Solution+HW19 - Problem 9.37 Design an active highpass...

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Unformatted text preview: Problem 9.37 Design an active highpass filter with a gain of 10, a corner frequency of 2 kHz, and a gain roll-off rate of 40 dB/decade. Solution: To secure a roll-off rate of 40 dB/decade we need to use two stages of the circuit in Fig. 9-24. R s C s R f 1 R f 2 V o V s + _ + _ + _ R s C s + _ The two stages have the same input impedances ( R s and C s ). We choose R f 1 = R s = 10 k , R f 2 = 100 k . Consequently, G 1 = R f 1 R s = 1 , G 2 = R f 2 R s = 10 . The overall response is: H ( ) = V o V s = G 1 G 2 parenleftbigg j / HP 1 + j / HP parenrightbigg 2 = 10 parenleftbigg j / HP 1 + j / HP parenrightbigg 2 , with HP = 1 R s C s . The problem statement specifies a corner frequency f c = 2 kHz with a corresponding angular frequency c given by c = 2 f c = 4 10 3 rad/s . By definition, c is the angular frequency at which the magnitude of H ( ) is equal to 0.707 of its maximum value. Thus, at = c , | H (...
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This note was uploaded on 02/21/2011 for the course MSE 231 taught by Professor Bedford during the Spring '10 term at University of Michigan.

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Solution+HW19 - Problem 9.37 Design an active highpass...

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