Questions

15.10 For the Colpitts oscillator in Fig 15.14(a), show that the admittance Y of the tuned circuit seen by the transistor between the drain and the source is zero at ω = ω0. (This is the reason the current I = 0.)

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15.9 Using C = 16 nF, find the value of R required for the circuit in Fig. 15.13 to produce 1-kHz sine waves. If the diode drop is 0.7 V, find the peak-to-peak amplitude of the output sine wave. (Hint: A square wave with peak-to-peak amplitude of V volts has a fundamental component with 4V/π volts peak-to-peak amplitude.) 10 kΩ; 3.6 V

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15.8 Use the expression derived in Exercise 15.7 to find the frequency of oscillation f0 and the minimum required value of Rf for oscillations to start in the circuit of Fig. 15.10.

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15.7 Consider the circuit of Fig. 15.10 without the limiter. Break the feedback loop at X and find the loop gain Aβ ≡ Vo( j ω)/Vx( j ω) in symbolic form (i.e., do not substitute the numerical values given). To do this, it is easier to start at the output and work backward, finding the various currents and voltages, and eventually Vx in terms of Vo.

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15.6 For the circuit in Fig. 15.8, find: (a) the setting of potentiometer P at which oscillations just start; (b) the frequency of oscillation. (a) 20 kΩ to ground; (b) 1 kHz

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15.5 For the circuit in Fig. 15.7: (a) Disregarding the limiter circuit, find the location of the closed-loop poles. (b) Find the frequency of oscillation. (c) With the limiter in place, find the amplitude of the output sine wave (assume that the diode drop is 0.7 V). (a) (105/16)(0.015 ± j); (b) 1 kHz; (c) 21.36 V (peak-to-peak)

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15.4 For the oscillator circuit in Fig 15.5, find the value of (r2/r1) to obtain an output amplitude of 5 V. 4.6

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15.3 For the oscillator circuit of Fig. 15.2(a), find the percentage change in ω0 that results from (a) L increasing by 1%, (b) C increasing by 1%, and (c) R increasing by 1%. (a) −0.5%; (b) −0.5%; (c) 0%

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15.2 For the oscillator circuit in Fig. 15.2(a), let r1 = 10 kΩ, r2 = 100 Ω, R = 10 kΩ, C = 10 nF, and L = 0.1 mH. Find the frequency of oscillation ω0. Is the condition of oscillation satisfied? 106 rad/s; yes, since r2 > 0.

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15.1 Consider a sinusoidal oscillator formed by connecting an amplifier with a gain of 2 and a second-order bandpass filter in a feedback loop. Find the pole frequency and the center-frequency gain of the filter needed to produce sustained oscillations at 1 kHz. 1 kHz; 0.5

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D 14.77 Design the circuit of Fig. 14.32(b) to realize, at the output of the second (noninverting) integrator, a maximally flat low-pass function with ω3dB = 104 rad/s and unity dc gain. Use a clock frequency fc = 200 kHz and select C1 = C2 = 2 pF. Give the values of C3, C4, C5, and C6. (Hint) 0.1 pF; 0.1 pF; 0.1414 pF; 0.1 pF

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D 14.76 Repeat Exercise 14.24 for Q = 40.

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D 14.75 Repeat Exercise 14.24 for a clock frequency of 500 kHz.

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14.74 For a dc voltage of 1 V applied to the input of the circuit of Fig. 14.30(b), in which C1 is 1 pF, what charge is transferred for each cycle of the two-phase clock? For a 200-kHz clock, what is the average current drawn from the input source? For a feedback capacitance of 10 pF, what change would you expect in the output for each cycle of the clock? For an amplifier that saturates at ±1 V and the feedback capacitor initially discharged, how many clock cycles would it take to saturate the amplifier? What is the average slope of the staircase output voltage produced?

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14.73 For the switched-capacitor input circuit of Fig. 14.30(b), in which a clock frequency of 100 kHz is used, what input resistances correspond to capacitance C1 values of 0.1 pF, 0.5 pF, 1 pF, 5 pF, and 10 pF? 100 MΩ; 20 MΩ; 10 MΩ; 2 MΩ; 1 MΩ

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D *14.72 Design a fifth-order Butterworth low-pass filter that has a 3-dB bandwidth of 10 kHz and a dc gain of unity. Use the cascade connection of two circuits of the type shown in Fig. 14.29 and a first-order low-pass circuit (Fig. 14.8). Use a 10- kΩ value for all resistors. Second-order section: R1 = R2 = 10 kΩ, C3 = 492 pF, C4 = 5.15 nF; Second order section: R1 = R2 = 10 kΩ, C3 = 1.29 nF, C4 = 1.97 nF; First-order section: R1 = R2 = 10 kΩ, C = 1.59 nF

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14.71 Use a cascade of the low-pass circuit in Fig. 14.29 and the high-pass circuit in Fig. 14.28(a) to realize a wide-band bandpass filter with 3-dB frequencies of 1 kHz and 100 kHz. The response of both circuits should be maximally flat; that is, each should have a Q of 0.707. Use capacitances in the nanofarad range. Sketch and label a Bode plot for the gain magnitude.

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14.70 Analyze the circuit in Fig. P14.70 to determine its transfer function T(s) ≡ Vo/Vi. Show that T(s) is that of a second-order bandpass filter and find ω0 and Q. For R1 = R2 = R, C4 = C, and C3 = C/m, find CR and m in terms of ω0 and Q. What center-frequency gain is obtained?

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D *14.69 Consider the bandpass circuit shown in Fig. 14.27(a). Let C1 = C2 = C, R3 = R, R4 = R/4Q2, and CR = 2Q/ω0. Disconnect the positive input terminal of the op amp from ground and apply Vi through a voltage divider R1, R2 to the positive input terminal as well as through R4 as before. Analyze the circuit to find its transfer function Vo/Vi. Find the ratio R2/R1 so that the circuit realizes a notch function

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D 14.68 Use the circuit in Fig. 14.27(a) to realize a bandpass filter with a center frequency of 10 kHz and a 3-dB bandwidth of 2.5 kHz. Give the values of all components and specify the center-frequency gain obtained. C1 = C2 = 10 nF, R3 = 12.73 kΩ, R4 = 200 Ω, gain = –32 V/V

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