## Related questions with answers

A CB amplifier is required to amplify a signal delivered by a coaxial cable having a characteristic resistance of $50 \Omega.$ What bias current $I_{C}$ should be utilized to obtain $R_{\mathrm{in}}$ that is matched to the cable resistance? To obtain an overall voltage gain of $G_{v}$ of 40 V/V, what should the total resistance in the collector $\left( i.e., R_{C} \| R_{L}\right)$ be?

Solution

VerifiedDue to the resistance of the co-axial cable $R=50\Omega$. To get an impedance match then

$\begin{equation} R_{i n}=R \end{equation}$

So,

$\begin{equation} R_{i n}=50 \Omega \end{equation}$

To calculate bias current $I_c$, we have:

$\begin{equation} \begin{aligned} R_{i n}&=r_{e}\\&=\frac{1}{g_{m}} \end{aligned} \end{equation}$

so,

$\begin{equation} r_{e}=\frac{V_{T}}{I_{E}} \approx \frac{V_{T}}{I_{c}} \end{equation}$

Since,

$\begin{equation} V_{T}=25 \mathrm{mV}=25.10^{-3} \mathrm{V} \end{equation}$

we get,

$\begin{equation} \begin{aligned} I_{c}&=\frac{V_{T}}{r_{e}}\\&=\frac{25 \cdot 10^{-3} V}{50 \Omega}\\&=0.5 \cdot 10^{-3} A\\&=0.5 \mathrm{mA} \end{aligned} \end{equation}$

$\begin{equation} \boxed{I_{c}=0.5 \mathrm{mA}} \end{equation}$

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