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10. (a) 180 rotation about the origin, P(x, y) A P ( x, y); (b) 90 clockwise rotation about the origin, P(x, y) A P0(y, x); (c) 270 clockwise rotation about the origin (or 90 counter-clockwise), P(x, y) A P-( x, y) 11. (a) P(x, y) A P (x cos 40 (b) P(x, y) A P (x cos 50 (c) P(x, y) A P (x cos 80 y sin 40 , y cos 40 x sin 40 ) P (0.766x 0.6428y, 0.766y 0.6428x); y sin 50 , y cos 50 x sin 50 ) P (0.6428x 0.766y, 0.6428y 0.766x); y sin 80 , y cos 80 x sin 80 ) P (0.1736x 0.9848y, 0.1736y 0.9848x)

Fig. 8-23

SPICE methods o er a frequency sweep option that allows a small-signal, sinusoidal steady-state analysis of a circuit. The frequency sweep is invoked by a control statement of the following format: .AC DEC points start freq end freq

12. (a) 120 ; (b) 60 ; (c) 72 ; (d) 360 (no rotational symmetry); (e) 90 ; ( f ) 180 13. (a) A (4, 5), B (5, 4), and C (5, 7); (b) A0(2, 5), B0(3, 6), and C0(0, 6); (c) A-( 1, 2), B-( 2, 3), and C-(1, 3); (d) A00( 4, 3), B00( 5, 4), and C00( 5, 1) 14. (a) R(x, y) A R0(x 6, y 1); (b) R(x, y) A R0(1 x, y 2); (c) R(x, y) A R0(y (d) R(x, y) A R0( y, 4 x); (e) R(x, y) A R0(6 x, 3 y) 3, x 6);

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Obtain H s for the network shown in Fig. 8-23, where the excitation is the driving current I s and the response is the voltage at the input terminals.

15. (a) reflect across the y axis and then move down 2 and to the right 3 spaces, P(x, y) A P ( x 3, y 2); (b) rotate about the origin counterclockwise 90 , then move to the left 1 space, P(x, y) A P0( y 1, x); (c) rotate around the origin 90 clockwise, then reflect across the x axis, then move down and to the right 1 space, P(x, y) A P-(y 1, x 1) 16. (a) P(x, y) A P (x, y 3); (b) P(x, y) A P (y 2, x); (c) P(x, y) A P ( x, y 4); (d) P(x, y) A P ( x, 4 y); (e) P(x, y) A P ( 7 x, y 3) 17. A ( 3, 6), B (3, 6), C (3, 3), and D ( 3, 3)

Node voltages and device currents are inherently complex number values. The magnitudes and phase angles of calculated quantities can be retrieved by the Probe feature of PSpice by appending a p and n, respectively, to the variable. For example, magnitude and phase angle of the voltage between nodes 2 and 3 are speci ed by Vm(2,3) and Vp(2,3).

CHAP. 8]

1 18. (a) P(x, y) A P (2x, 2y); (b) P(x, y) A P (8x, 8y); (c) P(x, y) A P (3 x, 1 x) 3

At the input terminals, KVL gives 15 V s 2sI s V 0 s 2s I s s Then H s V s 2s2 15 I s s

Example 8.9. For the BJT ampli er circuit of Fig. 3-10, assume CC ! 1. The small-signal equivalent circuit is given by Fig. 8-4 where RB R1 kR2 . Let hoe hre 0, hfe 90, R1 1 k , R2 16 k , RE 500 , CE 330 F, RC 1 k , and RL 10 k . Use SPICE methods to determine the low-frequency cuto point.

(17.1)

For the two-port network shown in Fig. 8-24 nd the values of R1 , R2 , and C, given that the voltage transfer function is Hv s Vo s 0:2 Vi s s2 3s 2

CHAP. 8]

h).]

Fig. 8-24 The impedance looking into xx 0 is Z0 Then, by repeated voltage division, Vo Vo Vxx 0 R2 Z0 R2 = R1 R2 C 0 1 2 Vi Vxx 0 Vi R1 R2 Z s1 s s 1 R1 R2 C C Equating the coe cients in this expression to those in the given expression for Hv s , we nd: C 1 F 2 R1 3

The netlist code that follows describes the circuit:

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