Inverting Voltage Amplifier and OP Amp Relaxation Oscillator

Inverting Voltage Amplifier

In this lab we wired the inverting voltage amplifier with a capacitor in parallel with the feedback resistor. The measured values for the capacitor and resistors are shown in the diagram. Our goal is to calculate the theoretical gain and change in phase angles when we apply a 2 V sinusoidal input and vary the frequency from 100 Hz, to 1 kHz, to 5 kHz.

The theoretical value for gain is calculated as 1/sqrt(ω^2*C^2*R^2+1), where ω is the angular frequency, C is the capacitance and R is the resistance. It's important to note that the input and feedback resistors are the same value in this experiment. The theoretical phase angle is calculated as ϴ = arctan(ωCR). We calculate all of these values prior to taking experimental data. These values are then compared directly with the experimental values with a percent error for accuracy analysis. They can be seen on the last picture of this lab.

Here we see our circuit wired up on the breadboard with oscilloscope probes that will measure the input voltage signal and the output voltage signal. We now apply a 2 V sine wave at the three frequencies mentioned and obtained the following graphs.

The experimental phase shift is calculated as the change in time between a set of current-voltage peaks divided by the period. This is then multiplied by 360 to change to degrees. Phase shift = ϴ =(Δt/T)*360 or more simply, ϴ = Δt*f*360, where f is the frequency. Two pictures were taken at each frequency to capture the current and voltage peak times (necessary to find Δt). The experimental gain is given by the ratio of the output voltage to the input voltage, G = V0/Vi. This is easily taken from the measurements window on the oscilloscope and is the blue curve amplitude divided by the orange curve amplitude or (C2/C1).

 2 V Sinusoid @ 100 Hz

 2 V Sinusoid @ 1 kHz

 2 V Sinusoid @ 5 kHz

Here we see a direct comparison between our theoretical and experimental gain and phase shift angles. The percent errors (PE%) are also shown on the table. We see that the percent error is acceptable for the most part. As a relatively quick experiment, we are pleased with our results.

OP Amp Relaxation Oscillator

In this lab we create an oscillator OP amp circuit that acts like a switch that goes on and off at a certain interval, or frequency. To design the circuit, we choose an arbitrary number, in our case, we choose the last three digits of my ID number, 195. Therefore, we will attempt to design an oscillator that switches at a frequency of 195 Hz. Below we see the calculation for the feedback resistor value necessary to make this possible. We arrive at a 23.34 kΩ resistance necessary to achieve the 195 Hz oscillation. Since we do not have a resistor of that value, we use a 21.4 kΩ (measured) resistor in series with a 10 kΩ pot to achieve the resistance necessary.

Here we see the capacitor voltage (orange) along with the OP amp output voltage. We are applying a +/- 5 V to the OP amp rails and no source to the input. We can see that the voltage charges and discharges in a periodic fashion. This output voltage spikes quickly and saturates at about 3.9 V. We see that the average frequency is 212 Hz. Adjusting the potentiometer gives us this value or higher. If we accept this value we get a percent error of 8.6 %.