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Ckt Diagram

Calculate the voltage gain for the network of Fig. 3.12 if the source has an internal resistance of 100 in series with Vi.Vi=500mV,R= 1K ?

For this problem I had tried a solution but I am not sure whether it is correct or not? Please Help. Below is the solution that i have found

Ii = Vi/Ri = 25mA For this ckt, Ie=Ii=25mA

Since, Ic is approx equal to Ie, Ic=25mA VL=Ic*R=25V Hence, Av=Vl/Vi=50.

Is my solution correct? I am assuming that the internal resistance of source will not have any effect on the circuit. Correct me if I am wrong.

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  • \$\begingroup\$ The 'key' point is, how the gain is defined? That is, which is the 'input' and which is the 'output'? \$\endgroup\$ – diverger Nov 9 '14 at 12:07
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From the given input resistance \$r_{i}=20\;Ohms\$ I deduce that the transconductance is \$g_{m}=\frac{1}{r_{i}}=0.05A/V\$. Because of

$$ I_{c}=g_{m} \times V_{t} \quad(V_{t}=temeperature\: voltage, V_{t}=25mV) $$

we can calculate the DC current \$I_{c}=I_{e}=0.05 \times 25 mA=1.25 mA\$ (neglecting \$I_{b}\$).

The voltage gain referred to the base node is \$A_{1}=g_{m} \times (r_{o}||R_{L})\$ and the gain referred to the signal source (with internal \$R_{s}=100\;ohms\$) is \$A_{0}=A_{1} \times r_{i}/(r_{i}+R_{s})\$.

For an input signal of Vi=0.5 V the resulting signal ouput is app. 4V.

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