Question:
For the two-port network shown below, the value of the \(Y_{21}\) parameter (in Siemens) is \(\_\_\_\_\).
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For the two-port network shown below, the value of the \(Y_{21}\) parameter (in Siemens) is \(\_\_\_\_\).
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\includegraphics[width=8cm]{60.png}
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Show Hint
To calculate admittance parameters in a two-port network, set the specified voltage to zero and compute the resulting current-to-voltage ratio. Ensure the circuit simplification aligns with the given conditions.
Updated On: Jan 31, 2025
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Solution and Explanation
Step 1: Define the admittance parameter \(Y_{21}\).
The admittance parameter \(Y_{21}\) is given by: \[ Y_{21} = \frac{I_2}{V_1} \bigg|_{V_2 = 0}. \] This represents the transfer admittance from input voltage \(V_1\) to output current \(I_2\) when the output voltage \(V_2\) is zero. Step 2: Circuit analysis.
When \(V_2 = 0\), the output terminal is short-circuited. This simplifies the circuit, allowing \(I_2\) to be calculated directly for a given \(V_1\). Substitute the values from the circuit to determine the current \(I_2\). The total admittance at the output is: \[ Y_{21} = \frac{I_2}{V_1} = 1.5 \, {S}. \] Final Answer: \[ \boxed{1.5 \, {S}} \]
The admittance parameter \(Y_{21}\) is given by: \[ Y_{21} = \frac{I_2}{V_1} \bigg|_{V_2 = 0}. \] This represents the transfer admittance from input voltage \(V_1\) to output current \(I_2\) when the output voltage \(V_2\) is zero. Step 2: Circuit analysis.
When \(V_2 = 0\), the output terminal is short-circuited. This simplifies the circuit, allowing \(I_2\) to be calculated directly for a given \(V_1\). Substitute the values from the circuit to determine the current \(I_2\). The total admittance at the output is: \[ Y_{21} = \frac{I_2}{V_1} = 1.5 \, {S}. \] Final Answer: \[ \boxed{1.5 \, {S}} \]
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