Chapter 4, Problem 4.1P

Find the voltage gain $v_O/v_S$ and current gain $i_O/i_x$ in Figure P4-1 for $r=10\text{kΩ}\text{.}$

To determine

Voltage gain $\frac{v_o}{v_s}$ and current gain $\frac{i_o}{i_x}$ .

Answer to Problem 4.1P

The values are

  $\begin{array}{l}\frac{v_o}{v_s}=-16\\ \frac{i_o}{i_x}=-4\end{array}$

Explanation of Solution

Given:

  

  $r=10\text{ k}\Omega$

Calculation:

Apply KVL to the first loop,

  $\begin{array}{l}vs-\left(100+400\right)ix=0\\ vs=500ix\end{array}$  (1)

Apply KVL to the second loop,

  $\begin{array}{l}rix+\left(2000+500\right)io=0\\ rix=-2500io\\ \frac{io}{ix}=\frac{-r}{2500}\\ \text{ =}\frac{-10000}{2500}\\ \text{ =}-\text{4}\end{array}$

But $vo=2000io$  (2)

Divide equation (2) by equation (1).

  $\begin{array}{c}\frac{vo}{vs}=\frac{2000io}{500ix}\\ \text{=}\frac{2000}{500}\times -4\\ \text{=}-16\end{array}$