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# An Analysis of the Frequency Response Representation

Introduction The frequency response is a representation of the systems response to sinusoidal inputs at varying frequencies The output of a linear system to a sinusoidal input is a sinusoid of the same frequency but with a different magnitude and phase The frequency response is defined as the magnitude and phase differences between the input and output sinusoids The frequency response comprises of two parts 1 Gain Response 2Phase Response The frequency response of a system can be viewed two different ways via the Bode plot or via the Nyquist diagram Both methods display the same information the difference lies in the way the information is presented These will be discussed in more detail in the theory section of this report The circuit design is shown below Circuit Functional Role of the Circuit The circuit can be viewed as a potential divider network Shown in Fig 2 The reactance of the capacitor is given as The circuit as a low pass filter A first order low pass RC filter is simply an RC series circuit across the input with the output taken across the capacitor We assume that the output of the circuit is not connected or connected only to high impedance so that the current is the same in both R and C The voltage across the capacitor is IXC IwC The voltage across the series combination is IZRC IR2 1wC212 so the gain is From the phasor diagram for this filter we see that the output lags the input in phase At the angular frequency w wo 1RC the capacitive reactance 1wC equals the resistance R We show this characteristic frequency on all graphs on this page For instance if R 1 kW and C 047 mF then 1RC wo 21 103 rads-1

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