Week 13 day 1

Lecture 

Using Nodal Analysis to calculate the output voltage of inverting op-amp, note that we have to convert all the capacitor into their phasor form first :

An op-amp with no feedback: when the voltage across the inverting and non-inverting input are equal, then the output voltage is equal to zero

 Instantaneous Power equation, given  sinusoidal current and voltage, applying Sum Trig identities  we can separate power to time independent average power

Op-Amp Relaxation Oscillator 

Pre Lab: 

Designing Op AMP relaxation oscillator  to produce 777 Hz  frequency  using 100 nF capacitance

we calculated a theoretical resistance of  7.32

We measured the  capacitance of 90 nF acorss the capacitor 

TO obtain resistance close to 7.5 K connected 5.49 K and  1K resistor in series

To check our circuit we run the model in every circuit, here we get a frequency of  769 Hz, which is really close to our desired frequency.  Don't forget to shake the op amp inorder to jump start !!

The final step we run our circuit with a +/- 5 V saturation:

view of our Circuit:

first, we scope the feedback resistor to compare our graph with every circuit graph:

Our frequency across the feedback resistor is 812 Hz, that's 4.5% difference from our desired Frequency 

Lastly, we scoped the voltage across the resistor and the output voltage of the OP AMP :

The result is identical with what our theoretical graph predicted, the output voltage of op amp is a step function, while voltage across the capacitor is a combination between an inverse exponential and exponential graph 

Summary 

In an AC OP  AMP circuit, we can apply nodal analysis to calculate output voltage by using phasor and impedance.  In our OP AMP Relaxation oscillation Lab, we use saturation of op amp as a way to create a periodical function. We designed a circuit that gives 777 Hz frequency, we then tested our design using both every circuit and oscilloscope. Our final design are able to produce oscillator with 813 Hz frequency. We obtained a 4.5% difference, these difference in values is caused by our inability to find a precise resistor.