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TUTORIAL AND
LAB GUIDE
DSOXBODE Bode Plot Training Kit
Using Keysight InfiniiVision X-Series Oscilloscopes
Creating gain and phase Bode plots based on the frequency response of electrical circuits — both
theoretical and measured in the lab — is typically a key part of the electrical engineering (EE) curriculum
in undergraduate studies. Many of Keysight Technologies’ InfiniiVision X-Series oscilloscopes support
automatic Bode plot measurements. Keysight also provides an optional Bode plot training kit
(DSOXBODE) to help engineering students learn about frequency response analysis measurements. This
training guide begins with background information on Bode plots, and then provides step-by-step
instructions on how to perform manual, as well as automatic Bode plot measurements using a Keysight
InfiniiVision X-Series oscilloscope along with the Bode plot training kit. If the Bode plot training kit is not
available in your EE teaching lab, you can easily create your own based on three passive devices
(resistor, capacitor, and inductor).
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Table of Contents
System requirements and prerequisites .................................................................................................................... 2
Frequency response analysis tutorial ........................................................................................................................ 3
Lab 1: Quick verification test of a bandpass filter ...................................................................................................... 6
Lab 2: Frequency response testing using traditional oscilloscope test methodology ................................................ 9
Lab 3: Automatic frequency response analysis of a bandpass filter ........................................................................ 12
Lab 4: Characterizing a low-pass filter ..................................................................................................................... 15
Summary .................................................................................................................................................................. 16
Related Literature ..................................................................................................................................................... 17
System requirements and prerequisites
The lab instructions in this document are based on the following Keysight InfiniiVision oscilloscopes and
required options.
• InfiniiVision 1000G X-Series oscilloscope (The “G” suffix in the model number indicates the scope
is preconfigured with the built-in waveform generator, which is required.) Frequency response
analysis (FRA) is standard in all “G” models.
• InfiniiVision 3000T, 4000, or 6000 X-Series oscilloscope configured with the WaveGen option
along with one of the following optional software packages that includes FRA.
o Embedded software package (D3000GENA, D4000GENA, D6000GENA)
o Automotive software package (D3000AUTA, D4000AUTA, D6000GENA)
o Aero software package (D3000AERA, D4000AERA, D6000AERA)
o Power software package (D3000PWRA, D4000PWRA, D6000PWRA)
o USB software package (D4000USBA, D6000USBA)
o Ultimate bundle software package (D3000BDLA, D4000BDLA, D6000BDLA)
The above oscilloscopes are available in a variety of bandwidth and number-of-channel configurations, all
of which are compatible with the lab instructions in this document. If your circuits lab is not equipped with
any of the above oscilloscopes, the tutorial section, as well as Labs 1 and 2 can be completed using any
vendor’s oscilloscope along with a standalone function generator, although some specific set up and
measurement instructions may differ. Although the Bode Plot Training Kit (DSOXBODE) is suggested for
these labs, you can also create your own using readily available passive components.
As a prerequisite for completing the labs, the student following this lab guide should already be familiar
with the graphical user-interface of Keysight InfiniiVision oscilloscopes and know how to set up the scope
(vertical scaling, horizontal scaling, and triggering) to view repetitive sine waves. The student should also
know how to perform basic measurements on these oscilloscopes using cursors and automatic
parametric measurements, as well as how to save screen images to a USB drive. This document does
not include every keystroke required to set up and perform the required measurements.
Prior to going into the circuits lab to perform the measurements outlined in labs 1 through 4, the student
should read/study the tutorial section of this guide (pages 1 through 5) and answer the questions on page
5.
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Frequency response analysis tutorial
Bode plots are theoretical straight-line approximations of gain and phase versus frequency of a system’s
output relative to the input (i.e. frequency response) based on poles and zeros of the circuit’s transfer
function. The result of a frequency response analysis test is a measured plot (not a straight-line
approximation) of gain and phase versus frequency. Frequency response analysis testing is often
equated with and called Bode plots.
For both Bode plot straight-line approximations, as well as frequency response analysis test results, the
magnitude of gain (A) of a circuit (V
OUT/VIN
) is typically converted into logarithmic units of dB.
Gain is plotted on the vertical axis versus frequency on a logarithmic horizontal axis. Units of frequency
can either be in radians/sec or Hertz.
Phase is also plotted on the vertical axis versus frequency on a logarithmic horizontal axis and is usually
plotted in units of degrees but can also be plotted in units of radians.
Sometimes gain and phase are plotted on separate graphs but gain
and phase can also be plotted on the same graph with units of gain
and phase labeled on opposite sides of the plot. This the way
Keysight’s InfiniiVision oscilloscopes plot the measured results of a
frequency response analysis test with gain in units of dB, phase in
units of degrees, and frequency in units of Hertz.
Let’s now consider the example of a series R-L-C circuit (Figure 1)
that forms a bandpass filter (output attenuated at lower frequencies
and higher frequencies but passes/transfers the input to the output
at mid-band frequencies). This is the circuit design of Keysight’s
DSOXBODE Bode plot training kit board you will be testing. The
transfer function, T(jω), of this series R-L-C passive circuit will have two poles and one zero (at 0 Hz)
based on the following formulas:
Figure 1. Series R-L-C bandpass filter.
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Figure 2 shows the Bode plot of gain and phase of a bandpass filter based
on a sine wave input at various frequencies. Bode plots, as well the
frequency response analysis tests, are always based on sine wave inputs.
The solid lines represent the straight-line approximated Bode plot of gain and
phase while the dashed line represents the actual/theoretical gain which can
be verified by testing.
Before we perform any measurements, let’s consider the extreme limits of
this series R-L-C circuit based on the schematic of Figure 1. This quick
analysis may provide you with a more intuitive understanding of why
bandpass filters behave the way they do.
Case 1: Frequency = 0 Hz
Z
C
= -j
, @ f = 0 Hz, |ZC| = Infinite Ohms (∞ Ω)
Z
L
= +j
, @ f = 0 Hz, |ZL| = Zero Ohms (0 Ω)
In this case all the input voltage (VIN) will be dropped across the series
capacitor since the reactance of the capacitor dominates the impedance of
the entire series circuit. The output voltage (V
OUT
) across R will then be 0 V
and the absolute gain (V
OUT/VIN
) will also be zero. The logarithmic gain
(20Log(V
OUT/VIN
)) will be negative infinite dB. Don’t punch it into your
calculator. It may explode!
Hendrik Wade Bode (1905 – 1982)
Hendrik Wade Bode was born in
Madison, Wisconsin (USA) on
December 24, 1905. Soon after
graduating from Ohio State University
where he received his B.A and M.A.
degree in 1926 in Mathematics, Bode
began an illustrious engineering and
scientific research career at Bell
Labs. While at Bell Labs, Bode
successfully completed his PhD in
physics at Columbia in 1935. In 1938,
Dr. Bode invented what is famously
known today by engineering students
as “Bode plots” for his namesake. But
that’s not what he called them. He
simply called them “asymptotic
frequency-domain magnitude and
phase plots”. During his time at Bell
Labs, Dr. Bode received numerous
academic medals and awards and
held 25 patents in various areas of
electrical and communications
engineering. He also collaborated
closely with other well-known
scientists and researchers at Bell
Labs including Claude Shannon and
Harry Nyquist.
Figure 2. Gain & phase Bode plots of a series R-L-C bandpass filter.
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Case 2: Frequency = Infinite Hz
Z
C
= -j
, @ f = Infinite Hz, |
Z
C
| = Zero Ohms (0 Ω)
Z
L
= +j
, @ f = Infinite Hz, |
Z
L
| = Infinite Ohms (∞ Ω)
For this case all the input voltage (VIN) will be dropped across the series inductor providing the same
output results as Case 1, which is an absolute gain (V
OUT/VIN
) of 0.0 and logarithmic gain of negative
infinite dB.
Case 3: Frequency where |
Z
C
| = |
Z
L
|
If
2πfL
, then f =
At the frequency where the absolute value of the impedance of the capacitor is equal to the absolute
value of the impedance of the inductor, the net impedance of the sum of these two series components is
0 Ω. This is because the phase angles of each component’s impedance (+j and -j) are 180° out of phase
with respect to each other. In this case all of VIN is dropped across the remaining component, R, which
makes V
OUT
= VIN for an absolute gain (V
OUT/VIN
) of 1 which equates to 0 dB. The frequency where this
occurs is called the center frequency (f
Center
) of the bandpass filter.
From this quick analysis of this circuit, based on these three data points, we can see that a series R-L-C
circuit has very low gain at low frequencies, very low gain at high frequencies, and a gain of 1 (0 dB) at a
mid-band frequency. Let’s now plug in real numbers based on the actual component values of Keysight’s
DSOXBODE Bode plot demo kit, which are:
C = 1 µF
L = 10 µF
R = 50 Ω
Using the equations provided on the preceding pages and from what you’ve learned so far, now
determine the following for Keysight’s DSOXBODE Bode training kit board:
f
Pole1
= __________
f
Pole2
= __________
f
Center
= __________
f
Pole1
and f
Pole2
are the frequencies where the ±20 dB/decade straight-line approximations intersect 0 dB of
the straight-line approximated Bode gain plot (refer back to Figure 2). But if you tested this passive circuit,
you would discover that the actual gain and phase traces would not be perfect straight lines, especially
near these pole frequencies. You would discover that the gain would be down approximately 3 dB at each
of the two pole frequencies. Let’s now make some measurements.
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Lab 1: Quick verification test of a bandpass filter
During this lab we will setup the oscilloscope to capture and display the input (VIN) and output (V
OUT
) of a
bandpass filter (DSOXBODE Bode Training Kit) while manually varying the frequency of an input sine
wave (using the scope’s built-in generator) to observe and compare the relative amplitudes of the input
and output across a range of frequencies. Note that your passive probes should be properly
compensated/calibrated before proceeding with the lab. Refer to the “Oscilloscope Probe Loading” tutorial
and lab guide listed at the end of this document to learn more
about probe compensation.
1. Connect the DSOXBODE training board directly to the
InfiniiVision oscilloscope’s Gen Out BNC.
If using a Keysight 4000 or 6000 X-Series oscilloscope,
connect the training board to the Gen Out 1 output BNC.
2. Connect a passive probe between the channel-1 input BNC
of your scope to the training board’s VIN CH1 test pin.
Connect the probe’s ground lead to one the test pins labeled
GND.
3. Connect a passive probe between the channel-2 input BNC
of your scope to the training board’s BPF OUT CH2 test pin.
Connect this probe’s ground lead to the other test pin labeled
GND.
4. If you are using a Keysight 1000 X-Series oscilloscope and
using the original probes that were supplied with this scope (black probes), these probes have
selectable attenuation settings (10X or 1X). Make sure the switch on each probe is set to the 10X
setting (not 1X). Also, make sure to set the probe attenuation factor to 10.0:1 for each channel of the
scope in the channel-1 and channel-2 probe menus.
a. Press the channel number key
b. Select the Probe menu
c. Set units to Volts
d. Set probe attenuation ratio to 10.0:1
5. If you are using a Keysight 3000T, 4000A, or 6000A X-Series oscilloscope, these scopes were
originally supplied with non-selectable 10X probes (gray probes) with automatic detection of the
attenuation factor by the scope.
6. Press the front panel [Default Setup] key on your oscilloscope (Note that a Default Setup does not
reset the probe attenuation factor).
7. Press the front panel [WaveGen] key (or [WaveGen1] key on the 4000 or 6000 X-Series
oscilloscope), and then establish the following initial generator settings to use as a test input source:
a. Waveform: Sine
b. Frequency: 100 Hz
c. Output Load (under Settings submenu): 50 Ω
d. Amplitude: 500 mVpp (note that the expected output load impedance must to established
before setting the amplitude)
Channel-1 probe
Channel-2 probe
Figure 3. DSOXBODE Bode Training Board.
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8. Turn on the displays of channel-1 (yellow trace) and channel-2 (green trace) of your oscilloscope and
then establish the following oscilloscope settings:
a. Channel-1 vertical scaling: 200 mV/div
b. Channel-2 vertical scaling: 200 mV/div
c. Timebase/Horizontal: 2.000 ms/div
d. Vertical Position: Using the vertical position knob(s), position the channel-1 waveform (VIN,
yellow trace) near the top of the scope’s display (-200 mV offset) and position the channel-2
waveform (V
OUT
, green trace) near the bottom of the scope’s display (+500 mV offset).
e. Triggering should already be set to rising edge transition on channel-1 at 0.0 V which was
establish by the Default Setup (step #6).
At these settings your scope’s display should look
like Figure 4. At an input frequency of 100 Hz you
can see that the amplitude of V
OUT
(channel-2,
green trace) is much lower than the amplitude of VIN
(channel-1, yellow trace) which means that the gain
is very low at this frequency (100 Hz). We’ll
measure the actual gain in Lab 2 and Lab 3.
We will now setup the scope to manually “sweep” to
higher frequencies. “Sweep” is the term most often
used when an input variable is changed during a
test from a lower initial setting to incrementally
higher settings.
9. Press the front panel [WaveGen] key (or [WaveGen1]) again to activate the WaveGen settings
menu, and then press the Frequency menu key
to activate this variable.
10. Using the entry knob, slowly increase the
frequency setting from 100 Hz up to 10 MHz
while observing the relative amplitudes of the
VIN and V
OUT
traces.
As you initially increase the frequency you should
observe the amplitude of V
OUT
getting larger. V
OUT
will eventually have the same approximate
amplitude as V
IN
(between ~8 kHz to ~300 kHz) as
shown in Figure 5. But as you increase the
frequency further you should observe the amplitude
of V
OUT
getting smaller again relative to VIN. Note that although you could change the timebase setting in
order to view individual cycles of these signals as frequency is increased, even if you leave the timebase
set at 2 ms/div, you can still easily see the peak-to-peak extremes of these signals. But of course, if we
wanted to measure phase, we would need to rescale the timebase to view just a few cycles.
Figure 4. Initial oscilloscope setup condition at 100 Hz.
Figure 5. VIN and VOUT near f
Center
.
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You may have also noticed that as frequency changed, the amplitude of VIN appeared to change as well
— but not as much as V
OUT
. But since VIN is being probed at the output of the generator, which is also the
input to the test circuit, shouldn’t V
IN
have a fixed amplitude since we originally set the generator’s
amplitude to 500 mVpp (Step 7d)?
Function generators have a series source
resistance (RS) of 50 Ω as shown in Figure 6.
The amplitude of the output of generator at the
BNC is relative to a fixed load impedance. In step
7c of this lab, we set the expected fixed load
impedance of the device-under-test (DUT) to 50
Ω. Our only choices were 50 Ω or High-Z. Some
higher performance function generators, such as
Keysight’s 33500/600 Series function/arbitrary
waveform generators, allow you to enter any
specific fixed value for load impedance. But the load impedance of our test circuit is not fixed. It varies
based on frequency because the reactance of the series capacitor and inductor vary as a function of
frequency. Only near f
Center
is the impedance of this test circuit approximately 50 Ω. At very low
frequencies, such as 100 Hz, the impedance of our circuit is very high, and at very high frequencies, such
as 10 MHz, the impedance is again very high. This is why VIN is changing by an approximate factor of 2 to
1 across the range of input test frequencies (100 Hz to 10 MHz).
For a linear system, such as our passive bandpass filter, relatively small variations in the amplitude of VIN
theoretically shouldn’t matter since we are measuring gain — not absolute amplitudes. If a linear circuit
has an absolute gain of 2 at a particular frequency, and if VIN = 1 Vpp, then V
OUT
= 2 Vpp. If VIN = 2 Vpp,
then V
OUT
= 4 Vpp. The gain should be the same regardless of the value of the input voltage.
Figure 6. Test circuit including function generator
equivalent circuit.
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Lab 2: Frequency response testing using traditional oscilloscope test methodology
Before performing an automatic frequency response analysis test, we will perform this test manually —
the same way students have been doing it for years, and probably the way Dr. Hendrik Bode did it nearly
a century ago. This is the method that most engineering students are still using today because very few
oscilloscopes can perform automatic frequency response analysis testing. Although testing the frequency
response of our bandpass filter manually will be a somewhat tedious exercise, it will help you to better
understand the fundamentals of frequency response analysis testing.
Note that if you just completed Lab 1, the DSOXBODE Bode plot training board should still be connected
to the scope’s WaveGen output BNC and probed by channel-1 and channel-2 using 10X passive probes.
If not, repeat steps 1 through 4 of Lab 1 before proceeding.
1. Press the scope’s [Default Setup] front panel key.
2. Press the [WaveGen] (or [WaveGen1]) front panel key, then establish the following generator
settings:
a. Waveform: Sine
b. Frequency: 100 Hz
c. Output Load (under Settings submenu): 50 Ω
d. Amplitude: 500 mVpp
3. Turn on the displays of channel-1 (yellow trace) and channel-2 (green trace) of your oscilloscope and
then establish the following oscilloscope settings:
a. Channel-1 vertical scaling: 200 mV/div
b. Channel-2 vertical scaling: 10 mV/div
c. Timebase/Horizontal: 2.000 ms/div
d. Vertical Position: The channel-1 waveform (yellow trace) and the channel-2 waveform (green
trace) should be vertically centered on-screen (0.0 V offset). It’s okay during this lab for the
waveforms to be overlaid. This will help us to better visualize the phase shift at each test
frequency.
e. Triggering should already be set to rising edge transition on channel-1 at 0.0 V which was
establish by the Default Setup action of step #1 above.
Although the peak-to-peak amplitudes of the
channel-1 and channel-2 waveforms may appear to
some to be similar as shown in Figure 7, note that
the channel-1 waveform is scaled at 200 mV/div
while the channel-2 waveform is scaled at 10
mV/div. The channel-1 amplitude (VIN) is much
larger than the channel-2 (V
OUT
) amplitude at this
initial 100 Hz input frequency. Also notice that the
channel-2 waveform (V
OUT
) appears very noisy.
Let’s now “clean it up” before attempting to make
accurate gain and phase measurements.
Figure 7. VIN and V
OUT
at 100 Hz.
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4. Select the [Acquire] front panel key, and then change the AcqMode from Normal to Averaging.
Averaging repetitive acquisitions of the waveforms will help to eliminate random noise and improve
measurement accuracy.
5. Using either the scope’s manually-placed
voltage cursors (Y1 and Y2) or automatic
measurements, measure the peak-to-peak
voltage of VIN (channel-1) and V
OUT
(channel-2).
VIN = ___________
V
OUT
= __________
A
(LINEAER)
(V
OUT/VIN
) = ___________
A
(LOGRITHMIC)
(20Log(V
OUT/VIN
) = ________
6. Using either the scope’s manually-placed timing
cursors (X1 and X2) or automatic
measurements, measure the phase shift of VIN
(channel-1) relative to V
OUT
(channel-2). Hint: If you use the scope’s automatic phase measurement
capability, Source1 should be assigned as channel-2 and Source2 should be assigned as channel-1
before pressing Add Measurement.
Phase (Ch-2 to Ch-1) = ______________
7. Enter the results of the above measurements and calculations from step #5 and step #6 into Table 1
on the next page of this lab guide.
8. Select the [WaveGen] front panel key and then change the frequency setting to 200 Hz.
9. If necessary, rescale vertical settings (V/div) to ensure that both waveforms are fully on-screen.
10. Rescale the timebase (sec/div) such that approximately 2 to 3 cycles of the waveform are displayed
on-screen. Note that if less than 1 cycle is displayed across screen, the scope will not be able to
measure phase.
11. Repeat the measurements performed in step #5 and step #6 above, and then enter the results into
Table 1 on the next page. Note that if you are using the scope’s automatic Vpp and phase
measurements, you do not need to re-select these measurements. But if you are using the manuallyplaces cursors for these voltage and timing (phase) measurements, then you will have to re-position
the cursors for each different frequency tested.
12. Repeat all measurements and scaling changes (V/div and sec/div) for f = 500 Hz, 1 kHz, 2 kHz, etc.,
up to 10 MHz.
Figure 8. Measuring VIN, V
OUT
, and phase at 100 Hz
using the scope’s automatic parametric measurements.
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Table 1: Amplitude (Vpp), Gain (A), and Phase Measurement Results
Frequency
V
IN
(Vpp)
V
OUT
(Vpp)
A
(LINEAR)
(V
OUT/VIN
)
A
(LOGARITHMIC
)
(20Log(V
OUT/VIN
))
Phase
(Degrees)
100 Hz
200 Hz
500 Hz
1k Hz
2k Hz
5k Hz
10k Hz
20 kHz
50k Hz
100k Hz
200 kHz
500 kHz
1 MHz
2 MHz
5 MHz
10 MHz
13. Plot the results documented in Table 1 above onto the semi-logarithmic graph provided below or
enter the values into a Mac or PC/laptop software application such as MatLab or an Excel
spreadsheet for plotting. Suggestion: If plotting manually, use different color pens for gain and phase.
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Lab 3: Automatic frequency response analysis of a bandpass filter
Now that you have done it the hard way during Lab 2 — and hopefully learned a few things during the
process — we will now perform the same measurements automatically and with significantly higher
resolution and accuracy.
Although there have been specialized instruments on the market for years — typically called frequency
response analyzers (FRA) or vector network analyzers (VNA) — that provide automatic gain and phase
measurements across a frequency spectrum, rarely have these types of instruments been found in the
undergraduate teaching lab due to cost. Keysight Technologies was the first test equipment vendor to
introduce this capability into low-cost oscilloscopes that are commonly used in university undergraduate
labs.
Note that if you just completed Lab 1 and Lab 2, the DSOXBODE Bode plot training board should still be
connected the scope’s WaveGen output BNC and probed by channel-1 and channel-2 using 10X passive
probes. If not, repeat steps 1 through 4 of Lab 1 before proceeding.
1. Press the [Default Setup] front panel key.
2. Press the [Analyze] front panel key.
3. Select the Features menu key, and then select
Frequency Response Analysis.
4. If using a Keysight 1000 X-Series oscilloscope,
select the Setup menu key (Figure 9).
If using a Keysight 3000T, 4000, or 6000 XSeries oscilloscope, select the Open Dialog…
menu key (Figure 10).
We will perform a “sweep” from 100 Hz (Start Freq)
to 10 MHz (Stop Freq) on our bandpass filter based
on a 500 mVpp input into a 50 Ω load impedance.
This is the same criteria as the manual testing that
was just accomplished during Lab 2. However, due
to the tedious nature of performing gain and phase
measurements manually, we performed tests at just
16 different frequencies during Lab 2. In this lab, we
will setup the scope to perform 300 gain and phase
measurements across the 100 Hz to 10 MHz
frequency span.
5. Change the Stop Freq setting from 20 MHz to
10 MHz.
6. Change the Points setting (number of different
frequencies to test) from 60 to 300.
7. Change the Amplitude from 200 mVpp to 500
mVpp.
8. If using a 1000 X-Series oscilloscope, press the
Back key, and then select Run Analysis.
If using a 3000T, 4000, or 6000 X-Series
oscilloscope, select Run Analysis.
Figure 9. InfiniiVision 1000 X-Series oscilloscope
frequency response analysis (FRA) setup menu.
Figure 10. InfiniiVision 4000 X-Series oscilloscope
frequency response analysis (FRA) setup menu.
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Figure 11 shows the test results after the 100 Hz to
10 MHz sweep. The scope automatically optimizes
the gain (dB) and phase scaling during and at the
completion of the sweep. However, you can
manually alter chart scaling after the completion of
a test if desired.
The blue trace represents gain with scale factors on
the left side of the plot. The orange trace represents
phase measurement results with scale factors on
the right side of the plot.
Let’s now measure the gain at the center frequency
(f
Center
) and then determine the actual/measured
pole frequencies (f
Pole1
and f
Pole2
).
9. Rotate the entry knob to move the pair of tracking markers (yellow triangles that ride along the gain
and phase traces at the same frequency) to the center frequency (f
Center
=
) that was previously
calculated in the introductory section of this tutorial/lab guide on page 4. The gain, phase, and
frequency readout for this pair of markers is below the plot on the right. Note that the Keysight 3000T,
4000, and 6000 X-Series have two pair of tracking markers, but for now we are just using Marker1 if
using one of these higher performance scopes.
Gain (A
Measured
in dB) @ f
Center
= _______
Why do you think that gain (A) is not exactly 0 dB at f
Center
as theoretically predicted? __________
________________________________________________________________________________
10. Rotate the entry knob to move the pair of markers to the approximate f
Pole1
frequency
)
as determined in the introductory section of this tutorial/lab guide on page 5. Now position these
markers (as close as possible) to the frequency where the gain is 3 dB below the actual center
frequency gain (A
Measured
@ f
Center
– 3 dB) as measured in step #9 above. For example, if A
Measured
at
f
Center
= -0.3 dB, then position the markers at the frequency where A(dB) = -3.3 dB. Note that for a
more precise placement of the markers, we could have performed this sweep based on 1000 points
across the frequency sweep span, but at the cost of throughput, or we could have limited our span of
the sweep to smaller ranges around each pole frequency.
f
Pole1-measured
= ______
11. If using a Keysight 1000 X-Series oscilloscope, now perform the same measurement for f
Pole2-measured
.
Note that
.
If using a Keysight 3000T, 4000, or 6000 X-Series oscilloscope, select the Scroll Marker2 menu key,
then rotate the entry to knob to determine f
Pole2-measured
using the second pair of tracking markers that
are available on these scopes using the same measurement technique as step #10 above.
f
Pole2-measured
= ______
What is the bandwidth of this bandpass filter (f
Pole2-measured
– f
Pole1-measured
)? _________
Figure 11. Gain and phase measurement results from
an automatic frequency response analysis test.
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12. Save a screen image (.png, .bmp, etc.) of your frequency response analysis test to a USB memory
device and attach a printout to your lab test results if required by your professor/lab instructor. Note
that the .png format is the most efficient.
If using a Keysight InfiniiVision 3000T, 4000, or
6000 X-Series oscilloscope, you can also view
the measured gain and phase data in a
scrollable tabular format as shown in Figure 12
by clicking on (touching) the “table” icon.
You can also export the measured data in a
.csv format using any InfiniiVision oscilloscope,
including the 1000G Series, and then upload
into an Excel spreadsheet or Matlab for
additional processing.
Figure 12. Displaying gain and phase data in a tabular
format using a Keysight InfiniiVision 3000T, 4000, or
6000 X-Series oscilloscope.
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Lab 4: Characterizing a low-pass filter
Refer back to Figure 1 on page 3 of this training guide and note that if you probe the output (channel-2) of
our R-L-C circuit at the node between the capacitor and the inductor, even though this series R-L-C circuit
is not a classic low-pass filter design, it will behave as a low-pass filter (attenuate signals at higher
frequencies) when probed at this point.
Answer the following questions based on probing V
OUT
at this node.
At low frequencies (approaching 0 Hz)…
What is the impedance of C? _________
What is the impedance of L? _________
What would the output voltage be (in terms of VIN) across the combination of the L and
R? ________
At high frequencies (approaching ∞Hz)…
What is the impedance of C? _________
What is the impedance of L? _________
What would the output voltage be across the combination of the L and R? ________
1. Move the channel-2 probe from the test pin labeled BPF CH2 to the test pin labeled LPF CH2.
2. Press the [Default Setup] front panel key.
3. Perform a frequency response test on this
device with this probing configuration based on
what you learned from Lab 3. The results
should look similar to Figure 13.
4. Measure the -3 dB cutoff frequency of this lowpass filter.
-3 dB cutoff frequency = _________
Bandwidth of the filter = _________
If you measured the amplitude of the V
OUT
at the cutoff frequency, what would the
approximate error be (in %) relative to VIN?
_______
5. Save a screen image (.png, .bmp, etc.) of this
frequency response analysis test to a USB memory device and attach a printout to your lab test
results if required by your professor/lab instructor.
Figure 13. Displaying gain and phase data in a tabular
format using a Keysight InfiniiVision 3000T, 4000, or
6000 X-Series oscilloscope.
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The frequency response of oscilloscopes is basically a low-pass filter
response similar to what you just tested, except that the cutoff frequency
would be much higher for most of today’s benchtop oscilloscopes. The cutoff
frequency of a 100 MHz bandwidth scope would be approximately 100 MHz
(but typically slightly higher to ensure that the scope meets warranted
specifications under all environmental conditions). The cutoff frequency of a
1 GHz bandwidth scope would be approximately 1 GHz (or slightly higher).
Keysight uses vector network analyzers (VNA) to test the frequency
response performance of their scopes. VNAs can test to higher frequencies
than a typical entry-level FRA.
Since a signal’s amplitude is down approximately 30% at the -3 dB cutoff
frequency based on a sine wave input, Keysight recommends that the
scope’s bandwidth be at least 3X higher than the highest sine wave
frequency anticipated to be tested. For example, if you anticipate the need to
test analog signals up to 100 MHz in frequency, you should use a scope with
a specified bandwidth of 300 MHz or higher. But for digital signals that
contain multiple odd and even harmonics higher than the actual clock rate,
Keysight recommends using scopes that have a specified bandwidth that are
at least 5X higher than the highest digital clock rate in order to capture up to
the 5th harmonic with reasonable accuracy. For example, if you need to test
digital signals in a system based on a 200 MHz clock, Keysight recommends
using a scope with a specified bandwidth of 1 GHz or higher. If you used a
200 MHz bandwidth scope to capture and display and 200 MHz digital clock
signal, it would appear more as a sine wave as opposed to the square wave.
Summary
Frequency response analysis testing (measured Bode plots) have a broad
range of applications. Besides being used to characterize passive filters for
audio applications or front-end system signal conditioning, frequency
response analysis can be used to characterize active circuitry such as op
amp circuits, as well for power supply characterization including power
supply rejection ratio (PSRR) and control loop response analysis to test the
stability and response timing of negative feedback amplifiers that regulate
output voltage of DC-to-DC converters during load changes. And as we just
discussed, frequency response analysis is used to test the bandwidth
performance of a broad range test equipment, including oscilloscopes.
To learn more about frequency response analysis and oscilloscope
specifications and theory, download Keysight’s application notes listed in the
table below.
About the Author
Johnnie L. Hancock
Johnnie Hancock is an oscilloscope
product manager at Keysight
Technologies. He began his career
with Hewlett-Packard in 1979 as an
R&D hardware designer and holds a
patent for digital oscilloscope triggerpath amplifier calibration. Johnnie
regularly speaks at technical
conferences on a variety of topics
related to oscilloscope
measurements including automotive
serial bus applications, power supply
characterization, and frequency
response testing. He is also the
author of many articles, white papers,
and application notes. Johnnie
graduated from the University of
South Florida with a degree in
electrical engineering, and he has a
passion for helping engineering
students learn how to more
effectively use test equipment. In his
spare time, he enjoys fishing,
kayaking, and spending time with his
four grandchildren.
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Related Literature
Publication Title
Publication Type
Publication Number
Frequency Response Analysis (Bode plots)
Application note
5992-4010EN
Control Loop Response Testing
Application note
5992-0593EN
Power Supply Rejection Ratio (PSRR) Testing
Application note
5992-0594EN
Understanding Oscilloscope Frequency Response
and Its Effect on Rise-Time Accuracy
Application note
5988-8080EN
Evaluating Oscilloscope Bandwidth
Application note
5989-5733EN
Evaluating Oscilloscope Sample Rates
Application note
5989-5732EN
How to Select Your Next Oscilloscope: 12 Tips on
What to Consider
Application note
5991-2714EN
Oscilloscope Fundamentals
Application note
5989-8064EN
Oscilloscope Probe Loading Experiment
Tutorial and Lab
Guide
5990-9175EN
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