Show that operating point does not depend on beta, Electrical Engineering

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Q. Prove mathematically that the operating point does not depend on beta, in a potential divider bias circuit ?

To determine the operating point, consider the input section of the voltage divider biasing circuit.

The base current IB is very small compared to the currents in R1 and R2.

I1 ~ I2

So,

VB=R2/ (R1+R2) * VCC

The voltage across the emitter resistor RE

VE=V2-VBE

Then the emitter current is

IE= V2-VBE

And

VC=VCC-ICRC

VCE=VC-VE = (VCC-ICRC)-IERE

Since collector current is approximately equal to emitter current

VCE=VCC-(RC+RE) IC

Since in the above analysis nowhere does beta appear in any equation, which means that operating point does not depend upon the value of beta.


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