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Lecture%2026_%20Mar%2030%202011

# Lecture%2026_%20Mar%2030%202011 - Example The function has...

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26 -1 Chapter 17 Amplifier Frequency Response Lecture 26 Cover Section: 17.0 – 17.2

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Transfer Functions 26 -2 For sinusoidal time variations, the input voltage to a amplifier can be written as: V i is the phasor input voltage, it has an amplitude and a phase. A sinusoidal signal is the only signal in nature that is preserved by a linear system. Therefore, if the amplifier is linear, its output voltage can be written : The ratio of V o to V i is called the voltage gain transfer function . It is a function of frequency. A( ϖ ) is the gain function and ϕ ( ϖ ) is called phase function.
Transfer Functions 26 -3 Use complex frequency, s, to replace j ϖ in writing transfer functions. In general, most transfer functions can be written in the form: Where K is a gain constant and N(s) and D(s) are polynomials in s containing no reciprocal powers of s. The roots of D(s) are called the poles of the transfer function. The roots of N(s) are called the zeros.

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Unformatted text preview: Example: The function has a zero at s = -4 and poles at s = -2 and s = -3. Transfer Functions 26 -4 s is an operator which represents d/dt in the differential equation for a system, the transfer function contains the differential equation. Above example: Replace s with d/dt: Bode Plots 26 -5 A Bode plot is a plot of either the magnitude or the phase of a transfer function T(j ϖ ) as a function of ϖ . The magnitude plot is more common since it represents the gain of the system. 1 st example: This function has a pole at s = -ϖ 1 and no zeros. When When When Bode Plots 26 -6 2 nd example: This function has a zero at s = -ϖ 1 and no poles. When When When Bode Plots 26 -7 3 rd example: This function has a zero at s = 0, and a pole at s = -ϖ 1. When When When Bode Plots 26 -8 4 th example: This function has a zero at s = -ϖ 2 , and a pole at s = -ϖ 1. When When When ϖ 1 < ϖ 2...
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