week 15 day 2*

Lecture 

Calculating Resonance frequency(⍵0), Half power Frequencies (ɷ1,ɷ2), Bandwidth and quality factor of RLC circuit in parallel :

 Finding Transfer Function of a filter, Cutoff frequency of Filter is equal to the half power frequency of  RLC circuit:

Lab

For our Pre-lab, we calculated the Theoretical Cutoff frequency of lowpass and highpass filter by finding the transfer function of RL circuit on the resistor and inductor respectively.   inspecting the behavior of transfer function (H) when the frequency is approaching zero and infinity we observed that we the circuit behave as a low pass filter when we took Output Voltage at the inductor and high pass Filter if we took the output voltage at the resistor.

We measured A 99.6-ohm resistance and 1 mH inductance with a theoretical Cutoff frequency of 15915 HZ. We use our oscilloscope to measure the voltage of our inductor and resistor. We also created a custom channel by adding the 2 voltage to measure our input voltage.The yellow line represents the voltage of resistor, blue represent the voltage at the inductor and red is our input voltage.  We measured the amplitude and phase shift of our voltage out from both the inductor and resistor

Oscilloscope at 1591 Hz

Oscilloscope at 159150 Hz

 Values of the amplitude and phase shift at 8 different frequency

Summary

Our circuit acted as a lowpass filter when we put our output voltage across inductor and highpass filter when we put our output voltage across the resistor. Our experimental gain at the cutoff frequency is 0.67 and 0.695 at lowpass and high pass respectively, which is close to our theoretical value of 0.707.