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Lectures 35+36

# Lectures 35+36 - Poles zeros transfer functions initial and...

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Lectures 35+35 Poles, zeros, transfer functions, initial and final value Theorems, constructed responses

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Transfer functions Can describe input-output relationships in RLC circuits with transfer functions Inputs can be: voltage or current sources Or initial conditions Outputs can be either voltages or currents Key idea: translate input, output, circuit into “s” domain If V out (s) = V in (s)·H(s) H(s) = V out /V in H(s) is the “transfer function” H(s) can be written as a ratio of two polynomials in s. Nth order polynomials can be factored into a product of N (s+x) terms. In the numerator, these are called “zeros”: when s=-z, H(-z) = 0 In the denominator these are called “poles”: when s=-p, H(-p) = ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29( 29 ( 29( 29 ( 29 ( 29( 29 ( 29 n m n n n n m m m m out in out in out p s p s p s z s z s z s b s a s a s b s b s b s s H s b s a c s s bs as ab c s s H s G s bs as ab V V s H s bs as ab c s V V s bs as ab s V s bs as ab c s s V s V + + + + + + = + + + + + + + + = + + + = + + + + = = + + + = = + + + + = + + + + + + + + = - - - - ... ... ... ... ) ( ) ( ) ( 1 ) ( 2 1 2 1 1 1 1 1 1 1 2 2 0 2 2 0 2 In General:
Poles • Poles give form of your solution. – Single, real poles give exponentials – Complex poles • Always come in conjugate pairs • Give exponential times sinusoid – Repeated poles: exponential times t • Can plot pole locations on

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Lectures 35+36 - Poles zeros transfer functions initial and...

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