Frequency Response and Filters

Mission (if you choose to except it): Calculate the gain across a capacitor (low pass filter frequency response) and resistor (high pass filter frequency response) and then compare it to the experimental results to verify the theory.

Low pass circuit design:

Note: we did not use an oscilloscope, but rather used two multimeters to measure the voltage across the voltage supply (Vin) and the voltage across the capacitor (Vout)

Set up: measuring voltage across capacitor

Set up: measuring voltage of the source (Thanks Micheal for being our hand model)

Experimental data measuring V(out) and Frequency

we maintained the Voltage of the source to be 5 Vrms

Theoretical Gain magnitudes (at 50Hz 320Hz 1280Hz 10,000Hz) 

Vout (40Hz) = 4.94 V => dividing by 5 we get 0.97 ..Hurray!

Vout (320Hz) / Vin = 2.3/5 = 0.46 ..life is good!

Vout (1280Hz) / Vin = .61/5 = 0.122 ..awesome sauce!

Vout (10,000) / Vin = 0.078/5 = 0.156 ..Epic!

We like graphs so lets plot this stuff

 High pass Filter Experimental Results

Note: The graph of this data appears to be bell shaped were the gain at low frequencies is small and you will reach a peak between 640Hz and 1280Hz and will begin to drop off as frequency in increased.

Plot of High pass data:

Conclusion:

The measured data fits the theoretical values extraordinarily well. The largest percent error we obtained was 2.5 % at the highest frequency of 10,000Hz. (0.016-0.0156)/0.016 *100 = 2.5% error.