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Unformatted text preview: Connexions module: m0028 1 Transfer Functions * Don Johnson This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License Abstract Introduction of transfer function(frequency response). The ratio of the output and input amplitudes for Figure 1 (Simple Circuit), known as the transfer function or the frequency response , is given by V out V in = H ( f ) = 1 i 2 fRC +1 (1) Implicit in using the transfer function is that the input is a complex exponential, and the output is also a complex exponential having the same frequency. The transfer function reveals how the circuit modi es the input amplitude in creating the output amplitude. Thus, the transfer function completely describes how the circuit processes the input complex exponential to produce the output complex exponential. The circuit's function is thus summarized by the transfer function. In fact, circuits are often designed to meet transfer function speci cations. Because transfer functions are complex-valued, frequency-dependent quantities, we can better appreciate a circuit's function by examining the magnitude and phase of its transfer function (Figure 2 (Magnitude and phase of the transfer function)). Simple Circuit v in + R C v out + Figure 1: A simple RC circuit. * Version 2.20: Aug 8, 2009 6:23 pm GMT-5 http://creativecommons.org/licenses/by/1.0 http://cnx.org/content/m0028/2.20/ Connexions module: m0028 2 Magnitude and phase of the transfer function-1 1 1 1 / 2 |H(f)| 1 2 RC 1 2 RC f (a)-1 1 / 4 / 4 / 2 / 2 H(f) f 1 2 RC 1 2 RC (b) Figure 2: Magnitude and phase of the transfer function of the RC circuit shown in Figure 1 (Simple Circuit) when RC = 1 . (a) | H ( f ) | = 1 (2 fRC ) 2 +1 (b) ( H ( f )) =- (arctan (2...
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This note was uploaded on 07/06/2011 for the course EE 110 taught by Professor Gupta during the Winter '08 term at UCLA.
- Winter '08