Consider the following relations for two- port network : 1. $A=\frac{h_{11}h_{22}-h_{12}h_{21}}{h_{21}}$ 2. $h_{22} = \frac{Y_{11}Y_{22} - Y_{12}Y_{21}}{Y_{21}}$ 3. $h_{12} = \frac{(AD-BC)}{D}$ Which of the above relations are not correct?
Analyze Relation 1: A vs. h-parameters
The relation given is $A=\frac{h_{11}h_{22}-h_{12}h_{21}}{h_{21}}$.
The standard conversion formulas from hybrid (h) parameters to ABCD parameters include:
- $A = -\frac{h_{11}}{h_{21}}$
- $B = -\frac{h_{11}h_{22}-h_{12}h_{21}}{h_{21}} = -\frac{\Delta h}{h_{21}}$
The formula provided for $A$ uses the expression typically associated with $B$. This mismatch makes relation 1 incorrect.
Analyze Relation 3: h12 vs. ABCD parameters
The relation given is $h_{12} = \frac{(AD-BC)}{D}$.
First, let's find the value of the determinant $AD-BC$ using the standard conversion formulas (where $\Delta h = h_{11}h_{22}-h_{12}h_{21}$):
$AD-BC = \left(-\frac{h_{11}}{h_{21}}\right) \left(-\frac{h_{22}}{h_{21}}\right) - \left(-\frac{\Delta h}{h_{21}}\right) \left(-\frac{1}{h_{21}}\right)$ $AD-BC = \frac{h_{11}h_{22} - \Delta h}{h_{21}^2} = \frac{h_{11}h_{22} - (h_{11}h_{22}-h_{12}h_{21})}{h_{21}^2} = \frac{h_{12}h_{21}}{h_{21}^2}$ $AD-BC = \frac{h_{12}}{h_{21}}$Now substitute this result and $D = -h_{22}/h_{21}$ into the given relation:
$h_{12} = \frac{(h_{12}/h_{21})}{(-h_{22}/h_{21})}$ $h_{12} = -\frac{h_{12}}{h_{22}}$This equality implies $h_{22} = -1$, which is not universally true for all two-port networks. Thus, relation 3 is incorrect.
Identifying Incorrect Two-Port Relations
Relations 1 and 3 have been shown to be incorrect based on standard two-port network parameter conversions.
Relation 2, $h_{22} = \frac{Y_{11}Y_{22} - Y_{12}Y_{21}}{Y_{21}}$, represents a correct conversion between admittance (Y) and hybrid (h) parameters.
Therefore, the relations that are not correct are 1 and 3 only.
Important Questions from Two Port Networks
A two-port network has scattering parameters given \(\left[ s \right] = \left[ {\begin{array}{*{20}{c}} {{s_{11}}}&{{s_{12}}}\\ {{s_{211}}}&{{s_{22}}} \end{array}} \right]\). If the port 2 of the two-port is short-circuited, the s11 parameter for the resultant one-port network is
With 10 V dc connected at port A, the current drawn by 7 Ω connected at port B is
With 6 V dc connected at port A, 1 Ω connected at port B draws 7/3 A. If 8 V dc is connected to port A, the open circuit voltage at port B is
In a linear two – port network, when 10 V is applied to Port 1, a current of 4 A flows through Port 2 when it is short-circuited. When 5 V is applied to Port, a current of 1.25 A flows through a 1 Ω resistance connected across Port 2. When 3 V is applied to Port 1, then current (in Ampere) through a 2 Ω resistance connected across Port 2 is __________.
A network is said to be reciprocal if
