expected?
4. In this amplifier, we are using a 1 nF capacitor to simulate a large base-collector capacitor (Cµ ). If we
are to design an amplifier with high bandwidth, is a transistor with a large Cµ desirable?
3
4
PROCEDURE
VCC
RC
IBIAS
vOUT
CM
−
VBIAS
+
−
vin
+
RS
Figure 2: Miller capacitor test setup
VCC
RC
IBIAS
vOUT
−
VBIAS +
−
vin
+
RS
CM
Figure 3: Output capacitance test setup
3.6
Output Capacitance
1. Let us examine the impact of output capacitance on a common emitter amplifier: reposition capacitor
CM , from the previous section, by placing it at the output (see Figure 3).
2. Create the Bode magnitude and phase plots. Do not exceed 500 kHz. Attach the Bode plot to the lab
report.
3. How does the dominant pole of this amplifier compare to the respective poles of the previous two
amplifiers? Is this result agreeable?
3.7
Common Collector Amplifier
1. The common collector amplifier is a wide bandwidth amplifier. Let us examine the frequency response
of this amplifier by first building the common collector amplifier shown in Figure 4. Let RS = 51 Ω,
RE = 1 kΩ, and VCC = 5 V.
2. Use a 2 Vpp input signal that has a DC offset of 3 V.
3. Create the Bode magnitude and phase plots. Attach the Bode plots to the lab report. Keep in mind
that the breadboard has a parasitic capacitance that will start to deform the output signal when the
frequency goes beyond 1 MHz. To observe this effect, plot the output voltage using the oscilloscope
and set the input frequency beyond 1 MHz. Because of this parasitic capacitance, the results of these
3
5
PROCEDURE
VCC
−
VBIAS
+
−
vin
+
RS
vOUT
RE
Figure 4: Common collector amplifier test setup
experiments are only an approximation. Note: Due to the limitations of the lab equipment, the pole
frequency might not be attainable. If this is the case, just mention that you cannot find the pole.
4. How does the bandwidth of this amplifier compare to the respective bandwidths of the previous amplifiers? Note: If you could not measure the dominant pole, a qualitative answer is sufficient (i.e. smaller,
larger, much larger).
c
University
of California, Berkeley 2008
Reproduced with Permission
Courtesy of the University of California, Berkeley and of Agilent Technologies, Inc.
This experiment has been submitted by the Contributor for posting on Agilents Educators Corner. Agilent has not tested it. All who offer or perform this experiment do so solely at their own risk. The Contributor
and Agilent are providing this experiment solely as an informational facility and without review.
NEITHER AGILENT NOR CONTRIBUTOR MAKES ANY WARRANTY OF ANY KIND WITH
REGARD TO THIS EXPERIMENT, AND NEITHER SHALL BE LIABLE FOR ANY DIRECT, INDIRECT, GENERAL, INCIDENTAL, SPECIAL OR CONSEQUENTIAL DAMAGES IN CONNECTION
WITH THE USE OF THIS EXPERIMENT.
Report 7: Frequency Response
Name:
Lab Section:
3.4.3 What are the respective values of IBIAS and VOUT (the DC voltage at the output)?
IBIAS =
VOUT =
3.4.4 Sketch the waveforms of vIN and vOUT .
3.4.5 At 1 kHz, what are the magnitude and phase of vout /vin as measured from the oscilloscope?
|vout /vin |dB =
∠vout /vin =
1
2
3.4.6 Attach the Bode plots to the lab report.
3.4.7 What is the frequency at which the gain drops by 3 dB? What is the phase at this frequency? Is the
phase consistent with the magnitude?
f−3 dB =
∠vout /vin |f−3 dB =
3.5.2 Attach the Bode plots to the lab report.
3.5.3 How does the dominant pole of this amplifier compare to the dominant pole of the previous amplifier?
Is this expected?
3.5.4 If we are to design an amplifier with high bandwidth, is a transistor with large Cµ desirable?
3.6.2 Attach the Bode plots to the lab report.
3.6.3 How does the dominant pole of this amplifier compare to the respective poles of the previous two
amplifiers? Is this result agreeable?
3.7.3 Attach the Bode plots to the lab report.
3.7.4 How does the bandwidth of this amplifier compare to the respective bandwidths of the previous amplifiers? Note: If you could not measure the dominant pole, a qualitative answer is sufficient (i.e. smaller,
larger, much larger).
c
University
of California, Berkeley 2008
Reproduced with Permission
Courtesy of the University of California, Berkeley and of Agilent Technologies, Inc.
3
This experiment has been submitted by the Contributor for posting on Agilents Educators Corner. Agilent has not tested it. All who offer or perform this experiment do so solely at their own risk. The Contributor
and Agilent are providing this experiment solely as an informational facility and without review.
NEITHER AGILENT NOR CONTRIBUTOR MAKES ANY WARRANTY OF ANY KIND WITH
REGARD TO THIS EXPERIMENT, AND NEITHER SHALL BE LIABLE FOR ANY DIRECT, INDIRECT, GENERAL, INCIDENTAL, SPECIAL OR CONSEQUENTIAL DAMAGES IN CONNECTION
WITH THE USE OF THIS EXPERIMENT.