AC Op amps and Oscillators

Today we began working with AC Op Amps using nodal analysis and converting the circuit into the frequency domain.

Here we found from the Barkousen Criteria that the gain has to be 3 or greater.   V2/Vo ratio has to be 1/3.

For the experiment here we have the every circuit.

Here we used mesh analysis to solve the circuit.

Effective or RMS value (Power)

We began the day with effecive and RMS values for power.  Here we plugged in power to solve for Irms.

Apparent power and power factor where S= VrmsIrms and P=VrmsIrmscos(thetav-thetai)

vrms of an inductor and a capacitor pictured below.

Notes on apparent and power factor.

An example solving for apparent power and the power factor.

More notes introducing the power phasor with real power and reactive power that being the imaginary power.

solving for power factor, apparent power and reactive power.

Another exercise using the power factor.

solving for power factor and reactive power.

Experiment pictures with changes of phase shift and power factor.

SINUSOIDAL STEADY STATE ANALYSIS

We began the day by learning about sinusoids with nodal analysis.  Here we worked on an example with Professor Mason.

Next we tried another example, but this time we used mesh analysis.

 Then we started the experiment of the day and created 3 different waveforms at 3 different frequencies. Here is the first one.

The Second one.

 The third one.
 Here we did an example using source transformation.

Here we worked on an example using v thevenin.

AC Equivalent of Resistance

We began the day by finding a relationship for Z.

Here we find the impedence of this entire circuit.

 Then we found the impedence across the capacitor.

Here we worked on an example with our group we corrected our results.

We then began to work on an experiment to calculate our current, gain and phase shift of the resistance, inductor and capacitor.

This is an exercise of inductor and capacitor in parallel and finding the voltage of a capacitor.

Sinusoids and phasors

We began the day by reviewing phasors from Electricity and Magnetism.

Here we write the graphical representation of the sinusoidal graphs and their equations.

For Rectangular coordinates its easier to add and subtract but for polar multiplication and division is simpler.

 Some equations for converting rectangular to polar.

Identities for sinusoids and phasors.

Overdamped, criitically damped, and Underdamped circuits

Today we learned about damped circuits.  Below we derived the equations for the RLC circuits.

A graph of critically damped from the Lab.

Other graphs related to our findings from the lab.

Below is the set up for this lab.

After calculations we got back the original equation.

Solving for A1 and A2 for an example.