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## Homework Statement

It is required to design the bias circuit as shown in figure for a BJT whose nominal [tex]{\beta} [/tex] is 100.

a.) Find the largest ratio [tex]{(R_B/R_E)}[/tex] that will guarantee [tex]{I_E}[/tex] remains within 10% of its nominal value for B as low as 50 and as high as 150.

b.) If the resistance ratio found in a.) is used, find an expression for the voltage [tex]{V_(bb) = V_(cc) *(R_2/(R_1+R_2)) }[/tex] that will result in a voltage drop of [tex]{V(cc)/3}[/tex] across [tex]{R_E}[/tex].

## Homework Equations

[tex]V(bb) = V(cc) * (R2/ (R1+R2))[/tex]

[tex]Rb = R1*R2 / (R1+R2)[/tex]

## The Attempt at a Solution

a.) Using the stability factor equation found somewhere else (not sure if it is a relevant equation).

[tex] S = (1+\beta) (1+ (R_B/R_E))/(1+\beta+(R_B/R_E)) [/tex]

For largest ratio, [tex]{\beta}[/tex] is low and S is high.

[tex] 1.1 = 51 * (1+(R_B/R_E))/(51+(R_B/R_E)) [/tex]

[tex] R_B/R_E = 0.1022 [/tex]

b.)

[tex] V_(bb) - R_B*I_B-0.7-I_E*R_E = 0 [/tex]

[tex] V_(bb) = R_B* (I_E)/(B+1) + 0.7 + V_(cc)/3 [/tex][/B]