Transcript conferenceLabManual - local.rose

UNDERSTANDING LEARNING DIFFICULTIES IN
CONTINUOUS-TIME SIGNALS AND SYSTEMS COURSES AND
MAKING THESE COURSES MORE ACCESIBLE
Lab Manual for Conference Workshops
Part 1: Overview of the Signals Exploration Platform (SEP)
Part 2: Exercises using the SEP
Part 1: Overview of the Signals Exploration Platform (SEP)
The Signals Exploration Platform (SEP) offers several types of inputs and processing
paths that can be quickly and easily configured while minimizing debugging
Inputs
Signal
MIC
ECG
Inst Amp
S
vy(t)
Pot
-5 to 5
1
Impulse
Pulse
ZOH
Bypass
1st order
Up to
6th order
0 vz(t)
DC clock
3
Speaker
Driver
Sampling
To
speaker
To
Scope/
Analyzer
The power supply is sufficient to drive an 8W load, has less than 5mV
ripple noise, and also protects the board.
•
•
•
•
•
•
•
+12 DC input with at least 2A capability
(5mm OD x 2.5mm ID adaptor)
Reverse polarity protection
1A fuse protection
9V switching supplies with short circuit
protection (CUI V7809-1000R)
P-filters to reduce switching noise
LED indicators for each rail
The fuse can be replaced with a PTC self
resetting device
J9
WK0001-ND
PWR
3
U10
+
-
1
1
U11
VIN
2
CDBHM260L
C16
10u 50V
V7809-1000R
GND
4
VOUT
L1
VDD
3
R32
3.9k
47u
+
C17
10u
2
J7
2
1
2
3
1
1A fast acting fuse
C18
22u
C19
820u
D5
LG R971
0
C20
10u 50V
VIN
V7809-1000R
GND
U12
2
1
VOUT
3
D6
LG R971
+
C21
10u
L2
4
47u
C22
22u
0
star ground
C23
820u
R33
3.9k
VSS
The input stage enables you to choose from a variety of signals and
then multiply or add to them.
vout (t )  vx (t )vy (t )  vz (t )
Inputs
Signal
MIC
ECG
Inst Amp
vx(t)
vy(t)
YIN
5
S
Pot
-5 to 5
1
vz(t)
0
ZIN
vout(t)
Instrumentation Amp
•
INA827 for generic differential to single-ended
conversion (gain =10)
•
9V supply posts provided for Wheatstone bridge
applications
ECG Input
•
ECG is isolated to 5000V with optoisolator
•
Three ports: ECG_POS (LH), ECG_NEG (RH), and RLD
(RL)
•
Requires a separate 9V battery and connector
•
LED indicator for the 9V battery
Microphone Input
•
Omnidirectional 100Hz-20kHz electret microphone
•
Gain of 90 and high-pass filter with -3dB at 40 Hz
Generic voltage signal input
•
10kW input impedance for function generator and
other general voltage signals
Multiplier and Adder
•
AD633 handles multiplication and addition of signals
•
Multiplying signal can be selected by switch: 1) time
varying input, 2) constant gain between 5, or 3)
unity.
•
Adding signal can nulled or set to time varying signal
The sampling stage is a loaded switch controlled by a clock. The type
of clock and load determine the form of sampling.
CTL
IN
OUT
load
6
How to control the sampling switch
• If the switch is set to SHORT the switch is
always closed and the signal passes
through unsampled
• If the switch is set to SAMPLE, then an
applied CLK signal will periodically open
and close the switch.
• OPEN switch when CLK = -9V, CLOSED
switch when CLK = +9V
• Low duty-cycle pulses will simulate impulse
sampling
• 50% duty-cycle pulses implements square
wave
Loading the switch
• Round fuse holder is for the loading
element
• Load with a 1-5kW resistor for regular
sampling
• Load with a 10-100nF capacitor for ZOH
type sampling
• Do not use polarized capacitors
The filter stage can implement 1st through 6th order filters.
• OpAmps are pre-wired on board
• Passive elements go straight across
sockets for standard filters
• Nodes are labeled on the board
• Stayed with lowpass topologies in
order to keep things simple
• 6th order path has 3 MFB 2nd order
stages, can easily bypass a stage
Single Stage of 6th Order Path
1st Order Path
load
load
V-
V+
7
Vout
Vin
load
Vx
load
Vin
load
load
load
load
VVout
V+
The output stage can drive both a high and low-impedance load
simultaneously with low distortion.
•
•
•
•
•
VDD
6 mA bias
•
R26
3k 20mW
8
D1
D1N4004
f ilter_out
5
-
7
D2
D1N4004
100mW
D3
D1N4004
R28
1
D4
D1N4004
R29
3k
VSS
8
R27
1
SPK_POS
TL072
4
6
+ U7B
+
Q1
BSP52
900mW
Need > 1 cm^2 pad
SPK_NEG
0
BSP62
Q2
V_OUT is before the driver and can only drive
high-impedance loads such as oscilloscope
SPK_POS and SPK_NEG come from a
darlington push-pull output that can drive
low-impedance loads
The output stage has thermal runaway
protection
Output voltage saturates at 5V
Into an 8W load, the current shouldn’t be
greater than 625mA DC
The supplies can drive up to 1A in either
direction so the load should not be less than
5W or the protection will shut down the
board
Now lets talk about the user interface for the Digilent equipment.
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10
11
12
Part 2: Exercises that use the SEP
Lab 1 focuses on signal modeling and LTI system properties to
determine the limitations of the board.
Materials
2 function generators and 3-channel scope
Mini Lab
Steps
Linearity of amplifiers
(Homogeneity)
1.
2.
3.
4.
5.
6.
Linearity of amplifiers
(Additive)
1.
2.
3.
Time Invariance
1.
2.
3.
4.
5.
6.
14
Questions for students
Set the input stage to have a gain of 1.
1.
Apply a triangle wave input with a 1V amplitude to the SEP.
Double the input amplitude and see if output doubles but
2.
doesn’t change shape
Continue to increase input amplitude until the output
3.
changes shape. Record this amplitude.
Change the gain of the input stage on the SEP to 3.
Change the amplitude of the input signal until the output just
begins to saturate. Compare this amplitude to the value
recorded previously
How would you describe the boundaries under
which the system behaves linearly?
How does the gain affect the linearity of the
system?
Why is it easier to work with linear systems?
Reset the gain of the board to 1.
1.
Apply two equal-amplitude triangle waves with 2x frequency
difference to the board such that the board adds them
together.
Change amplitudes of the two inputs to observe both linear
and nonlinear operation. Record the amplitude limitations
for which the system behaves linearly.
How do the amplitude limitations change when
adding signals together?
Set the SEP’s gain to be controlled by the potentiometer.
Apply a square wave with very short duty-cycle pulses to the
signal input. (acts like impulses)
Observe that the impulse response is always the same.
Set the multiplying signal to be YIN.
Set YIN to be a sinusoid (time-varying gain).
Observe that the impulse response is now different
depending on when it is applied.
1.
Explain how this experiment relates to the definition
of time invariance “A delay in the input causes an
equal delay in the output, but otherwise the output is
unchanged.”
Lab 2 focusses on periodic signals with DTMF signals and musical
instruments as realistic applications
Materials
2 function generators, 3-channel scope, spectrum/frequency
analyzer, DTMF generator, musical instrument
Mini Lab
Steps
Frequency, amplitude,
phase, and power
1.
2.
3.
4.
5.
Sums of sinusoids and
periodicity
1.
2.
3.
4.
5.
6.
15
Questions for students
Apply a sinusoid to the primary input of the SEP
1.
Measure the output of the board with both a scope and
spectrum analyzer
2.
Verify that the power and frequency measured on the
spectrum analyzer correspond to the scope.
Adjust the phase, frequency, and amplitude of the sinusoid
and observe how the time and freq measurements change
Connect the speaker. Increase the amplitude of the sinusoid
until the system no longer behaves linearly. Observe what
happens in the time and frequency domains and the sound.
Why is the power of the sinusoid not affected by
phase or frequency?
What happens to the frequency domain
measurements and the sound when the system
behaves nonlinearly?
Apply sinusoids to the primary and summing inputs of the
1.
SEP and set frequency, amplitude, and phase to be same.
Measure the SEP output with the spectrum analyzer and
2.
scope and the two inputs with the scope and connect the
output to a speaker.
Observe what happens to the measurements and sounds as 3.
you adjust the phase of one of the sinusoids.
Increase the frequency of one of the sinusoids to be 1.1x
greater than the other. Change its phase and amplitude.
Increase the frequency of one of the sinusoids to be 2x
greater than the other. Change its phase and amplitude.
Use the DTMF tones of 697Hz and 1209Hz for the number 1.
Change the phase and amplitude of one of the signals.
Why does phase affect the power level only when
the signals have the same frequency?
Why does the scope have difficulty capturing the
output signal for the DTMF frequencies but the
spectrum analyzer does not?
Why is the waveform stable on the scope when the
frequencies are 2x different but not for the DTMF
frequencies?
Spectra of other signals
1.
2.
3.
4.
5.
6.
Realistic periodic signals 1.
2.
3.
16
Apply a 50% duty-cycle square wave to the primary input of
the SEP.
Adjust the amplitude, frequency, delay, and duty cycle of
the square and measure how the spectrum changes.
Increase the amplitude of the square wave so that the
system no longer behaves linearly. Measure the spectrum
again.
Apply a triangle wave to the primary input of the SEP and
record the spectrum.
Adjust the amplitude, frequency, delay, and symmetry of
the triangle wave. Record the spectrum again.
Increase the amplitude of the triangle wave until the system
no longer behaves nonlinearly. Record the spectrum again.
1.
Switch to the microphone input on the SEP
Connect the scope and the spectrum analyzer to measure
the SEP output.
Play an instrument into the microphone and record the
measurements. (a straw flute or empty water bottle work
well, also online keyboard synthesizer
http://www.bgfl.org/custom/resources_ftp/client_ftp/ks2/
music/piano/guitar.htm )
1.
2.
3.
4.
2.
Both the square and triangle waves have multiple
frequencies. What is the relationship between
these frequencies?
Why do the nonlinearities of the system change the
spectrum of the triangle wave more than the
square wave?
Why does the time-delay not affect the power
spectrum of the signal?
Why does the number of harmonics present
change with duty-cycle? Explain this
mathematically.
Determine the fundamental frequency of the signal
in both the time and frequency domains. Are they
the same?
Using a note/frequency chart, determine what note
is being played by using the time and frequency
domain measurements.
Lab 3 introduces filtering and uses the ECG and DTMF signals as the
realistic applications
Materials
2 function generators, 3-channel scope, ECG electrodes, DTMF
generator, passive parts for filtering
Mini Lab
Steps
Using an impulse train
1.
to measure the
2.
frequency response of a
filter
3.
4.
5.
6.
7.
Filtering Single Sinusoid
1.
2.
3.
4.
5.
6.
17
Questions for students
Set the input stage to have a gain of 1.
1.
Apply a very small duty-cycle square wave to the primary
input (behaves like impulse train).
2.
Observe the input signal in the time and frequency domain.
Measure the power level of the harmonics.
3.
Insert passives to make a first-order lowpass filter that has a
-3dB frequency equal to the 4th harmonic of the impulse
train. Set the jumpers to filter the signal.
Measure the power levels of the first 10 harmonics at the
output of the filter, and record the time and frequency plots.
Change the passive elements to be a highpass filter.
Record the power levels of the first 10 harmonics and the
output of the filter in the time domain.
What does the output of the filter in the time
domain represent?
How do the different filters affect the harmonics
differently?
Using the mathematical model of the filters,
estimate how each harmonic of the input signal
should change and compare this to the measured
values.
Reset the gain of the board to 1.
Insert passives to make a first-order lowpass filter with a 3dB frequency of 500Hz.
Apply a sinusoid to the primary input of the filter with a 1V
amplitude and frequency of 50Hz.
Sweep the frequency of the sinusoid to 5kHz, taking regular
measurements of phase shift and amplitude.
Reset the frequency to 50Hz, set the gain and amplitude so
that the nonlinearities of the system are very evident.
Sweep the frequency of the input signal again over the same
range and measure the output in time and frequency.
Predict what the output of the filter will be at
several different frequencies and verify it with
measurements.
When the system behaves linearly, what are the
only properties of the input that can change?
When the system behaves nonlinearly, how does
the filter affect each of the harmonics of the signal?
1.
2.
3.
Filtering a square wave
1.
2.
3.
4.
5.
Filtering a DTMF signal
1.
2.
3.
4.
5.
Looking at an ECG Signal 1.
2.
3.
4.
5.
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Apply a 50% duty-cycle square wave to the primary input.
Insert passives to create a first-order lowpass filter with a 3dB frequency that is approximately equal to the 3rd
harmonic of the square wave.
Measure the power at each of the first 10 harmonics of the
square wave with and without filtering.
Record the output of the filter in the time domain.
Change the capacitor value of the filter. Then measure the
harmonics and record the time domain again.
1.
Set the primary input to be the DTMF signal for the number
3.
Insert passives to make a first-order lowpass filter with a
-3dB frequency of 700Hz and a highpass filter with a -3dB
frequency of 1400Hz.
Record the input signal in both the time and frequency
domains.
Record the output signals of each filter in both the time and
frequency domains.
Compare the input recordings to the output recordings.
1.
Set up the SEP to measure ECG signals.
Insert passives to create a first-order lowpass filter with a 3dB frequency of 100Hz.
Record the ECG signal both with and without filtering.
Change the -3dB frequency of the filter to be 10Hz.
Record the output of the filter again.
1.
Using the mathematical modeling, predict how each
of the harmonics of the square wave will change
due to the filter and verify with measurements.
2.
2.
3.
4.
2.
For each of the filters, why is one frequency
approximately -6dB below the other frequency?
Does the larger amplitude frequency at the output
of each filter correspond to the number 3 in the
DTMF code?
Why are the filters unable to completely eliminate
the second tone?
Design a continuous-time system that would be able
to completely decode the full range of DTMF
signals.
With the 100Hz filter, at what frequency was most
of the “noise” in the signal?
Why does the 10Hz filter eliminate most of the
noise but not significantly affect the “shape” of the
ECG signal?
Lab 4 compares the 6th order to 1st order filter and introduces the
different types of filters with the real application of filtering a speech
signal
Materials
2 function generators, 3-channel scope, spectrum/frequency
analyzer, passive parts for a 1st order lowpass filter and 6th order
Butterworth, Chebychev, and Bessel lowpass filters.
Mini Lab
Steps
For each of the types of
filters, perform the
following steps
1.
2.
3.
4.
Filtering a speech signal 1.
2.
3.
19
Questions for students
Apply a very low duty cycle pulse wave to the input signal
1.
and adjust the scope to capture just a single impulse
response of the filter.
Use the spectrum analyzer to display the power spectrum of
the impulse response.
2.
Change the input signal to be a sinusoid with 1V amplitude
Plot the input and output signals on the scope and measure
the change in amplitude and phase as you sweep the
frequency of the input signal
Why is the power spectrum of the impulse
response similar to the plot of the gain that you
measured from the sinusoids at different
frequencies?
Explain why the phase shift jumps from negative to
positive between adjacent frequency steps for the
6th order filter. Why doesn’t it jump like this for the
first order filter?
Apply the “these” waveform to the input signal
1.
st
Using each of the three filter pathways in turn: unfiltered, 1
order, and 6th order, listen to the output of the filter on the
speaker.
2.
Working with a partner, switch to the microphone input and
have one partner speak into the microphone while the other 3.
listens to the speaker
Why do the 1st order and 6th order filters make the
speech sound different even though they have the
same cutoff frequency?
What sounds from the word “these” are eliminated
by the filters and which remain? Explain.
When speaking into the microphone, which
consonant and vowel sounds pass through the filter
mostly unaltered? Explain.
FilterPro from Texas Instruments is an excellent piece of software for
designing op-amp based filters.
http://www.ti.com/tool/filterpro
20
Here is the circuit schematic for the filters and the table that is used
to collect data.
1st order filter
+
+
Name
Value
R1 (Stage 1)
6.2K
R2 (Stage 1)
6.2K
C1 (Stage 1)
100nF
Op Amp
V-
-
Vin
+
+
0
TL074
3 stage cascade of 2nd order MFB circuits for 6th order Chebychev Type I lowpass filter with fc=250Hz and 2dB of ripple in the stopband.
21
Table 1: Data from the 1st Order Filter
Freq
Amp (Vpp)
Gain (dB)
Delay (ms)
Phase (deg)
10
50
100
150
200
250
300
500
1k
2.5k
25k
200
250
300
350
400
450
500
200
250
300
350
400
450
500
Table 2: Data from the 6th Order Butterworth Filter
Freq
Amp (Vpp)
Gain (dB)
Delay (ms)
Phase (deg)
10
50
100
150
Table 3: Data from the 6th Order Chebychev Filter
Freq
Amp (Vpp)
Gain (dB)
Delay (ms)
Phase (deg)
22
10
50
100
150
This is what the unfiltered speech signal should look like for the word
“these”.
23
Lab 5 introduces sampling and filtering to recover a sampled signal
with speech as the realistic example
Materials
2 function generators, 2-channel scope, and passive for a 1st order
and 3rd order filter, a 1kW resistor and 10nF capacitor for
sampling
Mini Lab
Steps
Sample and recover a
COS4 waveform using
impulse sampling
1.
2.
3.
4.
5.
Questions for students
Install a 1kW resistor into the sampling -switch load socket
Apply a 100ms pulse signal at 1kHz to the CLK input
Apply the COS4 signal to the input signal at 50Hz
Observe the input and output signals on the scope in both
time and frequency for the following conditions:
1.
Unfiltered
2.
1st order filter
3.
6th order filter
Repeat the experiment with sampling frequencies of 500Hz
and then 200Hz
Sample and recover a
COS4 waveform using
square wave sampling
1.
Repeat the same series of experiments but change the CLK
signal to be a 50% duty cycle square wave.
Sample and recover a
COS4 waveform using
ZOH sampling
1.
Replace the 1kW resistor in the sampling -switch load socket
with the 10nF capacitor.
Repeat the same series of experiments but change the CLK
signal back to the 100ms pulse at 1kHz.
Sampling a speech
signal
1.
2.
2.
3.
24
Go back to the setup for the impulse sampling, but change
the input signal from COS4 to “these”
Design a first order filter to recover the speech signal.
Starting at 500Hz, increase the sampling frequency until the
word sounds normal.
1.
2.
3.
4.
5.
Why does the 1st order filter create a better
recovered signal for the ZOH sampling than the
other forms of sampling?
Explain how aliasing can occur even if the sampling
frequency is higher than the Nyquist rate.
Explain why the 6th order filter does a better job of
recovering the signal than the 1st order filter.
Explain how and why the copies of the original
spectrum are different for the three different forms
of sampling.
Explain why you can recover the signal with a lower
order filter when using ZOH sampling.
1. Explain why the sampling frequency had to be
increased in order for the word to sound normal.
2. Explain the relationship of the necessary sampling
frequency to the spectrum of the word “These”