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In the CB ampli er of Fig. 5-9, the transistor leakage current is shown explicitly as a current source ICBO . (a) Find ICQ as a function of ICBO ; VBEQ ; and . (b) Determine the stability factors that should be used in (5.13) to express the in uence of ICBO ; VBEQ ; and on ICQ .

For two complex numbers in exponential form, the quotient follows directly from the laws of exponents. z1 r1 e j 1 r1 j 1 2 e z r2 e j 2 r2 Again, the polar or Steinmetz form of division is evident from reference to the exponential form. z1 r1 1 r1 z2 r2 2 r2 1 2

Fig. 11-19

Division of two complex numbers in the rectangular form is performed by multiplying the numerator and denominator by the conjugate of the denominator (see Section A8). z1 x1 jy1 x2 jy2 x x y1 y2 j y1 x2 y2 x1 x1 x2 y1 y2 y x y2 x1 j 1 2 1 2 2 2 2 2 z2 x2 jy2 x2 jy2 x2 y2 x2 y2 x2 y2 2 2

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Fig. 5-9 (a) By KVL, VEE VBEQ IEQ RE Substituting (5.5) into (1) and rearranging yield ICQ 1 VEE VBEQ ICBO RE 2 1

Fig. 11-20

EXAMPLE A5 Given z1 4e j =3 and z2 2e j =6 , z1 4e j =3 2e j =6 z2 2e j =6 EXAMPLE A6 Given z1 8 308 and z2 2 608, z1 8 308 4 308 z2 2 608 EXAMPLE A7 Given z1 4 j5 and z2 1 j2, z1 4 j5 1 j2 6 13 j 5 5 z2 1 j2 1 j2

(b) Direct application of (5.10) through (5.12) to (2) gives the desired stability factors as S @ICQ 1 VEE VBEQ 2 @ RE SI @ICQ 1 @ICBO SV @ICQ 1 RE @VBEQ

11.11. Excluding points lying outside square ABCD in Fig. 11-20, how many points are there that are (a) Equidistant from its vertices (b) Equidistant from its sides (c) 5 units from E and on one of the diagonals (d) 5 units from E and equidistant from AD and BC (e) 5 units from FG and equidistant from AB and CD (f) 20 units from A and 10 units from B 11.12. Prove that the locus of points equidistant from the sides of an angle is the bisector of the angle.

CONJUGATE OF A COMPLEX NUMBER The conjugate of the complex number z x jy is the complex number z x jy. Thus, Re z z z 2 Im z z z 2j jzj p zz

(11.4)

In the complex plane, the points z and z are mirror images in the axis of reals. In exponential form: z re j , z re j . In polar form: z r , z r . In trigonometric form: z r cos j sin , z r cos j sin . Conjugation has the following useful properties: i z z ii z1 z2 z z 1 2 iii z1 z2 z z 1 2 z1 z iv 1 z2 z 2

The CB ampli er of Fig. 5-9 has VCC 15 V; VEE 5 V; RE 3 k ; RC 7 k ; and 50. At a temperature of 258C, the Si transistor has VBEQ 0:7 V and ICBO 0:5 A. (a) Find an expression for ICQ at any temperature. (b) Evaluate that expression at T 1258C.

(11.5)

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