ECE 1212 Electronic Circuit Design Lab Summer 2017 …cjs188/labreport.pdf · · 2017-09-01PART C...
Transcript of ECE 1212 Electronic Circuit Design Lab Summer 2017 …cjs188/labreport.pdf · · 2017-09-01PART C...
ECE 1212
Electronic Circuit Design Lab
Summer 2017
Laboratory #3 – Active Filters and Oscillators
Instructor: Ahmed Dallal
Prepared By: Chris Siak, Erick Bittenbender
INTRODUCTION:
In this lab, different active filters were explored, including two active low pass filters, one
bandpass filter, and one oscillator design. By designing, constructing, and modifying these circuits, more
information could be obtained about how different circuit components impact the input-output
relationship of the operational amplifier. Additionally, the work done in the testing phase provided an
opportunity to test expectations on changes in circuit behavior. In all, this lab was broken into three parts.
The first part of the lab, Part A, explored the design and construction of two active low pass
filters. Each of the filters were given unique design constraints that impacted component selection and
varied the output seen for each circuit. After designing and testing these circuits, small changes were
made to the circuit to determine the impact of various components on active low pass filters.
Following Part A, the next part of the lab sought to design and implement a bandpass filter. Much
like Part A, this part of the lab centered around designing and constructing an active filter given certain
design constraints and determining the impact of slight changes to the design of the circuit.
Lastly, in Part C, an oscillator circuit is explored. Following a similar process as the one found in
Parts A and B, this section of the lab sought to optimize the design of the circuit after the initial design
and construction.
PROCEDURE:
PART A
1. To begin this lab, two low pass active filters were designed, constructed, and tested based on
given design criteria. The first low pass filter, referred to as Filter 1, had a corner frequency
of 380 Hz and a quality factor of 0.707. The second low pass filter, referred to as Filter 2, had
a cutoff frequency of 380 Hz as well with a quality factor of 1. Constraints were also applied
to the capacitor values and negative feedback resistances for Filter 1 and 2, respectively. The
circuit configuration can be seen in Figure 1.
a. In the design phase of this experiment, all resistance and capacitor values were
determined for each filter based on the restrictions laid out in the lab. For Filter 1,
capacitors C1 and C2 were to have the same value. For Filter 2, RA was replaced with
an open circuit and RB was replaced with a short circuit. For both filters, values for
R1 and R2 were chosen such that R1 equaled R2. Each resistor value in Filter 1 can be
found in Table 1, and each capacitor value in Table 2. The impedance values for
Filter 2 can be found in Tables 3 and 4, respectively.
b. Following the calculation of resistor and capacitor values in each filter’s circuit, the
magnitude and phase response of the filters were simulated using MATLAB. In order
to do this, the following transfer function of a low pass filter was used:
𝑇(𝑠) =𝐾𝜔𝑜
2
𝑠2 + (𝜔0𝑄 ) 𝑠 + 𝜔0
2
where K is the dc gain, ωo is the corner frequency of the filter in radians per second, and
Q is the quality factor of the filter. With the appropriate values plugged into the transfer
function, a MATLAB code was written that replicated the magnitude and phase of the
filter’s frequency response. Filter 1’s frequency response can be seen in Figure 2 and
Filter 2’s can be seen in Figure 3.
2. After obtaining theoretical expectations for the circuit, construction and testing of the circuit
was underway.
a. In order to measure the magnitude frequency response of these circuits, the Sweep
Tool was used to test the output voltage of the circuit while the frequency of the input
voltage was changed. The sweep covered from near 0 Hz to well past the corner
frequency of the filters. Once these sweeps were conducted, the data points collected
by the Sweep Tool were exported to Excel. From here, the output voltages could be
divided by the input voltage to obtain the gain of the circuit at a given frequency.
With these calculations, the gain could then be converted to decibels and graphed
against the frequency. The equation used to convert the ratio of output voltage to
input voltage to decibels is as follows:
|𝐴|𝑑𝐵 = 20𝑙𝑜𝑔|𝐴𝑣|
where Av is the ratio of output voltage to input voltage. The results of the sweep for Filter
1 can be seen in Figure 4 and the measured magnitude frequency response can be seen in
Figure 5. These same results can be seen for Filter 2 in Figures 6 and 7, respectively.
b. In addition to testing the filters as-built, there were additional tests conducted to
determine the effect of changing the resistance of RB in Filter 1. For these tests, the
resistor RB was increased by 15% and decreased by 15% from its original value.
After adjusting the value of RB, the magnitude frequency response of Filter 1 was
again measured in the same way that it had been for the original circuit construction.
The sweep for the 15% increase can be seen in Figure 8 and the sweep for the 15%
decrease can be seen in Figure 9. The measured magnitude frequency response for
each can be found in Figures 10 and 11, respectively.
PART B
3. The second experiment in this lab was to design and analyze a band pass filter with a center
frequency of 620Hz and a Q value of 7, just as we did with the two low pass filters in Part A.
We started off with building the first band pass filter on our breadboard according to the
schematic in Figure 12 using a 741 op amp chip and the following resistor and capacitor
values: R1=1kΩ, R2=440kΩ (built with 430kΩ and 10kΩ resistors in series), and C=12nF
(built from 10nF and two 1nF capacitors in parallel).
4. After the circuit was built, it was fed an input from the frequency generator and the output
was connected to the multimeter, and the Sweep VI software was opened to measure the
output rms voltage for a varied input frequency (from 10Hz to 4000Hz) on a 0.1Vpp sine
wave. The Sweep software screenshot showing the graph of output rms voltage vs. input
frequency can be seen in Figure 13.
5. This data was exported to Microsoft Excel as in Part A and a graph was made of 20 times the
log10 of the gain of the circuit (output rms voltage / input rms voltage) vs. input frequency
( |T(jω)| vs. ω ). This graph, as well as the measured values of the center frequency and
bandwidth for this circuit, can be seen in Figure 14. A comparison of this graph to the
expected |T(jω)| vs. ω from the prelab calculations can be found in the Discussion below.
6. Steps 3-5 were repeated twice more, this time with altered R2 values of 484kΩ and 396kΩ,
so that R2 was changed to be 10% above and below its original value. The frequency
response graphs for the bandpass filter circuits with R2 changed to 10% above and below its
original value, as well as values for each graphs center frequency and bandwidth, can be seen
in Figures 15 and 16, respectively. In addition, a discussion of the value of R2’s effect on the
center frequency and bandwidth of the filter can be found in the Discussion below.
PART C
7. The final experiment in this lab began with constructing a Wein-bridge oscillator circuit on
our breadboard according to Figure 17 in the Results below, using a 741 op amp chip and the
following resistor and capacitor values: R=12kΩ, C=0.01µF, R1=1kΩ, and R2=2kΩ. The
device was powered using the DC power supply and the output of the circuit was connected
to the oscilloscope, and a basic photo of the output of the circuit can be seen in Figure 18.
8. A potentiometer was added in series with R2 (one terminal of the pot was connected to the
inverting input and the wiper of the pot, and the other terminal was connected to R2) so that
the value of R2/R1 could be varied by twisting the knob on the pot. The potentiometer was
then varied until the value of R2+pot was at the point where the circuit initially began to
output oscillations (below this, the circuit will have no output). At this point, the frequency of
these oscillations was measured with the scope, and the total resistance of the R2+pot series
combination was measured. These values, as well as the scope display of the minimum
output, can be found in Figure 19. Further comparison was done on these measured values
with estimates based on the Barkhausen criterion; this analysis can be found in the Discussion
below. In addition, the potentiometer was adjusted so that very large oscillations would
occur, and the effect on the frequency can also be found in the Discussion. (A display of the
output with the potentiometer adjusted to a very large resistance can be seen in Figure 20.)
9. Last, the Wein-bridge oscillator circuit was adjusted so that it could be stabilized and produce
a stable output sinusoid not effected by too large of a gain. We did this by replacing R1 with
a small incandescent lamp rated at 24V and 50mA. A schematic for the updated stabilized
circuit can be seen in Figure 21. The scope was connected to the output of this circuit, and a
scope output of the circuit for a high input gain (high R2+pot value) for both a stabilized an
un-stabilized circuit can be seen in Figure 22. In addition, an explanation of how the addition
of the lamp works to stabilize the output can be found in the Discussion below.
RESULTS:
PART A
Prior to constructing the filters described by the schematic in Figure 1, component measurements
were taken for each resistor and capacitor. Tables 1 and 3 list the resistor, nominal resistance, and
measured resistance for all resistor components used in each filter. Tables 2 and 4 list the capacitor,
nominal capacitance, and measured capacitance for all capacitor components used in each filter. As stated
previously, MATLAB was used to provide theoretical magnitude and phase frequency responses for the
two low pass filters, which would be used as a basis of comparison after the low pass filters were properly
tested. Filter 1’s theoretical frequency response can be seen below in Figure 2, and Filter 2’s theoretical
frequency response can be seen in Figure 3. Each of these figures list the magnitude in terms of the ratio
of output voltage to input voltage. To compare these expectations to our circuit implementation, the
magnitude is converted to decibels using the equation:
|𝐴|𝑑𝐵 = 20𝑙𝑜𝑔|𝐴𝑣|
yielding a magnitude of approximately 4.02 dB for Filter 1 and a magnitude of 0 dB for Filter 2, peaking
at 1.21 dB.
FIGURE 1
TABLE 1
Resistor Nominal (kΩ) Measured (kΩ)
R1 1 0.985
R2 1 0.983
RA 1.708 1.768
RB 1 0.982
TABLE 2
Capacitor Nominal (µF) Measured (µF)
C1 0.419 0.401
C2 0.419 0.399
TABLE 3
Resistor Nominal (kΩ) Measured (kΩ)
R1 1 0.982
R2 1 0.982
RA ∞ -
RB 0 -
TABLE 4
Capacitor Nominal (µF) Measured (µF)
C1 0.838 0.878
C2 0.209 0.195
After obtaining these preliminary measurements and theoretical expectations, sweeps were
performed on both of the low pass filters. Because each had a corner frequency of 380 Hz, both were
swept over the same range of 10 Hz to 1 kHz in steps of 10 Hz with an input voltage of 0.1 Vpp. The
results of the sweeps can be seen in Figures 4 and 6 for Filter 1 and 2, respectively. With these data points
collected and exported to Excel, the magnitude frequency response of the filters could be obtained, as
described in the Procedure. The frequency response of Filter 1 can be seen in Figure 5 and the frequency
response of Filter 2 can be seen in Figure 7. The decibel gain for Filter 1 was approximately 4.19 dB
according to the extracted data points, and the decibel gain for Filter 2 was approximately 0.37 dB with a
peak of 1.71 dB.
FIGURE 4
FIGURE 5
FIGURE 6
-12
-10
-8
-6
-4
-2
0
2
4
6
10 100 1000
Gai
n (
dB
)
Frequency (Hz)
Filter 1 Magnitude Frequency Response
FIGURE 7
After constructing and testing the original specifications of these filters, some further work was
done to test the impact on the circuit if changes are made to resistor values in the construction. For Filter
1, the resistor RB was adjusted to by ±15% to determine the impact this would have on the quality factor
and magnitude frequency response of the circuit. Below are the sweeps conducted on Filter 1 after
adjusting the resistor RB in both directions. RB + 15% was calculated to be 1.15 kΩ with a measured value
of 1.130 kΩ. RB - 15% was calculated to be 850 Ω with a measured value of 855 Ω. Each sweep used an
input voltage of 0.1Vpp, and tested frequencies from 10 Hz to 1000 Hz in steps of 10 Hz. Figure 8 shows
the sweep conducted for +15% and Figure 9 shows the sweep conducted for -15%. Figures 10 and 11,
respectively, show the plotted magnitude frequency response in Excel for each of the aforementioned
tests.
-16
-14
-12
-10
-8
-6
-4
-2
0
2
4
10 100 1000G
ain
(d
B)
Frequency (Hz)
Filter 2 Magnitude Frequency Response
FIGURE 10
FIGURE 11
After testing the output voltage with these adjusted RB values, the new magnitude frequency
responses were compared with Figure 5 for a qualitative comparison of the effect on quality factor, and an
estimation of the gain for each before rejection was made using the exported Excel data points from the
Sweep Tool. The gain for +15% was approximately 4.70 dB and the gain for -15% was approximately
3.70 dB. By using the equation relating the dc gain with RB and RA and the equation relating the dc gain
with the quality factor, the quality factor for each of these tests could be obtained. The quality factor for
+15% was calculated to be 0.735, and the quality factor for -15% was calculated to be 0.659. The
equations used can be seen below:
-12
-10
-8
-6
-4
-2
0
2
4
6
10 100 1000
Gai
n (
dB
)
Frequency (Hz)
Filter 1 Magnitude Frequency Response with RB +15% Original Value
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
10 100 1000
Filter 1 Magnitude Frequency Response with RB -15% Original Value
𝐾 = 1 +𝑅𝐵
𝑅𝐴
𝐾 = 3 −1
𝑄
where K is the dc gain and Q is the quality factor.
PART B
Figure 12 – Schematic of Bandpass Filter
Figure 12 shows the schematic of the bandpass filter built for Part B of this lab. Note that the
nominal values for the resistors and capacitors, R1=1kΩ, R2=440kΩ, and C=12nF, were all measured at
R1=0.985kΩ, R2=439.56kΩ, and C=11.90nF, respectively.
Figure 13 – Sweep VI Display of Output RMS Voltage vs. Input Frequency for Bandpass Filter
Figure 13 shows the results of running the Sweep VI analysis of the bandpass filter circuit. The
graph displays the output Vrms values for varied input frequencies on a 0.1Vpp sinusoid input, from
10Hz to 4000Hz. Note that the output is relatively near zero for all input frequencies expect for a certain
middle range of about 400 to 1400Hz. This is the band of frequencies that are allowed to pass through this
specific bandpass filter and produce an amplified output.
Figure 14 – |T(jω)| vs. ω , Frequency Response Plot of Bandpass Filter, Measured Center
Frequency and Bandwidth of Filter
Figure 14 shows the graph of the decibel gain of the bandpass filter circuit plotted against the
input frequencies for which those gains occur. Note that the filter only allows a certain bandwidth of
frequencies to pass through, which is the purpose of the bandpass filter. To find the center frequency, we
used the data in Excel that used to make the plot and found the highest gain (42.67488 dB). The
corresponding frequency (610 Hz) is our center frequency, which is within 5% of the desired 620Hz, as
given in the lab manual. The bandwidth was found by dividing the center frequency by sqrt(2) and finding
the range of the two closest corresponding frequencies (850Hz – 450Hz = 400 Hz).
Center
Frequency
610 Hz
Bandwidth 400 Hz
Figure 15 – Sweep VI Display of Output RMS Voltage vs. Input Frequency for Bandpass Filter;
|T(jω)| vs. ω , Frequency Response Plot of Bandpass Filter, Measured Center Frequency and
Bandwidth of Filter (changed R2 value to 396kΩ, -10%)
Figure 15 shows what Figures 13 and 14 show, but for the altered bandpass filter with
R2=396kΩ, a -10% difference. The Sweep IV analysis was performed under the same settings, with input
frequencies varied from 10 to 4000Hz on a 0.1Vpp sinusoid. With the decrease in the value of R2 and
thus R2/R1, you can see that the maximum output Vrms has shifted slightly to the right. This is also true
for the Frequency Response |T(jω)| vs. ω plot, and while this graph looks nearly identical to that of Figure
14, an analysis of the point-by-point data in Excel shows that the center frequency is now 650 Hz, with a
dB gain of 42 here. The bandwidth also increased very slightly to 420Hz, with a range of 470 to 890Hz
providing a dB gain of at least 29.7.
Center
Frequency
650 Hz
Bandwidth 420 Hz
Figure 16 – Sweep VI Display of Output RMS Voltage vs. Input Frequency for Bandpass Filter;
|T(jω)| vs. ω , Frequency Response Plot of Bandpass Filter, Measured Center Frequency and
Bandwidth of Filter (changed R2 value to 484kΩ, +10%)
Figure 16 shows what Figure 15 shows, but for the altered bandpass filter with R2=484kΩ, a
+10% difference. The Sweep IV analysis was performed under the same settings as the previous two
tests, with input frequencies varied from 10 to 4000Hz on a 0.1Vpp sinusoid. With the increase in the
value of R2 and thus R2/R1, you can see that the maximum output Vrms has shifted slightly to the left,
occurring before 600Hz. This is again also true for the Frequency Response |T(jω)| vs. ω plot. An analysis
of the point-by-point data in Excel shows that the center frequency is now 590 Hz, with a dB gain of
43.655 here. The bandwidth also decreased very slightly to 380Hz, with a range of 430 to 810Hz
providing a dB gain of at least 30.869, which is equal to 43.655/sqrt(2).
Center
Frequency
590 Hz
Bandwidth 380 Hz
PART C
Figure 17 – Schematic of Wein-Bridge Oscillator Circuit
Figure 17 shows the schematic of the Wein-bridge oscillator circuit built for Part C of this lab.
Note that the nominal values for the resistors and capacitors, R=12kΩ, R1=1kΩ, R2=2kΩ, and C=0.01µF,
were all measured at R=11.809/11.811kΩ (connected to Vo / connected to GND), R1=0.985kΩ,
R2=1.970kΩ, and C=9.95/10.13nF (connected to Vo / connected to GND), respectively.
Figure 18 – Scope Display of Functioning Wein-Bridge Oscillator Circuit Output
Figure 18 shows the output sinusoid of the Wein-bridge oscillator circuit built in Part C of this
lab. Note that the circuit is outputting a sinusoidal waveform even though no sinusoids are being inputting
into the circuit. The waveform generator is not powered on or being used here, and the only power
coming in to the circuit is from the Vcc = ±15V.
Figure 19 – Scope Display of Minimum Output Sinusoid of Oscillator; Frequency of Sinusoid,
Measured Resistance of Potentiometer and 2kΩ Series System
Figure 19 shows the output of the oscillator circuit was the potentiometer was adjusted so that its
resistance was the smallest it could be with the oscillator still producing an output. The frequency of this
output was measured at 1.351kHz, and the measured resistance of the series system of the potentiometer
and the 2kΩ resistor was 2.027kΩ. Note that this resistance is makes the R2/R1 value equal to 2.027,
which is within 5% of 2, the expected smallest possible R2/R1 value that would allow the circuit to still
produce an output, as obtained in the prelab.
Figure 20 – Scope Display of Oscillator Output with Potentiometer Adjusted to Maximum
Resistance
Figure 20 shows the scope display of the oscillator output when the potentiometer was adjusted
so that the R2+pot resistance value (and thus R2/R1) was maximized. It is apparent that the sinusoid is
clipped at ±15V, which is Vcc, which explains why the Vpp of the sinusoid is close to 30V. Because of
the clipped and highly-gained sinusoid, the waveform almost appears to be a square wave. Lastly, note
that the frequency of the waveform has decreased to 1.136kHz. This will be further discussed below.
Frequency 1.351 kHz
Resistance of
potentiometer
+ 2 kΩ resistor
2.027 kΩ
Figure 21 – Schematic of Stabilized Wein-Bridge Oscillator Circuit
Figure 21 shows the schematic of the stabilized Wein-bridge oscillator circuit that was built for
the last part of Part C. Note that the resistor R1 has been replaced with an incandescent lamp, which is the
key component to stabilizing the oscillator. This is further discussed below. This was done so that as the
R2 resistance is increased, the lamp can burn brighter and absorb more power, thus having a higher
resistance and balancing out the R1/R2 value. Also note that the R2 value has been changed to 470Ω,
which was measured by the ohmmeter as 468.75Ω.
Figure 22 – Scope Display of both Un-stabilized (Left) and Stabilized (Right) Wein-Bridge
Oscillator Outputs When Supplied High-Gain Input
Figure 22 shows the difference between having a fixed resistor in place of R1 and having the
incandescent lamp in place of R1. For both cases, the potentiometer was adjusted so that the R2+pot
resistance value was very high, making the R2/R1 value high. Clearly, the output waveform on the right,
which has the lamp in place of the resistor, results in an unclipped output, while the fixed R1 resistor
cannot compensate for the high R2 value and leaves the waveform clipped. The reason this happens is
further discussed below.
DISCUSSION:
PART A
After simulating the filters from Part A in MATLAB and implementing the design on our
breadboard, we believe that the gain of our circuit matched the expectation for the output in both cases.
As can be seen in Figure 2, which shows the theoretical gain, and Figure 5, which shows the measured
gain, the expected decibel gain of Filter 1 before the corner frequency was approximately 4.02 dB and the
measured decibel gain of Filter 1 was 4.19 dB. The same information can be extracted for Filter 2 from
Figures 3 and 7, respectively. The theoretical decibel gain of Filter 2 was 0 dB with a peak of 1.21 dB,
and the measured decibel gain was 0.37 dB with a peak of 1.71 dB. While there are some discrepancies
with the measured values of Filter 2, we believe that these measurements indicate circuits that generally
functioned as expected with the same overall shape of the theoretical magnitude frequency response.
Most of the deviation can be attributed to electrical noise or tolerance of the constituent resistors and
capacitors (i.e. measured resistances and capacitances not exactly matching nominal resistances causing
compounding variation in the output). As a result, the measured frequency response will not match
exactly with the theoretical expectation.
Once the resistor RB was adjusted for Filter 1 in the two tests conducted in this lab, it was evident
that altering this resistor changes the gain of the filter and the quality factor of the circuit. When RB was
increased by 15%, the gain of the passband section of the filter was approximately 4.70 dB, jumping up
from the gain of 4.19 dB measured for the original circuit. The quality factor for this construction also
increased to 0.735 from the original measured quality factor of 0.725, as would be expected with an
increase to the dc gain of the circuit. Conversely, the 15% reduction of RB resulted in a decreased gain,
dropping to 3.70 dB, and a decreased quality factor, dropping to 0.659. All of these results were expected,
as indicated by the relationship between the dc gain and the resistance RB, and both the relationship
between the dc gain and the quality factor and the plots of the magnitude frequency responses of each
circuit after RB was adjusted. In terms of the plots, the increased RB Excel plot shows a sharper drop-off
in the stopband region of operation while the decreased RB Excel plot shows a flatter drop-off in the
stopband region compared against each other and the original plot for Filter 1. These changes in the
flatness or sharpness of the rejection are consistent with the calculated changes in quality factor.
Following the evaluation of Filter 1, some calculation and theoretical evaluation of Filter 2 was
conducted. The primary focus of this evaluation was the impact of a larger Q value on component
selection for the filter. When Q is made sufficiently large, the value of C1 becomes larger, as can be seen
in the following equation used for component selection and calculations:
𝜔𝑜
𝑄=
1 − 𝐾
𝑅2𝐶2+
1
𝑅1𝐶1+
1
𝑅2𝐶1
where ωo is the corner frequency in radians per second, Q is the quality factor, and K is the dc gain. With
a dc gain of 1 and assuming R1 and R2 are held constant and equal to each other, the equation can be
solved for C1, yielding the following result:
𝐶1 =2𝑄
𝜔𝑜𝑅
where R is the value of R1 and R2. In addition to finding this relationship, we can also relate C1, C2, and
ωo using the following equation:
𝜔𝑜2 =
1
𝑅1𝑅2𝐶1𝐶2
With this equation, ωo can be solved for and plugged back into the equation for C1 above. After doing
some algebra, the following ratio of C1 to C2 is found:
𝐶1
𝐶2= 4𝑄2
As can be seen by this ratio, as Q gets large, the ratio of C1 to C2 gets large as well. As this ratio gets
larger, the selection of component values for C1 and C2 gets more difficult because either C1 must get
larger or C2 must get smaller to satisfy the relationship. With a sufficiently large Q, the ratio of C1 to C2
could become large enough to cause problems with component selection due to lack of availability of
very large or very small capacitors.
PART B
For the initial design of the bandpass filter, all of our in-lab measurements and calculations were
as expected and agreed with predictions and calculations made in the prelab. For the prelab, we derived
the expected |T(jω)| vs. ω plot, and then while performing the lab, we produced the measured |T(jω)| vs. ω
plot, as previously seen in Figure 14. These plots matched in overall shape, and while our experimentally-
determined graph did not look like the ideal symmetrical bandwidth curve, the center frequency we found
in-lab was only 10 Hz different from the given specification in the prelab.
In addition, when we adjusted the R2 resistor value, we found that the center frequency and
bandwidth were also altered, due to the changing value of the R2/R1 gain. We found that by increasing
the resistance of R2 by 10% would result in about a 5% decrease in the center frequency, and a decrease
in R2 by about 10% would result in a 7% increase in the center frequency. This is a negative relationship
between the resistance R2 and the center frequency: as the resistance increases, the center frequency
moves to the left on the x-axis, and vice versa. This is because when looking at the formula given in
lecture for the center frequency ( 𝜔𝑜2 =
1
𝐶2(𝑅1𝑅2+𝑅12)
), you can see that as the value of R2 increases, the
value of ωo must decrease. Technically, the difference for a plus and minus 10% change in R2 should
have resulted in equal but opposite changes in ωo, but the fact that this did not happen was likely due to
the lack of precision with the Sweep IV analysis, with only so many data points being taken.
The relationship between bandwidth and R2 resistance can also be analyzed just as with the
center frequency and R2. We found experimentally that as the R2 resistance is increased by 10%, the
bandwidth of the frequency response plot decreases by 5% (20Hz difference from 400 to 380Hz). In
addition, we found that as the R2 resistance is decreased by 10%, the bandwidth of the frequency
response plot increases by an equal but opposite 5% (20Hz difference from 400 to 420Hz). This is
perfectly explained by the equation for finding bandwidth as given in lecture: 𝐵𝑊 = 3
𝐶(𝑅1+𝑅2) . Clearly, a
negative relationship should exist between the bandwidth and the resistance R2, and if R2 is changed in
equal but opposite values, the bandwidth should do the same.
PART C
Our constructed Wein-bridge oscillator circuit worked as expected, and outputted oscillations for
and DC Vcc input supply, as seen in Figure 18 and 19 above. Our findings were in agreeance with the
Barkhausen stability criterion, which states that the gain must be over a certain threshold in order to
produce the oscillations, which in our case was equal to 2.027 = R2/R1, which was only slightly different
from the prelab-calculated minimum gain of 2.
As the gain of the circuit was increased (in other words, as the potentiometer in series with R2
was adjusted to a high resistance across), we found that the oscillations grew in peak-to-peak voltage, and
the sinusoids continued to grow even as the peaks were clipped by the lack of voltage supplied to Vcc.
The lab manual discusses finding voltages higher or lower than our set Vcc, but for our maximum
potentiometer resistance, we found that the peak-to-peak voltage of our clipped output sinusoid was still
slightly under our ±Vcc gap. In addition, we found that as R2 and the gain is increased via the
potentiometer, the frequency of the oscillations decreases (frequency of the output at minimum
oscillations was 1.531kHz, and at maximum was 1.136kHz). This was as expected, as the larger the gain
gets, the higher the peak-to-peak voltage of the output, and the more it gets stretched out horizontally.
The incandescent lamp was added to the circuit in order to stabilize the output. By using a lamp
in place of R1, the lamp can absorb more power and have a higher internal resistance as needed. So, when
the gain of the circuit is increased with the potentiometer, the lamp in place of R1 can adjust to the high
gain and absorb more power and burn brighter / at a higher temperature, thus having a higher internal
resistance than before and balancing out the R2/R1 gain of the circuit, allowing for unclipped outputs as
the R2 value is increased, which explains the Results in Figure 22.
CONCLUSION:
After conducting the lab, we gained valuable insight on the operation and design of simple active
filters and oscillators. By going through the process of designing, testing, and modifying each of the
circuits described in this lab, our knowledge of these circuits and our expectation of their operation has
been bolstered. With this information, we can confidently design and construct low pass and bandpass
filters with operational amplifiers.
In all, the results we obtained were either similar to what we expected, or could be explained
based on conclusions drawn about the operation of the different circuits in this lab. As a result, we are
confident that the work we did in this lab was fruitful and operation of these circuits is understood.
By exploring these different circuit configurations, we were able to continue building off of
previous lab experiments and further develop our understanding of operational amplifiers and the various
implementations for these devices. The work done in designing and implementing these circuits can be
used beyond the scope of this class for signal processing and can be a valuable tool for future design work
in this class and in others.
REFERENCES:
• Lecture material for Lab 3 available on Courseweb
o Including Lecture slides, notes, experiment guides
• Prof. Ahmed Dallal
• TA Daud Emon