Chap6StudentSolutions

5 j 10 j 995 j 20 10 000 2 j 20 j 20 2 10000

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Unformatted text preview: w asymptotic and exact magnitude and phase Bode diagrams for the frequency responses of the following circuits and systems. (a) R1 = 1 kΩ R 2 = 10 kΩ + vi (t) + C1 = 1 µF C2 = 0.1 µF - v 2(t) C - From Exercise 26(b) Solutions 6-22 M. J. Roberts - 8/16/04 H( jω ) = 1 1 − ω R1R2C1C2 + jω (C1 + C2 ) R1 + R2C2 [ 2 H( jω ) = 1 1 − 10 ω + j 2.1 × 10 −3 ω −6 2 0 -20 |H(jω)|dB -40 -60 -80 -100 -120 -140 1 10 2 3 10 10 4 ω 5 10 6 10 10 0 Phase of H(jω) -0.5 -1 -1.5 -2 -2.5 -3 -3.5 1 10 2 3 10 10 4 ω 5 10 6 10 10 (b) X(jω) (c) jω jω+10 10 jω+10 Y(jω) A system whose transfer function is H( jω ) = H( jω ) = j 20ω = ( jω + 10 − j 99.5)( jω + 10 + j 99.5) j 20ω 10, 000 − ω 2 + j 20ω j 20ω ω ω2 − 10000 1 + j 500 10000 30. Find the transfer function for the following circuit. What function does it perform? if(t) Rf i i(t) C i + vi (t) vx(t) + vo(t) - - 31. Design an active highpass filter using an ideal operational amplifier, two resistors and one capacitor and derive its transfer function to verify that it is high pass. Solutions 6-23 M. J. Roberts - 8/16/04 Use an inverting amplifier configuration. Let the feedback impedance be a simple resistor. Choose an input impedance that is high at low frequencies and approaches a Z f ( jω ) constant at high frequencies so that the transfer function, − approaches zero at Zi ( jω ) low frequencies and approaches a constant at high frequencies. Vo ( f ) , of these active filters and identify them as Vi ( f ) lowpass, highpass, bandpass or bandstop. 32. Find the transfer functions, H( f ) = (a) C4 R1 R5 vx(t) + C3 + vi (t) - vo(t) R2 - Sum currents to zero at node, vx ( t ) , and at the input node of the operational amplifier, which must be at zero volts because the ideal operational amplifier gain is infinite. Remember the input impedance of the operational amplifier is infinite so no current flows into its input terminals. Vx ( f )(G1 + G2 + j 2πfC3 + j 2πfC4 ) − Vi ( f )G1 − Vo ( f ) j 2πfC4 = 0 − Vx ( f ) j 2πfC3 − Vo ( f )G5 = 0 Solve for the transfer function. H( f ) = j 2πfR5C3 (2πf ) 2 R1R5C3C4 − j 2πfR1(C4 + C...
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