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Reasons An angle may be bisected. To bisect is to divide into two congruent parts. Given Reflexive property SAS Corresponding parts of congruent triangles are congruent.

(a) From Section 12.14, 1 1 !a p q LC 1 Q 2 ind or C !2 L 1 a 1 Q 2 ind 31:6 pF 1 2 10 106 2 8:0 10 6 1 1600 1

The driving-point impedance Zo is found after deactivating the independent source vi . vgs vi 0 and Zo rds RF 40 103 5000 103 39:68 k rds RF 5040 103

Given: ^ABC To Prove: m/A m/B m/C 180 Plan: When a line is drawn through one vertex parallel to the opposite side, a straight angle is formed whose parts can be proved congruent to the angles of the triangle.

Using Section 12.15 to convert the series RL branch of Fig. 12-25 to parallel at the resonant frequency, ! L Rp R 1 Q2 a 1 Q2 ind ind Qind Then, from Section 12.13, ! !2 L ! Q 2 10 106 40 rad=s a a a ind 2 Rp 1 1600 Qa 1 Qind or 0.25 MHz. (b) The circuit is shown in Fig. 12-44; part (a) gives the resistance of the practical inductor as R !a L 4 Qind

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For the JFET ampli er of Fig. 7-5, gm 2 mS; rds 30 k ; RS 3 k ; RD RL 2 k ; R1 200 k ; R2 800 k ; and ri 5 k . If CC and CS are large and the ampli er is biased in the pincho region, nd (a) Zin ; b Av vL =vi ; and (c) Ai iL =ii .

PROOF:

Also, from the given dissipation factor, it is known that 1 0:005 !a CRC The input admittance is 1 1 1 R !L j!C Yin j !C 2 RC R j!L RC R2 !L 2 R !L 2 which di ers from the input admittance for part (a) only in the real part. Since the imaginary part involves the same L and the same R, and must vanish at the same frequency, C must be the same as in part (a); namely, C 31:6 pF. For xed C, bandwidth is inversely proportional to resistance. With the practical capacitor, the net parallel resistance is R0 Rp RC Rp RC

Reasons 1. Through an external point, a line can be drawn parallel to a given line. 2. A straight angle is an angle whose measure is 180 . 3. The whole equals the sum of its parts. 4. Alternate interior angles of parallel lines are congruent. 5. Substitution Postulate

CHAP. 7]

Fig. 12-44

Given: ^ABC, /A > /C To Prove: AB > BC Plan: When the bisector of /B is drawn, the sides to be proved congruent become corresponding sides of congruent triangles.

where Rp is as calculated in part (a).

(a) The current-source small-signal equivalent circuit is drawn in Fig. 7-11. Since the gate draws negligible current, Zin RG

PROOF:

Therefore,

_ _ S _

Statements 1. 2. 3. 4. 5. 6. Draw BD bisecting /B. /1 > /2 /A > /C BD > BD ^BDA > ^BDC AB > BC 1. 2. 3. 4. 5. 6.

Rp Rp ! L=Qind 1 Q2 ind 0 1 1 a 0:25 MHz R 1=!a C 0:005 RC 1 1 Q2 0:005 ind Qind 1 Q 2 ind 1 1600 0:005 1:2 1 1 40 1 1600

Reasons An angle may be bisected. To bisect is to divide into two congruent parts. Given Reflexive property SAA Corresponding parts of congruent triangles are congruent.

and so 0:30 MHz. A lossy capacitor has the same e ect as any loading resistor placed across the tank; the Qa is reduced and the bandwidth increased, while fa is unchanged.

LL _

12.18 A lossy capacitor, in the series-circuit model, consists of R 25 and C 20 pF. Obtain the equivalent parallel model at 50 kHz.

4. Two right triangles are congruent if the hypotenuse and a leg of one are congruent to the corresponding parts of the other.

Fig. 7-11 (b) By voltage division at the input loop, vgs RG 160 103 vi vi 0:97vi R G r1 165 103 1

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