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HW_16 - T s 1 form and the other one is in the form and in...

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EE 438 Homework #16 1. For the circuit of Fig. 1 derive the transfer function, ( ) ( ) ( ) s V s V s A i o v = , in which all of the parenthesis terms are in the ( form and in which all of the constants appear as numerical values. The component values in the circuit are ) T s / 1 + R 1 = 9 k , R 2 = 1 k , C 1 = 1 µ F. 2. For the circuit of Fig. 2 derive the transfer function, ( ) ( ) ( ) s V s V s A i o v = , in which all of the parenthesis terms are in the ( form and in which all of the constants appear as numerical values. The component values in the circuit are ) Ts + 1 R 1 = 25 k , R 2 = 100 k , C 1 = 5 nF. 3. The circuit of Fig 3 has a transfer function, ( ) ( ) ( ) s V s V s A i o v = , which consists of an isolated s term in the numerator and two parenthesis terms in the denominator. Solving a quadratic equation is required to find the denominator parenthesis terms. The component values in the circuit are R 1 = 1 k , R 2 = 1 k , C 1 = 5 µ F, C 2 = 20 nF. (a) Find the expression for the transfer function arranged so that the parenthesis term involving the larger of the two T values is in the
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Unformatted text preview: ( T s / 1 ) + form and the other one is in the ( form and in which all constants appear as numerical values. ) Ts + 1 (b) Use the low frequency approximation to find the low frequency transfer function, , arranged so that any parenthesis term is in the ( ) ) ( s A A s A l mid vl = ( ) T s / 1 + form and in which all constants appear as numerical values. (c) Use the high frequency approximation to find the high frequency transfer function, , arranged so that any parenthesis term is in the ( ) ) ( s A A s A h mid vh = ( ) Ts + 1 and in which all constants appear as numerical values. (d) Form the approximate transfer function ( ) ( ) s A s A A s A h l mid v ) ( = using the expression found in parts (b) and (c). (Note: Observe the differences between this expression and the one derived exactly in part (a)). 1 2 Fig. 1 _ + V i V o + _ R 1 C 1 R 2 Fig. 2 C 2 _ + V i R 1 R 2 V o + _ Fig. 3 C 2 _ + V i R 1 C 1 R 2 V o + _...
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