## Monday, August 12, 2019

### Frequency Response of Networks Essay Example | Topics and Well Written Essays - 1250 words

Frequency Response of Networks - Essay Example The essay "Frequency Response of Networks" talks about the theory behind frequency response in inductive and capacitive reactances and presents the plot of frequency response of the RC filter and which regions that these filters operate in. Frequency domain analysis is easier than time domain analysis It is important to obtain the frequency response of a circuit because we can predict its response to any Input signal. There are four general types of filters: Low-pass filters (LPF), Band-pass filters, High-pass filter (HPF) and Band-Reject (Stop). In this laboratory experiment, we will plot the frequency response of a network by analyzing RC passive filters. Capacitive reactance derivation from equation Vcos(Ãâ€° t + p) where V is the amplitude (can be current or potential), Ãâ€° is the angular frequency, t is time, and ÃŽ ¦ is a phase shift. The current flowing through a capacitor is given by i = C(dv/dt). Naturally, since v = V cos(Ãâ€°t+ ÃŽ ¦), DV/dt would equal - Ãâ€° Vsin(Ãâ€°t+ ÃŽ ¦). Using trigonometric identity we can rewrite sin as cos and get Ã¢â‚¬â€œÃâ€°Vcos (Ãâ€°t+ {ÃŽ ¦ -90}) (subtracting 90 degrees from sin to get cosine) by taking the derivative of the voltage and multiplying it by the capacitance we get the current flowing through the capacitor i = - Ãâ€°CVcos(Ãâ€°t+ [ÃŽ ¦ -90]). This is in the time domain. In order to derive the impedance/reactance, it must be converted to the frequency domain by writing the voltage and current as a phasor solving using Euler's Identity where ejx = cosx + jsinx j is the imaginary number.