Problems

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Problems

Section 14.2 Transfer Function

14.1 Find the transfer function Io∕Ii of the RL circuit in Fig. 14.68. Express it using ω0 = R∕L.

Figure 14.68 For Prob. 14.1.

14.2 Using Fig. 14.69, design a problem to help other students better understand how to determine transfer functions.

Figure 14.69

• For Prob. 14.2.
• 14.3 For the circuit shown in Fig. 14.70, find H(s) = Vo(s)/I*ⁱ* (s).

Figure 14.70

For Prob. 14.3.

14.4 Find the transfer function H(s) = Vo∕Vi of the circuit shown in Fig. 14.71.

14.5 For the circuit shown in Fig. 14.72, find H(s) = Vo∕Is.

Figure 14.72 For Prob. 14.5.

14.6 For the circuit shown in Fig. 14.73, find H(s) = Vo(s)∕Vs(s).

Figure 14.73 For Prob. 14.6.

Section 14.3 The Decibel Scale

14.7 Calculate ∣H(ω)∣ if HdB equals

(a) 0.1 dB (b) −5 dB (c) 215 dB

14.8 Design a problem to help other students calculate the magnitude in dB and phase in degrees of a variety of transfer functions at a single value of ω.

Section 14.4 Bode Plots

14.9 A ladder network has a voltage gain of

etwork has a voltage gain of

\n

$$\mathbf{H}(\omega) = \frac{10}{(1 + j\omega)(10 + j\omega)}$$

Sketch the Bode plots for the gain.

• 14.10 Design a problem to help other students better understand how to determine the Bode magnitude and phase plots of a given transfer function in terms of jω.
• 14.11 Sketch the Bode plots for

$$\mathbf{H}(\omega) = \frac{0.2(10 + j\omega)}{j\omega(2 + j\omega)}$$

14.12 A transfer function is given by

$$T(s) = \frac{100(s+10)}{s(s+10)}$$

Sketch the magnitude and phase Bode plots.

14.13 Construct the Bode plots for

$$G(s) = \frac{0.1(s+1)}{s^2(s+10)}, \qquad s = j\omega$$

14.14 Draw the Bode plots for

the Bode plots for
\n

$$\mathbf{H}(\omega) = \frac{250(j\omega + 1)}{j\omega(-\omega^2 + 10j\omega + 25)}$$

14.15 Construct the Bode magnitude and phase plots for

$$H(s) = \frac{2(s+1)}{(s+2)(s+10)}, \qquad s = j\omega$$

14.16 Sketch Bode magnitude and phase plots for

h Bode magnitude and phase pl

$$H(s) = \frac{1.6}{s(s^2 + s + 16)}, \quad s = j\omega$$

14.17 Sketch the Bode plots for

Let the Bode plots for

\n

$$G(s) = \frac{s}{(s+2)^2(s+1)}, \qquad s = j\omega$$

14.18 A linear network has this transfer function

ar network has this transfer function
\n

$$H(s) = \frac{7s^2 + s + 4}{s^3 + 8s^2 + 14s + 5}, \qquad s = j\omega$$

Use MATLAB or equivalent to plot the magnitude and phase (in degrees) of the transfer function. Take 0.1 < ω< 10 rad/s.

14.19 Sketch the asymptotic Bode plots of the magnitude and phase for ____________________ (^s + 10)(s + 20)(s + 40) , s = j^ω

$$H(s) = \frac{80s}{(s+10)(s+20)(s+40)}, \qquad s =$$

14.20 Design a more complex problem than given in Prob. 14.10, to help other students better understand how to determine the Bode magnitude and phase plots of a given transfer function in terms of jω. Include at least a second order repeated root.

14.21 Sketch the magnitude Bode plot for

ch the magnitude Bode plot for
\n

$$H(s) = \frac{10s(s + 20)}{(s + 1)(s^2 + 60s + 400)}, \qquad s = j\omega$$

14.22 Find the transfer function H(ω) with the Bode magnitude plot shown in Fig. 14.74.

Figure 14.74 For Prob. 14.22.

14.23 The Bode magnitude plot of H(ω) is shown in Fig. 14.75. Find H(ω).

Figure 14.75

• For Prob. 14.23.
  • 14.24 The magnitude plot in Fig. 14.76 represents the transfer function of a preamplifier. Find H(s).

For Prob. 14.24.