Name:
______________________________________________
Date of lab:
______________________
Lab 6
Section number:
M E 345._______
Precalculations – Individual Portion
Filter Lab: Building and Testing Electrical Filters
Precalculations Score (for instructor or TA use only):
_____ / 20
1. (4) Draw the circuit diagram for a simple first-order low-pass filter, constructed from one resistor and one
capacitor. Be sure to label both the input and output voltages.
2. (4) Draw the circuit diagram for a simple first-order high-pass filter, constructed from one resistor and one
capacitor. Be sure to label both the input and output voltages.
3. (4) Suppose a capacitor is available with a capacitance of 0.0100 microfarads. A low-pass filter is to be
constructed with a cutoff frequency around 800 Hz. Calculate the appropriate resistance of the resistor that
should be used, in units of k. Show all your calculations, and be sure to include all units.
Required resistance, R = ___________ k
4. (4) Suppose that you need a resistance of 15 k, but all you have available is a bunch of 10 k resistors. Draw a
schematic diagram showing how could use only 3 resistors to generate the desired resistance.
5. (4) Instruments are commercially available that contain Butterworth low-pass filters of various orders (for
example n = 1, 2, 4, 6, and 8). Suppose you are using one of these instruments, and have it set to a cutoff
frequency of 800 Hz. Compare the gain (both G and GdB) at a frequency of 10,000 Hz for the cases with n = 1, n
= 2, and n = 4.
n
1
2
4
G
GdB
Lab 6, Filter Lab Page 1
Cover Page for
Lab 6
Lab Report – Group Portion
Filter Lab: Building and Testing Electrical Filters
Name 1:
___________________________________________________
Section M E 345._______
Name 2:
___________________________________________________
Section M E 345._______
Name 3:
___________________________________________________
Section M E 345._______
[Name 4:
___________________________________________________
Section M E 345._______ ]
Date when the lab was performed:
______________________
Group Lab Report Score (For instructor or TA use only):
Lab experiment and results, plots, tables, etc.
_____ / 50
Discussion
_____ / 30
TOTAL
______ / 80
Lab Participation Grade and Deductions – The instructor or TA reserves the right to deduct points for any of the
following, either for all group members or for individual students:







Arriving late to lab or leaving before your lab group is finished.
Not participating in the work of your lab group (freeloading).
Causing distractions, arguing, or not paying attention during lab.
Not following the rules about formatting plots and tables.
Grammatical errors in your lab report.
Sloppy or illegible writing or plots (lack of neatness) in your lab report.
Other (at the discretion of the instructor or TA).
Name
Reason for deduction
Comments (for instructor or TA use only):
Points deducted
Total grade (out of 80)
Lab 6, Filter Lab Page 2
Filter Lab: Building and Testing Electrical Filters
Author: John M. Cimbala; also edited by Mikhail Gordin and Savas Yavuzkurt, Penn State University
Latest revision: 13 October 2014
Introduction and Background (Note: To save paper, you do not need to print this section for your lab report.)
This lab involves building some electrical circuits on a breadboard. To refresh your memory, the circuit for two
resistors in series is shown below. One way to wire these on a breadboard is also sketched below.
VB
R2
Short bus
Note: The
color stripes
R1
R2
VB
VA
on the
resistors
are
I1
I2
of arbitrary
colors.
R1
VA
Similarly, the circuit for two resistors in parallel is shown below, along with one way to wire these on a breadboard.
R2
R1
Note: The
color
stripes
I1
on
the
R1
VB
VA
resistors are
of arbitrary
Itotal
R2
colors.
VA
VB
I2
When taking measurements, there is often the presence of “noise” in addition to the desired signal. In such
circumstances, the desired signal must be separated from other competing signals. Unwanted signals can arise from
external sources such as electrical devices (vacuum cleaner, radio, or television) or can result directly from the
measurement technique itself. Generally, a priori knowledge of the desired signal and of the noise is required in
order for noise to be adequately reduced while retaining the desired signal. Since the exact results are rarely known
before an experiment is performed, selection of a proper filter incorporates some degree of trial and error.
There are four basic categories of filters: low-pass, high-pass, band-pass, and band-stop. These are described in the
learning modules, and the details are not repeated here. These filter circuits may be approximated by the response of
simple first-order (RC) type circuits.
In practice, a filter does not completely eradicate signals whose frequencies fall above, below, or outside the
designated cutoff frequency, but attenuates them to some degree. For example, consider a low-pass filter. The
amplitude of the signal at frequencies much lower than the cutoff frequency fcutoff are not attenuated at all. The
amplitude of the signal at frequencies near the cutoff frequency are attenuated somewhat, and the amplitude at
frequencies which are much greater than the cutoff frequency are attenuated significantly. The rate at which this
attenuation occurs, given in dB/octave, depends on the order of the filter. A first-order Butterworth filter has a cutoff rate of 6 dB/octave; a second-order Butterworth filter has a cut-off rate of 12 dB/octave (one octave is defined as
two times the original frequency). In general, for an nth-order Butterworth low-pass filter, the gain G is
V
Vout
1
1
G  out 

G

20log
G

20log
,
and
the
gain
in
decibels
is
, where the
dB
10
10
2n
2n
Vin
Vin
  
 f 
1 
1 


 cutoff 
 f cutoff 
cutoff radian frequency for a simple first-order RC filter is cutoff 
1
1
. The physical frequency is fcutoff 
.
RC
2 RC
Filter circuits impart a phase shift to the signal. This phase shift is normally not a problem unless synchronization
between the input and output signals is required. Phase shift will be investigated in this lab for a simple first-order
Lab 6, Filter Lab Page 3
 f 
low-pass filter. Theoretically, the phase shift for a first-order low-pass Butterworth filter is    arctan 
.
 f cutoff 
In previous labs (and also in class and homework), it has been shown that aliasing can be a serious problem with
digital data acquisition if the experimenter is not careful. One way to avoid aliasing is to employ a low-pass filter to
attenuate undesired high frequencies. Such a filter is called an anti-aliasing filter. For example, suppose we are
interested in signals around 100 to 500 Hz. For adequate resolution at these frequencies, we choose to sample data at,
say, 5000 Hz. But suppose there is also some high frequency noise (above 5000 Hz) in the signal. The problem is that
the high frequency noise will cause aliasing. One possible solution is to put in an anti-aliasing filter with a cutoff
frequency of around 1000 Hz. This filter will allow the desired signal to pass through without much effect, but will
significantly attenuate the high frequency noise, thereby reducing the aliasing. In this lab, such a case will be
demonstrated.
Objectives
1. Practice combining resistors in series and/or parallel to produce a desired resistance from available resistors.
2. Construct simple first-order low-pass and high-pass filters, using only resistors and capacitors.
3. Apply a low-pass filter to some music to see how the music is changed
4. Measure the amplitude (gain) and phase characteristics of a low-pass filter as a function of frequency, and
compare to theory.
5. Construct Bode plots for a low-pass filter based on experimental measurements.
Equipment
 digital oscilloscope
 function generator
 six resistors of nominal value 10 kohm (10,000 )
 two capacitors of nominal value 0.010 microfarad (0.010  10-6 F)
 capacitor decade box
 Music player (cell phone, MP3 or MP4 player, iPod, this computer, etc.)
 2 stereo patch cords (1/8-inch for iPod, cell phones, and MP3 players)
 2 1/8-inch stereo plugs with connections soldered to jumper wires (green to ground and yellow to signal)
 powered breadboard (plugged in for the ground connection, but turned off – power not needed for this lab)
 various BNC and banana cords and breadboard jumper wires as needed
 digital multimeter
 computer with digital data acquisition system (DAQ) and software
Lab 6, Filter Lab Page 4
Procedure
Basic set-up and measurements
1. (1) Measure and record the resistance of three of the available resistors. (The nominal value of each resistor
should be 10,000 ohms.)
Measured resistances: R1 = ___________ , R2 = ___________ , and R3 = ___________ 
2. (1) (a) Measure and record the capacitance of one of the available capacitors. (The nominal value of each
capacitor should be 0.010 microfarads.)
Measured capacitance, Ccapacitor = ___________ F
(1) (b) Dial in the same capacitance value (about 0.010 microfarads) on the capacitor decade box. Measure
and record the capacitance of the capacitor decade box.
Measured capacitance from the capacitor decade box, Cdecade box = ___________ F
From now on, for convenience, you may use the capacitor decade box instead of the physical capacitor.
3. (4) For this capacitance, calculate the resistance needed to create a simple first-order low-pass filter with a
cutoff frequency of 1000 Hz. Show your work here, including all units.
Required resistance, R = ___________ 
4. (4) Combine your resistors (in series and/or parallel) on the breadboard in such a way that the total resistance
is close to the required resistance (say within 10% or so). Sketch a schematic diagram.
5. (2) Measure and record the equivalent resistance of your resistor circuit, and compare to the theoretical
value.
Measured equivalent resistance, R = ___________ 
Percentage error between measured and theoretical equivalent resistance = ___________ %
Important note: In all the circuits you will build in this lab (and in several other labs), it is critical that the
ground bus be connected to a physical ground, such as the black ground post of the powered breadboard
with the breadboard plugged in (but turned off) to secure the ground.
Lab 6, Filter Lab Page 5
Low-pass filtering of music
1. Construct a first-order low-pass filter using a combination of resistors and the capacitor decade box, with a
cutoff frequency of approximately 1000 Hz. A circuit diagram for a simple first-order low-pass filter is
provided below, along with a sketch of one possible wiring configuration on the breadboard.
R
R
Vout
Vin
Vin
C
Ground
Ground
bus
C
Vout
Note: A single resistor
(of arbitrary colors) is
shown here, but it is
replaced by a
combination of resistors.
Note: A capacitor is
shown here, but it is
replaced by the
capacitor decade box.
2. (3) Test your filter by connecting the function generator to the filter input and the filter output to the
oscilloscope. Start with a sine wave input of about 100 Hz and amplitude 1 V. Increase the frequency of the
sine wave until you start noticing that the output amplitude decreases – the low-pass filter is doing its job.
Keep increasing the frequency until the filter output amplitude is 90% attenuated – in other words, G = 0.1;
the output amplitude is about 10% of the input amplitude, or 0.1 V. At what frequency does this occur?
Frequency at which G = 0.1: f = ___________ Hz
3. Connect the output of a music player as the input to your low-pass filter, using a stereo patch cord and stereo
plug. Note: We use only one channel (Left or Right) – ignore the other channel. The green wire is the ground,
and the yellow wire is the signal. Using the second stereo plug and stereo patch cord, connect the filter output
directly into the computer’s speaker input.
Note: If you’re trying to play music from a web browser, make sure the speakers are plugged in when you
start playing; if the speakers aren’t plugged in to begin with or you need to unplug them for some reason,
you will need to refresh the browser window to hear anything.
4. (5) Play a song [a song with good range (both high notes and low notes) is best] on your music player and
test whether this simple low-pass filter works – does it attenuate high frequencies and let low frequencies
pass through? Hint: A quick way to turn the filter on or off is to dial the capacitance on the capacitor decade
box to zero (filter off), and then to the required value (filter on). Record qualitative results in the space
below.
5. (3) Adjust the capacitance on the capacitor decade box to decrease the cutoff frequency of the low-pass filter
to about 100 Hz, noting that higher capacitance means lower cutoff frequency since fcutoff = 1/(2RC). Play a
song again and record your observations below. How does this low-pass filter affect the music?
Lab 6, Filter Lab Page 6
Testing the performance of the low-pass filter
1. Connect the output of the function generator
To Ch. 1 of scope.
to the input of your low-pass filter and to one
Call this Vin
channel of the oscilloscope (use a T-splitter).
2. Wire the output of the low-pass filter to
another channel of the oscilloscope, as
T-splitter R
sketched to the right.
Signal from
To Ch. 2 of scope.
1. Important: Push the DC offset button on
C
function
the function generator in (or out in some
Call this Vout
generator
cases) to remove any DC voltage from
the signal, so that the DC offset does not
Ground bus
Ground
influence the measurements.
2. Notation: Vin is the signal coming into the low-pass filter, and Vout is the signal coming from the low-pass
filter, as indicated in the above diagram. Our goal is to compare these two signals.
3. (3) Adjust R and C as necessary to generate a low-pass filter with a cutoff frequency of around 1000 Hz.
Measure the values of R and C, and calculate the physical cutoff frequency of the filter, showing your work
below. Note: The cutoff frequency should be around 1000 Hz, but may not be exact  say within 10%.
Measured resistance, R = ___________ 
Measured capacitance, C = ___________ F
Physical cutoff frequency, fcutoff = ___________ Hz
4. Set the function generator to supply a sine wave of frequency equal to the filter’s cutoff frequency, such that
the amplitude of the signal we are calling Vin is around 8 V peak-to-peak.
5. Now we are ready to test the performance of the low-pass filter. The digital oscilloscope can be set up to
display the frequency of each signal and the peak-to-peak voltage of both channels as follows:
1. Push the Measure button on the oscilloscope.
2. Select channel 1 by pushing Ch 1.
3. Scroll on the right-side menu to select Frequency and Pk-Pk.
4. Repeat for channel 2.
5. Push Menu Off.
6. At this point, two signals should be visible on the oscilloscope screen: the input to the filter, Vin, and the
output from the filter, Vout, along with the frequency and peak-to-peak amplitude of each signal.
7. Consult the instructor or teaching assistant if you are unable to accomplish this yourself.
6. Measure and record the frequency of the signal, the peak-to-peak amplitude going into the low-pass filter, the
peak-to-peak amplitude coming out of the low-pass filter, and the time shift t between the two signals.
Then, using these measured values, calculate the gain G of the low-pass filter and the phase angle shift .
Here are some hints regarding these measurements and calculations:
1. Gain G is the ratio of output voltage amplitude |Vout| to input voltage amplitude |Vin|, i.e., G = |Vout| / |Vin|.
Note that peak-to-peak voltage is twice the amplitude, i.e., |Vin|p-to-p = 2|Vin| and |Vout|p-to-p = 2|Vout|.
2. The voltage scale on the scope can be adjusted as necessary for better amplitude resolution.
3. To measure the time shift, use the oscilloscope’s cursor feature. You can measure the time increment
between peaks or troughs in the two signals. Or, you can measure the time increment between the zero
crossing of the input signal and the zero crossing of the output signal. Note: If zero crossings are used, it
is critical that the vertical position of each oscilloscope trace be adjusted so that zero volts corresponds to
a grid line. Otherwise it will be very difficult to tell (by eye) where the signal crosses zero.
4. The time scale on the scope can be adjusted for better time shift resolution.
5. The period of the signal is calculated as T = 1/f.
t
 360o . The sign of  is positive if
6. (4) The absolute value of phase angle  is then calculated as  
T
the output leads the input, and negative if the output lags the input.
Lab 6, Filter Lab Page 7
Signal frequency, fsignal = ___________ Hz
Peak-to-peak amplitude going into the low-pass filter, |Vin|p-to-p = ___________ V
Peak-to-peak amplitude coming out of the low-pass filter, |Vout|p-to-p = ___________ V
Time shift between the two signals, t = ___________ s
Gain of the low-pass filter, G = ___________
Period of the signal, T = ___________ s
7.
8.
9.
10.
Phase angle shift (in degrees) of the low-pass filter,  = ___________ o
Create an Excel file with the following columns of data, one row for each frequency:
1. input frequency f (Hz)
2. normalized input frequency f /fcutoff
3. input peak-to-peak amplitude |Vin|p-to-p (volts)
4. output peak-to-peak amplitude |Vout|p-to-p (volts)
5. gain G = |Vout|p-to-p / |Vin|p-to-p
(4 for #7,8) Take data for several frequencies, and enter the results into your spreadsheet. The following are
recommended as a minimum to start with:
1. approximately 100 Hz
2. approximately 200 Hz
3. approximately 400 Hz
4. approximately 750 Hz
5. approximately 1,000 Hz
6. approximately 2,000 Hz
7. approximately 4,000 Hz
8. approximately 7,500 Hz
9. approximately 10,000 Hz
Create a Bode diagram, namely a frequency response diagram – a plot of gain G as a function of relative
frequency f /fcutoff – within your Excel spreadsheet. Use symbols only (no line) for your data points:
Here are some specifics about the plots:
1. Use your actual calculated value of fcutoff, not 1000 Hz, for better accuracy.
2. Use a log scale for both horizontal and vertical axes.
3. At this point, data have been collected for about nine frequencies. This should be sufficient to start to
see a trend in the plot. However, many more data points are needed to produce an acceptable plot.
Repeat the measurements for a wide range of frequencies.
4. Hint: Enter data and update the plot as data are taken, so that the plot can be used as a guide to
determine which frequencies to study.
5. Make sure you take enough data to create a smooth curve of gain vs relative frequency. Start with the
lowest possible stable frequency, and end with frequencies at least 100 times fcutoff. (This will generate
a minimum of four decades in the horizontal scale.) Fill in with as many frequencies as necessary to
obtain a nice-looking plot  this should be 10-20 data points.
6. A significant part of the grade for this lab report will be determined by the quality of your plot  make
sure there are enough data points before you leave the lab.
(2 for #9,10) Attach a printout of your tabulated data.
Excel table – See attached page(s) from the spreadsheet ___________
11. (3) On the same graph as your frequency response diagram, plot the theoretical gain for a first-order passive
low-pass filter for comparison. For consistency, use symbols only (no line) for your data, and a line only (no
symbols) for the theoretical curve. For plot of theoretical gain line , data should be in descending or
ascending order. Label, number and attach your frequency response diagram.
Frequency response diagram – See attached, Figure number ___________
12. When all finished, disconnect your circuits (clean off the breadboard) so that the next group has to build the
circuits from scratch like you did.
Lab 6, Filter Lab Page 8
High-pass filter
1. Construct a simple first-order high-pass filter with fcutoff  1000 Hz. The circuit diagram is sketched below,
along with one possible wiring configuration on the breadboard.
C
C
Vout
Vin
R
Vin
Vout
R
Note: A capacitor is
shown here, but it is
replaced by the
capacitor decade box.
Ground
bus
2.
Note: A single resistor
(of arbitrary colors) is
shown here, but it is
replaced by a
combination of resistors.
Ground
(2) Show here any necessary calculations to verify the cutoff frequency of your circuit.
3.
(4) Connect the function generator output as Vin and connect Vout to the oscilloscope. Play around with sine
waves of various frequencies and DC offsets, and test whether this simple high-pass filter works – does it
remove the DC offset, attenuate low frequencies, and let high frequencies pass? Record qualitative results.
4.
Now imagine that the resistor is of infinite value. In other words, it isn’t even there, as sketched below. This
circuit represents the simplest possible high-pass filter; it has a cutoff frequency of zero. In other words, all it
does is cut off DC (zero frequency) signals, but lets AC signals of any frequency pass through.
C
C
Vin
Vin
R
R
Vout
Ground
Vout
Ground
bus
5. Remove the resistor from your high-pass filter circuit so that you are left with the simplest possible high-pass
filter, as sketched above (just a capacitor in series with the voltage signal).
6. (4) Play around with the input frequency and DC offset of the function generator, and record your
observations. In particular, see if this simple circuit removes DC offset from the signal. Just record
qualitative results.
7. Remove the high-pass filter from the breadboard – we no longer need it.
Lab 6, Filter Lab Page 9
Discussion Questions
1. (8) How does a low-pass filter affect music? Discuss how this might be useful in concerts or recordings.
2. (8) Do the experimental gain measurements of your low-pass filter agree with the theoretical values? If not,
suggest possible reasons why not.
3. (7) Did the simplified high-pass filter perform as expected? Briefly justify your answer.
4. (7) Discuss how the predicted and actual cutoff frequency compare, based on your Bode plot.