Question

The h-parameters of a two port network are shown below. The condition for the maximum small signal voltage gain $\dfrac{V_{out}}{V_s}$ is _____________

• A. $h_{11}=0,\, h_{12}=0,\, h_{21}=\text{very high and } h_{22}=0$
• B. $h_{11}=\text{very high},\, h_{12}=0,\, h_{21}=\text{very high and } h_{22}=0$
• C. $h_{11}=0,\, h_{12}=\text{very high},\, h_{21}=\text{very high and } h_{22}=0$
• D. $h_{11}=0,\, h_{12}=0,\, h_{21}=\text{very high and } h_{22}=\text{very high}$

Hint:

With the h-model, think “series at input, shunt at output.” Maximize forward gain ($h_{21}$), kill reverse coupling ($h_{12}\!\to\!0$), minimize input series loss ($h_{11}\!\to\!0$), and maximize output resistance ($h_{22}\!\to\!0$) to boost voltage gain.

Answer 1

The Correct Option is A

For h–parameters: $v_1=h_{11}i_1+h_{12}v_2$ and $i_2=h_{21}i_1+h_{22}v_2$.
To maximize the small-signal voltage gain $\dfrac{V_{out}}{V_s}$ with a given source:
$\bullet$ Make the forward gain large $\Rightarrow h_{21}$ very high.
$\bullet$ Avoid reverse feedback from output to input $\Rightarrow h_{12}\approx 0$.
$\bullet$ Minimize input drop so that most of $V_s$ appears across the device $\Rightarrow h_{11}\approx 0$ (low input resistance in series).
$\bullet$ Make the output Norton resistance large so the controlled current develops a large voltage on $R_L$ $\Rightarrow h_{22}\approx 0$ (zero output admittance $\Rightarrow$ very high output resistance).
These conditions are exactly listed in option (A).
\[ \boxed{h_{11}=0,\; h_{12}=0,\; h_{21}\ \text{very high},\; h_{22}=0} \]