#### Question

A CE amplifier utilizes a BJT with $\beta=100$ biased at $I_{C}=0.5 \mathrm{mA}$ and has a collector resistance $R_{C}=12 \mathrm{k} \Omega$ and a resistance $R_{e}=250 \Omega$ connected in the emitter. Find $R_{\mathrm{in}}, A_{v o},$ and $R_{o}.$ If the amplifier is fed with a signal source having a resistance of $10 \mathrm{k} \Omega,$ and a load resistance $R_{L}=12 \mathrm{k} \Omega$ is connected to the output terminal, find the resulting $A_{v}$ and $G_{v}.$ If the peak voltage of the sine wave appearing between base and emitter is to be limited to 5 mV, what $\hat{v}_{\text { sig }}$ is allowed, and what output voltage signal appears across the load?

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#### Step 1

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For the given BJT amplifier,

$\alpha =\dfrac{\beta}{1+\beta} =\dfrac{100}{101}$

$r_e = \dfrac{V_T}{I_E}=\dfrac{\alpha V_T}{I_C}=\dfrac{100}{101} \times \dfrac{25\mathrm{~mV}}{0.5\mathrm{~mA}} =49.5 \mathrm{~\Omega}$

$g_m =\dfrac{\alpha}{r_e} = \dfrac{100/101}{49.5} = 20\mathrm{~mA/V}$

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