Chapter 6, Problem 6.8PT

Solve for the transfer function H( f )= V out / V in and draw the asymptotic Bode magnitude and phase plots for the circuit shown in Figure P6.57.

Determine an expression for the circuit of FigureP6.54(a) for the equivalent impedance in standardform. Choose the Bode plot from Figure P6.54(b) thatbest describes the behavior of the impedance as a function of frequency, and describe (a simple one-linestatement with no analysis is sufficient) how youwould obtain the resonant and cutoff frequencies andthe magnitude of the impedance where it is constantover some frequency range. Label the Bode plot toindicate which feature you are discussing.

a. Determine the frequency responseVout( jω)/Vin( jω) for the circuit of Figure P6.1. b. Plot the magnitude and phase of the circuit forfrequencies between 10 and 107 rad/s on graphpaper, with a linear scale for frequency. c. Repeat part b, using semilog paper. (Place thefrequency on the logarithmic axis.) d. Plot the magnitude response on semilog paper withmagnitude in decibels.

Consider a circuit for which the output voltage is the running-time integral of the input voltage, as illustrated in Fig­ure P6.14. If the input voltage is given by v in ( t )= V max cos( 2πft ). find an expression for the output voltage as a function of time. Then, find an expression for the transfer function of the integrator. Plot the magnitude and phase of the transfer function versus frequency.

Sketch the magnitude of the transfer function H( f )= V out / V in to scale versus frequency for the circuit shown in Figure P6.30. What is the value of the half-power frequency? [Hint: Start by finding the Thévenin equivalent circuit seen by the capacitance.]

Figures (a) to (e) below show the asymptotic Bode diagrams (magnitude and phase) of the constituent parts of five different open-loop transfer functions, ??(?). The Bode diagrams are colour coded. Write the transfer function corresponding to the pair of Bode plots in the space provided to the right of each figure. No need to show any working – just write the standard form of transfer function equation for each diagram.

In the circuit of Figure P6.9: R = 1.3 k2 R2 = 1.9 k2 C = 0.5182 µF Determine: a. How the voltage transfer function V.(jo) V.(jo) Hy(j») = behaves at extremes of high and low frequencies. b. An expression for the voltage transfer function and show that it can be manipulated into the form H. H,(jo) =TFjf(@)

In Chapter 4, we used the time constant to characterize first-order RC circuits. Find the relationship between the half-power frequency and the time constant.

6 For the filter circuit shown in Figure P6.26: a. Determine if this is a low-pass, high-pass, bandpass, or bandstop filter. b. Compute and plot the frequency response function if L = 11 mH C = 0.47 nF R = 2.2 k2 R2 = 3.8 k2 eee T. V Go) R c+ Vja)