Inverting Voltage Amplifier / Op Amp Relaxation Oscillator Labs

Inverting Voltage Amplifier Lab

Overview:

In this lab, we measured the gain and phase responses of an inverting voltage amplifier circuit, and compared the measurements with expected values.

Design:

We designed the following circuit to conduct the lab:

^^^^ C is the capacitor on top ^^^^

The resistors 'R' were both set to 10K ohms

The capacitor 'C' was set to .1 microFarads

The op amp used was an OP27

Based on the fact that the input voltage and the output voltage are complex exponentials, we can 

Calculate the circuit's input/output relationship using the equation:

Vout/Vin =   1/(1+j*omega*R*C)

Calculate the circuit's amplitude gain using the equation:

| Vout/Vin | =   -1/sqrt(1+(j*omega*R*C)^2)

and finally calculate the phase shift relationship between input and output using the equation:

angle(Vout) - angle(Vin) = 180 - arctan(1/(omega*R*C))

Construction and Execution:
We began by measuring the resistance and capacitance of the elements. A few sample pictures are shown below:

^^^^ (Left) Measured resistance of left resistor and (Right) measured resistance of top resistor ^^^^

Measured values of elements:

R left: 9.85 Ohms

R top: 9.94 Ohms

C: .099 microFarads

Naturally, the slight differences in measured values from ideal values would propagate to a huge level of uncertainty, so we had to do all of our calculations twice. Once before measuring the values, and once after measuring the values, to recieve more accurate predictions.

We calculated gain and phase shift values at three different frequencies: 100 Hz, 1 KHZ, and 5 KHZ. The table of calculated values are below, with the 'updated' (and more accurate) values being on the right:

We then constructed the circuit, and subjected it to a sinusoidal input voltage of varying frequency (as mentioned above) and amplitude of 2V. Below is a snapshot of it:

Results:

Beginning with 100 Hz, these are our results:

Measured gain: 1.48/2 = .74
Expected gain: .847
% difference in gain: 12.6 % (yikes)

Measured phase shift: 31.50 degrees
Expected phase shift: 32.01 degrees
% difference in phase shift: 1.60 % (sweet)


Now, 1 KHz:

Measured gain: 0.32/2 = .16
Expected gain: .16
% difference in gain: 0 % (holy crap)

Measured phase shift: 82.03 degrees
Expected phase shift: 80.82 degrees
% difference in phase shift: 1.50 % (sweet)

Now 5 KHz:

Measured gain: .08/2 = .04
Expected gain: .032
% difference in gain: 25 % (yikes)

Measured phase shift: 87.76 degrees
Expected phase shift: 88.15 degrees
% difference in phase shift: .45 % (sweet)

Analysis:
Overall, the values were all pretty much perfect other than the gains. A possible source of error though, is that we didn't record the exact values, so the analysis was based on simply eyeballing the graph. We wont make that mistake again. Obviously, the method is accurate though.

Op Amp Relaxation Oscillator Lab

Overview:

In this lab, we designed an Op Amp Relaxation Oscillator having a frequency of 921 Hz.

Design:

We designed the following circuit to execute the objective:

**** Ignore the wires going up to the top left of the schematic and out to the right of the schematic. Also, ignore the inverted poles for the +/- 5 V supplies. ****

R was 10K ohms

R1 was 1K ohms

Ca was 1 microFarad

R2 was our controlling variable, creating the oscillation frequency of choice (in our case 921 Hz)

Using the equations:

T = 2RC ln {(1+beta)/(1-beta)}

-and-

beta = R1/(R1+R2)

We were able to calculate the necessary value for R2.

R2 = 35,413 Ohms.

Below are our calculations:

Construction and Execution:

With the calculations completed, we tested our circuit virtually in EveryCircuit:

^^^^ SMASHING SUCCESS!!! ^^^^

We then constructed the circuit as seen below. *Note* R2 was a rather unique resistance, and we had very limited selection of resistors, so we threw several in series to achieve the desired result (Net resistance equaled 35K ohms)

Results:
After supplying power to the voltage rails, these were our results:

^^^^ Voltage across the capacitor ^^^^

^^^^ Voltage out of the Op Amp ^^^^

Measured Values:

T = 1.09 ms

Therefore the measured frequency is 917.4 Hz

desired frequency is 921 Hz

% error: .39%

Analysis:

Things went great; I feel like a million bucks. With a percent error of a marginal .39%, the method of creating relaxed oscillators via Op Amps is flawless.