Bandwidth and Signal Analysis

Introduction:
Power in an AC RLC circuit can be maximized if there is no power lost in the capacitor and inductor. This is achieved at a particular frequency known as the resonant frequency. For our purposes we can limit the frequency to a theoretical bandwidth.

Our circuit contained in:
10 Ohm and 100 Ohm resistor
1 uF and 100 uF capacitor
2.2 mH capacitor
Vmax=4.0V

To find the resonant frequency we first calculated the theoretical value for each case.

Measuring the maximum current in the circuit gave us the maximum power since Pmax=kVI
CASE 1

CASE 2

The bandwidth of the each circuit allowed us range to find the maximum current. According to the experiment the power was maximized at 34.1 mA and 148.7 mA at frequencies of 503 Hz and 5436 Hz. This disagrees with the theoretical calculation so no conclusion about resonant frequency can be reached except that resonant frequency is inversely proportional to capacitance.

Frequency Response and Filters

Objective:
A filter can be used to separate frequencies in a circuit. Two ways to do so is to use a high pass or low pass filter by adding a capacitor. We are able to test and show a filter in use by measuring the gain and voltage of a circuit with a capacitor.

First we set up a circuit for a high pass filter then a low pass filter according to the following diagrams.

This is what the circuit looked like set up

From measuring the voltage across the capacitor and resistor for a low high pass and low pass filter respectively, here are the results.

The graphs were created using a logarithmic scale and the gain can be seen as a function on the graph.

Conclusion:

Matching the theoretical gain of a high pass filter to our actual gain shows a close agreement which validates the theory of frequency filters.