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

FIGURE 2

FIGURE 3

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 8

FIGURE 9

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