Day 17: First Order Op Amp Circuits (Cont'd)

First Order Op Amp Circuits

Today we learned about Integrator and and differentiator circuits. These are made by adding capacitors into specific places of an inverting op amp circuit.

Shown below is an integrator circuit. This is created by putting a capacitor in place of the feedback resistor. The voltage and gain equations are shown above as well. 

Another example of an integrator circuit. This one has a very large resistor on top, which doesn't change too much. We were instructed to draw output waves given square, sine, and triangle input waves.

Inverting Differentiator



Our circuit schematic. We were asked to build a differentiator circuit to verify that the output of the circuit, V_out(t), is proportional to the inverse of the derivative of the input voltage, V_in(t).

Because we needed to use both oscilloscope inputs, out breadboard looks pretty messy, but it's quite a simple circuit.

Sinusoidal input voltage with frequency = 1kHz, amplitude = 1V, and offset = 0V to the circuit.

Sinusoidal input voltage with frequency = 2kHz, amplitude = 1V, and offset = 0V to the circuit.

Here is the range and base of each channel, for reference.

 Sinusoidal input voltage with frequency = 500Hz, amplitude = 1V, and offset = 0V to the circuit.

Here is the range and base of each channel, for reference.

You can see that as the frequency decreases, V_in remains proportionally smaller than V_out.

This whiteboard holds the values used in our circuit. As you can see, our resistor value changed quite a bit. We had a lot of issues with the Op amp saturating so our output wave would look more like a square wave. We tried lower and lower resistance values so that we could make the time constant smaller (Tau = 1/RC. Smaller R, smaller time constant, smaller output values). We eventually had to go down all the way from 1MΩ to 1kΩ. In addition, we also had to lower the input amplitude down to approximately .5V. This allowed us to get the necessary data.

Today we also learned about several switching functions. This exercise we were supposed to find and graph the current function given the voltage function across the capacitor.

Piecewise function of current, given voltage.

Another application of the switching functions. Find Voltage and current, given V_s(t).

Our final example today. Instead of capacitors in this one, we were given a large inductor with a switch. Work shown above.