Bandwidth and Signal Analysis

In an AC powered RLC circuit the power delivered to a resistor will be maximum at some resonant frequency. This property of RLC circuits allows people to tune into specific radio stations without picking up on other frequencies that are being broadcast simultaneously.

In this experiment our goal is to solve theoretically for the resonant frequency for a circuit of known elements, and compare with measured results. We will do this two times with different elements in the circuit for each trial.

To find the bandwidth experimentally we will adjust the frequency until we get a current reading Im/squrt 2

Trial 1

R = 10 ohm

C =  1 micoF

L = 2.2 mH

Bandwidth threshold is between 3393 +/- ~360 Hz

Percent error in bandwidth (1420-723)/723 *100 = 97%

Trial 2

R=100

C = 100 micro F

Percent error in Bandwidth (8070 - 7230)/7230*1100 = 11.6%

Conclusion: 

We were able to obtain experimental results that matched reasonably well to theoretical values.

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.