10.52 An amplifier with a dc gain of 60 dB has a single-pole,high-frequency response with a 3-dB frequency of 100 kHz.(a) Give an expression for the gain function A(s).(b) Sketch Bode diagrams for the gain magnitude and phase.(c) What is the gain–bandwidth product?(d) What is the unity-gain frequency?(e) If a change in the amplifier circuit causes its transferfunction to acquire another pole at 1 MHz, sketch theresulting gain magnitude and specify the unity-gainfrequency. Note that this is an example of an amplifierwith a unity-gain bandwidth that is different from itsgain–bandwidth product.

D **2.93 Derive the transfer function of the circuit in Fig. P2.93 (for an ideal op amp) and show that it can be written in the form Vo Vi = −R 2/R1 [1+(ω1/jω)][1+j(ω/ω2)] whereω 1 =1/C1R1 andω2 =1/C2R2. Assuming that the circuit is designed such that ω2  ω1, find approximate expressions for the transfer function in the following frequency regions: (a) ω  ω1 (b) ω1  ω  ω2 (c) ω  ω2 V o Figure P2.93 Use these approximations to sketch a Bode plot for the magnitude response. Observe that the circuit performs as an amplifier whose gain rolls off at the low-frequency end in the manner of a high-pass STC network, and at the high-frequency end in the manner of a low-pass STC network. Design the circuit to provide a gain of 40 dB in the “middle-frequency range,” a low-frequency 3-dB point at 200 Hz, a high-frequency 3-dB point at 200 kHz, and an input resistance (at ω  ω1) of 2 k.

1.78 For the circuit shown in Fig. P1.78, first evaluate Ti (s) = Vi(s)/Vs(s) and the corresponding cutoff (corner) frequency. Second, evaluate To(s) = Vo(s)/Vi(s) and the corresponding cutoff frequency. Put each of the transfer functions in the standard form (see Table 1.2), and combine them to form the overall transfer function, T(s) = Ti(s) × To (s). Provide a Bode magnitude plot for |T(jω)|. What is the bandwidth between 3-dB cutoff points?

1.77 A voltage amplifier has the transfer function A v = 1000 1+j 10 f 5 1+ 10 jf 2  Using the Bode plots for low-pass and high-pass STC networks (Figs. 1.23 and 1.24), sketch a Bode plot for |Av|. Give approximate values for the gain magnitude at f =10 Hz, 102 Hz, 103 Hz, 104 Hz, 105 Hz, 106 Hz, 107 Hz, and 108 Hz. Find the bandwidth of the amplifier (defined as the frequency range over which the gain remains within 3 dB of the maximum value).