Consider the following statements>regarding two-port network : 1. A network is termed to be reciprocal, if the ratio of the response variable to the excitation variable remains identical even if the positions of the response and excitation in the network are interchanged. 2. A two-port network is said to be symmetrical, if the input and output ports can be interchanged even after altering the port voltages and currents. 3. The condition for symmetry is $Z_{11} =-Z_{22}$. Which of the above statements are not correct?
Evaluating Two-Port Network Statements
Statement 1: Reciprocity
- Definition: A network is reciprocal if the relationship between excitation and response remains the same when their positions are interchanged.
- Check: This aligns with the standard definition of reciprocity in electrical networks. For two-port parameters, this generally means $Z_{12} = Z_{21}$ or $Y_{12} = Y_{21}$.
- Conclusion: Statement 1 is correct.
Statement 2: Symmetry
- Definition Provided: A two-port network is symmetrical if input/output ports can be interchanged even after altering port voltages/currents.
- Check: Symmetry means the network's characteristics are identical regardless of which port is considered input or output. The phrasing "even after altering..." is non-standard and confusing. A standard definition implies invariance of parameters like $Z_{11} = Z_{22}$ and $Z_{12} = Z_{21}$.
- Conclusion: Statement 2 is not correct due to its ambiguous and non-standard definition.
Statement 3: Symmetry Condition
- Condition Stated: $Z_{11} = -Z_{22}$.
- Correct Condition: The necessary and sufficient conditions for symmetry of a two-port network using Z-parameters are $Z_{11} = Z_{22}$ and $Z_{12} = Z_{21}$.
- Check: The statement $Z_{11} = -Z_{22}$ is incorrect.
- Conclusion: Statement 3 is not correct.
Identifying Incorrect Statements
The question asks to identify the statements that are not correct.
- Statement 1 was determined to be correct.
- Statement 2 was determined to be not correct.
- Statement 3 was determined to be not correct.
Therefore, the incorrect statements are 2 and 3.
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
