Op Amp Relaxation Oscillator Lab

Objective:
The purpose of today's class meeting was to focus on Op Amp AC circuits. The key to analyzing op amp circuits is to treat them as ideal op amps. This means that no current enter the positive and negative intervals of the op amp. The voltages at the positive and negative inputs are zero. The first step in dealing with op amp ac circuits is to transform the circuit to the frequency domain and then apply the ideal op amp analyzation to find the output voltage. We also covered the idea of producing or converting dc to ac by the process of an oscillator. An oscillator is circuit that produces an ac waveform as output when powered a by a dc input. However, in order for sine wave oscillators to sustain oscillation, they must meet the Barkhausen criteria which is that the overall gain must equal 1 or greater and the overall phase shift must be zero. Finally, we covered instantaneous power and average power.

Group Practice:
1. The problem shows an ac op amp and the first step is to convert its frequency domain. We then apply the idea that the op amp is ideal. With this in mind, we can solve for the voltage output more easily. Though, we must first apply nodal analysis at node 1 and 2 as show in figure 1.

Figure 1. AC op amp

2. The problem below shows how to solve for the instantaneous power which is the power at any instant time. If the voltage and current are in the form of a cosine as seen in figure 2, we can calculate the power by multiplying the voltage and current. We then apply trigonometric identity and express in the form as seen below.

Figure 2. Solving for instantaneous power while applying a trigonometric identity. 

3. Below, we have circuit and are told to find the current flowing through the resistor and capacitor, as well as finding the current flowing through the inductor. In order to find the currents, we must first solve for the overall current flowing through the AC power source. Then we can apply a current divider. Though, we must transform the circuit to its phasor domain. We will then find the Zeq in order to find the overall current.

Figure 3. Solving for the currents in the circuit.

Op Amp Relaxation Oscillator Lab:
1. The lab requires us to create an oscillator in which a dc source is converted to ac. Based on figure 4, we must design an op amp relaxation oscillator having a frequency of Hz. However, we must find a convenient capacitor and β = R1/(R1+R2). We choose β=1/2, so R1 and R2 will be 1KΩ. We will use the equation as seen in figure 5 to find the resistance R. But first we find the Period which is t=1/f. Thus, out theoretical T = .00196. We substitute the period, β, and capacitor into the equation in figure 5 and acquire a theoretical resistance R =896ohms

Figure 4. Op Amp Relaxation Oscillator

Figure 5. Theoretical Calculations.

2. We measure our component as follows, R= 874Ω±.5, R1=.985KΩ±.005, R2= .985KΩ±.005, C=.95 μF±.005. The actual set can be seen below.

Figure 6. Actual circuit set up.

3. We tested our oscillator id did not acquire an expected waveforms. We tried fixing the problem but were unable to find the solution on why our plot looked uneven.

Figure 7. Results for voltage across the capacitor. 

4. The results should be similar to the image as seen in figure 8.

Figure 8. Expected results.