Signals with Multiple Frequency Components

Signals with Multiple Frequency Components

Overview: 

In this lab, we predicted the magnitude response of an electrical circuit when an input signal is applied to it. Then, we actually applied the signals, and compared the circuit's response to our predicted response. The types of signals that applied were a signal composed of multiple sin waves with different frequencies, and a sinusoidal wave with a time varying frequency (also known as a sinusoidal sweep).

Design:
We designed the following circuit to execute the measurements:

Both R's were set to 1300 Ohms

^^^^^ C was set to 100 nF ^^^^

Based on simple nodal analysis, we find that the magnitude response (the ratio of amplitude of the output sinusoid to the input sinusoid) is equal to:

H(w)=(Vout/Vin)=[1/(2+(S/(10^5))]

This implies that as the frequency fluctuates with time, so does the magnitude response of the circuit: If the frequency is low, the capacitor acts as an open circuit, which results in an output that is half of Vin. When the frequency is high, the capacitor acts as a short, resulting in a Vout of zero.

Construction and Execution:

 ^^^^ Resistances of both R values ^^^^

 ^^^^ Measured capacitance of C ^^^^

Completed Circuit from side ^^ and above >>

^^^^ 500 Hz Vout ^^^^

 ^^^^ 1000 Hz Vout ^^^^

 ^^^^ 10KHz Vout ^^^^

The yellow line of the graphs is the circuit's Vout. As the frequency increases, the Vout amplitude decreases accordingly. This is what we predicted.

^^^^ Sweep circuit response ^^^^

The yellow line is once again the circuit's Vout. Once again, as the frequency of the input wave increases, the Vout amplitude decreases. This confirms our suspicions and calculations.

Analysis: 

As the oscilloscope outputs suggest, our predictions were correct. As the frequency of the input wave increases, the Vout amplitude progressively drops to zero. Also, the output of a signal with multiple sinusoidal frequencies successfully filtered out the high frequency portion of the wave, leaving only the low frequencies of the input wave. 

Conclusion:

Filters like these are incredibly useful for transmission of data, as they can easily decode things like radio waves. Filters of all sorts can be used to filter out unwanted frequencies.