Two Port Networks MCQ Quiz - Objective Question with Answer for Two Port Networks - Download Free PDF
Last updated on Jun 10, 2025
Latest Two Port Networks MCQ Objective Questions
Two Port Networks Question 1:
For a two port network to be reciprocal:
Answer (Detailed Solution Below)
Two Port Networks Question 1 Detailed Solution
Explanation:
Reciprocity in Two-Port Networks
Definition: A two-port network is said to be reciprocal if the transfer of signal or energy between port 1 and port 2 is the same in either direction under the same conditions. Reciprocity is a property often associated with linear passive networks and is crucial in the design of electrical systems such as filters, amplifiers, and communication networks. Mathematically, this property ensures that the forward and reverse transmission characteristics are identical under certain conditions.
Conditions for Reciprocity: Reciprocity of a two-port network can be analyzed using different network parameters such as impedance (Z), admittance (Y), hybrid (h), and transmission (ABCD) parameters. The condition for reciprocity varies depending on the type of network parameters being used. Here’s a breakdown:
- Impedance Parameters (Z): For the network to be reciprocal using Z-parameters, the condition is Z12 = Z21.
- Admittance Parameters (Y): For the network to be reciprocal using Y-parameters, the condition is Y12 = Y21.
- Hybrid Parameters (h): For the network to be reciprocal using h-parameters, the condition is h12 = -h21.
- Transmission Parameters (ABCD): For the network to be reciprocal using ABCD parameters, the condition is AD - BC = 1.
Correct Option Analysis:
The correct option is:
Option 4: AD - BC = 1
This condition pertains to the transmission (ABCD) parameters of a two-port network. The ABCD parameters, also known as transmission parameters, describe the input and output voltages and currents of the two-port network. They are expressed as:
V1 = AV2 + BI2
I1 = CV2 + DI2
Here, A, B, C, and D are the transmission parameters. For a network to be reciprocal, the determinant of the ABCD parameter matrix must equal 1, i.e.,:
AD - BC = 1
This means that the energy transfer between port 1 and port 2 is identical in both directions, confirming reciprocity. This condition is widely used in the analysis of transmission lines, filters, and communication systems to ensure symmetry in signal transmission.
Additional Information
To further understand the analysis, let’s evaluate the other options:
Option 1: Z11 = Z22
This option is incorrect. The condition Z11 = Z22 does not imply reciprocity in a two-port network. Instead, it suggests symmetry in the impedance parameters. Reciprocity in Z-parameters is defined by the condition Z12 = Z21.
Option 2: Y21 = Y21
This option is incorrect and is a typographical error. The correct condition for reciprocity in terms of Y-parameters is Y12 = Y21. This ensures that the admittance between the two ports is identical in both directions.
Option 3: h21 = h22
This option is incorrect. The condition h21 = h22 does not imply reciprocity in a two-port network. Reciprocity in terms of h-parameters is defined by the condition h12 = -h21, which involves a specific relationship between the forward and reverse hybrid parameters.
Option 5: No option is mentioned for Option 5, so it is irrelevant to the problem.
Conclusion:
Understanding the concept of reciprocity in two-port networks is vital for analyzing and designing electrical systems. The correct condition for reciprocity depends on the type of network parameters being used. In this case, the transmission (ABCD) parameters define reciprocity with the condition AD - BC = 1. This ensures symmetry in energy transfer between ports, making the network reciprocal. By analyzing the incorrect options, we see that they either misrepresent the reciprocity condition or describe different properties of the network parameters.
Two Port Networks Question 2:
For a two port symmetric bilateral network, if A= 3Ω and B = 1Ω, the value of parameter C will be
Answer (Detailed Solution Below)
Two Port Networks Question 2 Detailed Solution
Explanation:
Two-Port Symmetric Bilateral Network
Definition: A two-port symmetric bilateral network is a type of electrical network that has two pairs of terminals, referred to as "ports." The network is termed symmetric when certain parameters are equal, and it is bilateral when the network behaves identically when the input and output ports are interchanged. These networks are often analyzed using transmission parameters (A, B, C, D), where the relationships between input and output voltages and currents are described as:
Equations:
\( V_1 = A \cdot V_2 + B \cdot I_2 \)
\( I_1 = C \cdot V_2 + D \cdot I_2 \)
For symmetric networks, the parameters satisfy the following conditions:
- \( A = D \) (Symmetry condition)
- \( A \cdot D - B \cdot C = 1 \) (Reciprocity condition)
Given:
- \( A = 3 \, \Omega \)
- \( B = 1 \, \Omega \)
We need to determine the value of the parameter \( C \).
Step 1: Use the Reciprocity Condition
From the reciprocity condition, we know:
\( A \cdot D - B \cdot C = 1 \)
Since the network is symmetric, \( A = D \). Substituting \( A = 3 \, \Omega \) and \( B = 1 \, \Omega \), we get:
\( 3 \cdot 3 - 1 \cdot C = 1 \)
\( 9 - C = 1 \)
Step 2: Solve for \( C \)
Rearranging the equation:
\( C = 9 - 1 \)
\( C = 8 \, \text{s} \)
Thus, the value of the parameter \( C \) is \( 8 \, \text{s} \).
Step 3: Evaluate the Correct Option
From the options provided, the correct answer corresponds to:
- Option 1: \( 8 \, \text{s} \)
Important Information:
To analyze why the other options are incorrect, let us revisit the reciprocity condition:
\( A \cdot D - B \cdot C = 1 \)
For a symmetric network:
- \( A = D = 3 \, \Omega \)
- \( B = 1 \, \Omega \)
Substituting these values into the equation, we calculated \( C = 8 \, \text{s} \). Any other value for \( C \) would violate the reciprocity condition. Let’s examine the incorrect options:
Option 2: \( C = 6 \, \text{s} \)
If \( C = 6 \, \text{s} \), substituting into the reciprocity condition:
\( 3 \cdot 3 - 1 \cdot 6 = 9 - 6 = 3 \)
Here, the result is \( 3 \), which does not satisfy the reciprocity condition (\( A \cdot D - B \cdot C = 1 \)). Thus, this option is incorrect.
Option 3: \( C = 4 \, \text{s} \)
If \( C = 4 \, \text{s} \), substituting into the reciprocity condition:
\( 3 \cdot 3 - 1 \cdot 4 = 9 - 4 = 5 \)
Here, the result is \( 5 \), which does not satisfy the reciprocity condition. Thus, this option is incorrect.
Option 4: \( C = 16 \, \text{s} \)
If \( C = 16 \, \text{s} \), substituting into the reciprocity condition:
\( 3 \cdot 3 - 1 \cdot 16 = 9 - 16 = -7 \)
Here, the result is \( -7 \), which does not satisfy the reciprocity condition. Thus, this option is incorrect.
Option 5: \( C = 1 \, \text{s} \)
If \( C = 1 \, \text{s} \), substituting into the reciprocity condition:
\( 3 \cdot 3 - 1 \cdot 1 = 9 - 1 = 8 \)
While the arithmetic is correct, the parameter \( C \) is defined as a reciprocal value in seconds (\( \text{s} \)), and the units here do not align with the requirements of the problem. Thus, this option is also incorrect.
Conclusion:
The correct value of \( C \) in the given two-port symmetric bilateral network is \( 8 \, \text{s} \), satisfying the reciprocity condition. This corresponds to Option 1. The other options fail to meet the necessary conditions or have incorrect units, as demonstrated in the analysis above.
Two Port Networks Question 3:
If a Two port Network “A” is cascaded with another two port Network B, then which of the following is true.
Answer (Detailed Solution Below)
Two Port Networks Question 3 Detailed Solution
The correct option is 3
Concept:
Two-port network parameters such as Z, Y, h, and T (ABCD) describe the relationship between voltages and currents at the input and output ports of a network. When two such networks are cascaded, their parameters combine in specific ways depending on the type of parameter used.
Calculation:
When two two-port networks A and B are cascaded:
- Impedance [Z] parameters cannot be directly multiplied. They are added when connected in series, not cascaded.
- Admittance [Y] parameters are added for parallel connection, not cascade.
- Hybrid [h] parameters cannot be used directly for cascading either.
- Transmission (ABCD) [T] parameters are specifically designed for cascade connection. When two networks are cascaded, the overall transmission matrix is the product of individual matrices:
[T] = [TA] × [TB]
Two Port Networks Question 4:
If a two-port network is represented with h-parameters, then the condition for reciprocity is _____.
Answer (Detailed Solution Below)
Two Port Networks Question 4 Detailed Solution
Explanation:
The h-parameters represent a two-port network with the following equations:
V1 = h11 * I1 + h12 * V2 I2 = h21 * I1 + h22 * V2
where:
- V1 is the input voltage
- I1 is the input current
- V2 is the output voltage
- I2 is the output current
- h11, h12, h21, and h22 are the h-parameters
The condition for reciprocity in a two-port network represented by h-parameters is:
h12 = -h21
Therefore, the correct answer is h12 = -h21.
Two Port Networks Question 5:
Find the Z parameters (Z11, Z12, Z21 Z22. respectively) for the above network.
Answer (Detailed Solution Below)
Two Port Networks Question 5 Detailed Solution
Solution:
To find the Z parameters (Z11, Z12, Z21, Z22) for the given network, we need to understand the two-port network analysis. The Z-parameters or impedance parameters are defined by the following set of equations:
V1 = Z11I1 + Z12I2
V2 = Z21I1 + Z22I2
Where:
- V1 is the input voltage
- V2 is the output voltage
- I1 is the input current
- I2 is the output current
To determine the Z-parameters, we need to perform the following steps:
Step 1: Calculate Z11
Z11 is found by setting I2 = 0 (open-circuit output). Under this condition, the input impedance is:
Z11 = V1 / I1 (with I2 = 0)
Step 2: Calculate Z12
Z12 is found by setting I2 = 0 (open-circuit output). Under this condition, the reverse transfer impedance is:
Z12 = V1 / I2 (with I1 = 0)
Step 3: Calculate Z21
Z21 is found by setting I1 = 0 (open-circuit input). Under this condition, the forward transfer impedance is:
Z21 = V2 / I1 (with I2 = 0)
Step 4: Calculate Z22
Z22 is found by setting I1 = 0 (open-circuit input). Under this condition, the output impedance is:
Z22 = V2 / I2 (with I1 = 0)
Let's now solve these for the given options:
Correct Option Analysis:
The correct option is:
Option 3: 30Ω, 20Ω, 20Ω, 30Ω
We will validate this by calculating each of the Z parameters for the given network:
Z11:
Given that I2 = 0, V1 = Z11I1. If Z11 = 30Ω, then:
V1 = 30Ω × I1
Z12:
Given that I2 = 0 and assuming Z12 = 20Ω, then:
V1 = 20Ω × I2
Z21:
Given that I1 = 0 and assuming Z21 = 20Ω, then:
V2 = 20Ω × I1
Z22:
Given that I1 = 0, V2 = Z22I2. If Z22 = 30Ω, then:
V2 = 30Ω × I2
Thus, the Z-parameters are correctly given by option 3: Z11 = 30Ω, Z12 = 20Ω, Z21 = 20Ω, Z22 = 30Ω.
Let's analyze the other options to understand why they are incorrect:
Option 1: 40Ω, 20Ω, 20Ω, 40Ω
While Z12 and Z21 are the same as in the correct answer, Z11 and Z22 are different. For the given network, these values do not match the correct Z-parameter values.
Option 2: 40Ω, 30Ω, 30Ω, 40Ω
All the Z-parameter values here differ from the correct option. These values do not satisfy the given network's conditions.
Option 4: 30Ω, 30Ω, 30Ω, 30Ω
In this case, Z12 and Z21 are incorrectly given as 30Ω instead of 20Ω. This does not align with the correct Z-parameter values.
Conclusion:
By understanding the principles of Z-parameters and carefully analyzing the network, we have determined that the correct Z-parameters for the given network are Z11 = 30Ω, Z12 = 20Ω, Z21 = 20Ω, and Z22 = 30Ω, which corresponds to option 3.
Top Two Port Networks MCQ Objective Questions
A short-circuit admittance matrix of a two-port network is
\(\left[ {\begin{array}{*{20}{c}} 0\\ {\frac{1}{2}} \end{array}\begin{array}{*{20}{c}} { - \frac{1}{2}}\\ 0 \end{array}} \right]\)
The two-port network is
Answer (Detailed Solution Below)
Two Port Networks Question 6 Detailed Solution
Download Solution PDFConcept:
Admittance Matrix:
- It is also known as a short circuit matrix or Y matrix.
- Y matrix is represented as:
\(\begin{bmatrix} Y_{11} & Y_{12}\\ Y_{21}& Y_{22} \end{bmatrix}\)= \(\begin{bmatrix} Y_{A}+ Y_{C}& -Y_{C}\\ -Y_{C}& Y_{B}+ Y_{C} \end{bmatrix}\)
- The condition of symmetry and reciprocity in Y parameters are given by:
Symmetry: \(Y_{11}= Y_{22}\)
Reciprocity: \(Y_{12}= Y_{21}\)
Explanation:
Given, that the Y matrix is \(\left[ {\begin{array}{*{20}{c}} 0\\ {\frac{1}{2}} \end{array}\begin{array}{*{20}{c}} { - \frac{1}{2}}\\ 0 \end{array}} \right]\)
Here, \(Y_{12}\neq Y_{21}\)
Hence Y matrix is not reciprocal.
The shunt admittance dissipates energy, hence it is a passive element.
Therefore, option 1 is correct.
A Two-Port Network is said to be symmetrical when the following equalities hold good
Answer (Detailed Solution Below)
Two Port Networks Question 7 Detailed Solution
Download Solution PDFA two-port network is said to be symmetrical if the input and output ports can be interchanged without altering the port voltages and currents.
A network is said to be reciprocal if the ratio of the response to the excitation is invariant to an interchange of the positions of the excitation and response of the network.
Conditions of reciprocity and symmetry in terms of different two-port parameters are:
Two Port Parameters |
Condition for Symmetry |
Condition for Reciprocal |
Z Parameters |
Z11 = Z22 |
Z12 = Z21 |
Y parameters |
Y11 = Y22 |
Y12 = Y21 |
ABCD parameters |
A = D |
AD - BC =1 |
H parameters |
h11h22 - h12h21 = 1 |
h12 = -h21 |
ABCD parameters are used in analysis of ______.
Answer (Detailed Solution Below)
Two Port Networks Question 8 Detailed Solution
Download Solution PDFThe application of different two port network parameters are shown below.
Two port network parameters |
Application |
Z parameters |
Open circuit analysis |
Y parameters |
Short circuit analysis |
h parameters |
Electronic circuits |
ABCD or T parameters |
Transmission lines |
Consider the following standard symbols for two-port parameters:
1. h12 and h21 are dimensionless
2. h11 and B have dimension of ohms
3. AD is dimensionless
4. C is dimensionless
Which of the above are correct?Answer (Detailed Solution Below)
Two Port Networks Question 9 Detailed Solution
Download Solution PDF
Two-port network parameters |
Equations |
Z parameters |
V1 = Z11I1 + Z12I2 V2 = Z21I1 + Z22I2 |
Y parameters |
I1 = Y11V1 + Y12V2 I2 = Y21V1 + Y22V2 |
h parameters |
V1 = h11I1 + h12V2 I2 = h21I1 + h22V2 |
g parameters |
I1 = g11V1 + g12I2 V2 = g21V1 + g22I2 |
T parameters (ABCD) |
V1 = AV2 – BI2 I1 = CV2 – DI2 |
Inverse T parameters |
V2 = A’V1 – B’I1 I2 = C’V1 – D’I1 |
h12 = V1/V2 → dimensionless
h21 = I2/I1 → dimensionless
h11 = V1/I1 → ohms
B = V1/I2 → ohms
C = I1/V2 → mho
AD → dimensionless
Answer (Detailed Solution Below)
Two Port Networks Question 10 Detailed Solution
Download Solution PDFConcept:
Z parameter:
We will get the following set of two equations by considering the variables V1 & V2 as dependent and I1 & I2 as an independent. The coefficients of independent variables, I1 and I2 are called Z parameters.
V1 = Z11I1 +Z12I2
V2 = Z21I1+ Z22I2
Calculation:
Apply KVL on loop 1:
⇒ V1 = 5I1 + 20(I1 + I2)
⇒ V1 = 25I1 + 20I2 ------------ (1)
Apply KVL on loop 2:
⇒ V2 = 10I2 + 20(I1 + I2)
⇒ V2 = 20I1 + 30I2 -------------(2)
Compare equation 1 and 2 with Z parameter equations:
Z11 = 25Ω, Z22 = 30Ω
Alternate Method For a T equivalent network as shown below
Z11 = (Z1 + Z3) = (5+20) = 25Ω
Z22 = (Z2 + Z3) = (10 + 20) = 30Ω
Z12 = Z21 = Z3 = 20Ω
For the 2-port network shown, determine the value of transfer impedance Z21.
Answer (Detailed Solution Below)
Two Port Networks Question 11 Detailed Solution
Download Solution PDFConcept:
The Z-parameter for a T-equivalent two-port network is,
\(\left[ Z \right] = \left[ {\begin{array}{*{20}{c}} {{Z_{11}}}&{{Z_{12}}}\\ {{Z_{21}}}&{{Z_{22}}} \end{array}} \right]\)
Where
Z11 is open circuit impedance
Z12 = Z21 = Transfer impedance
Z22 = Open circuit output impedance
Calculation:
By using delta to star conversion, the given circuit can be reduced.
\({R_1} = \frac{{4 \times 2}}{{4 + 2 + 2}} = \frac{8}{8} = 1\;{\rm{\Omega }}\)
\({R_2} = \frac{{2 \times 2}}{{4 + 2 + 2}} = \frac{4}{8} = \frac{1}{2}\;{\rm{\Omega }}\)
\({R_3} = \frac{{4 \times 2}}{{4 + 2 + 2}} = \frac{8}{8} = 1\;{\rm{\Omega }}\)
The modified circuit is,
Now, by comparing the above circuit with T-equivalent network of Z-parameter matrix,
\(\left[ Z \right] = \left[ {\begin{array}{*{20}{c}} 4&3\\ 3&{3.5} \end{array}} \right]\)
Transfer impedance = Z21 = 3 ΩFor a two-port network, the condition of symmetry in terms of z-parameters is
Answer (Detailed Solution Below)
Two Port Networks Question 12 Detailed Solution
Download Solution PDFA two-port network is said to be symmetrical if the input and output ports can be interchanged without altering the port voltages and currents.
A network is said to be reciprocal if the ratio of the response to the excitation is invariant to an interchange of the positions of the excitation and response of the network.
Conditions of reciprocity and symmetry in terms of different two-port parameters are:
Two Port Parameters |
Condition for Symmetry |
Condition for Reciprocal |
Z Parameters |
Z11 = Z22 |
Z12 = Z21 |
Y parameters |
Y11 = Y22 |
Y12 = Y21 |
ABCD parameters |
A = D |
AD - BC =1 |
H parameters |
h11h22 - h12h21 = 1 |
h12 = -h21 |
For the two-port network shown below, the short-circuit admittance parameter matrix is
Answer (Detailed Solution Below)
Two Port Networks Question 13 Detailed Solution
Download Solution PDFConcept:
Y parameters
These are also called the admittance parameters.
The Y parameters for the two-port network are shown as:
\(\left[ {\begin{array}{*{20}{c}} {{I_1}}\\ {{I_2}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{Y_{11}}}&{{Y_{12}}}\\ {{Y_{21}}}&{{Y_{22}}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{V_1}}\\ {{V_2}} \end{array}} \right]\)
I1 = Y11V1 + Y12V2
I2 = Y21V1 + Y22V2
Calculation:
When V2 = 0 or short circuit port 2
Then, I1 = Y11 V1
I2 = Y21 V1
V1 and I1 relation can be drawn from current division rule as
\(V_1 = 0.5\times ({\frac{0.5}{0.5+0.5}})I_1\)
V1 = 0.25I1
I1 = 4V1
Y11 = 4 S
similarly, V1 and I2 relation can be drawn as
V1 = 0.5(-I2)
I2 = -2V1
Y21 = -2 S
By applying the same procedure for port 1
When V1 = 0 or short circuit port 1
Then, I1 = Y12 V2
I2 = Y22 V2
V2 and I2 relation can be drawn from current division rule as
\(V_2 = 0.5\times ({\frac{0.5}{0.5+0.5}})I_2\)
V2 = 0.25I2
I2 = 4V2
Y22 = 4 S
similarly, V1 and I2 relation can be drawn as
V2 = 0.5(-I1)
I1 = -2V2
Y12 = -2 S
\( \left[ {\begin{array}{*{20}{c}} {{Y_{11}}}&{{Y_{12}}}\\ {{Y_{21}}}&{{Y_{22}}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {4}&{-2}\\ {-2}&{4} \end{array}} \right]~S\)
Hence option 1 is correct
For the given π network
Y parameter can be calculated by
\(\left[ {\begin{array}{*{20}{c}} {{I_1}}\\ {{I_2}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{Y_1} + {Y_2}}&{ - {Y_2}}\\ { - {Y_2}}&{{Y_2} + {Y_3}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{V_1}}\\ {{V_2}} \end{array}} \right]\\ \)
Substituting the value of Y1, Y2, and Y3
\(= \left[ {\begin{array}{*{20}{c}} {\left( {2 +2} \right)}&{\left( { - 2} \right)}\\ {\left( { - 2} \right)}&{\left( {2 + 2} \right)} \end{array}} \right] \\\)
\(= \left[ {\begin{array}{*{20}{c}} {4}&{ - 2}\\ { - 2}&{4} \end{array}} \right]~S\)
When port 1 of a two port cirucit is short circuited, I1 = 4I2 and V2 = 0.25I2, which of the following is true?
Answer (Detailed Solution Below)
Two Port Networks Question 14 Detailed Solution
Download Solution PDFConcept:
I1 = Y11 V1 + Y12 V2
I2 = Y21 V1 + Y22 V2
When port 1 is short cirucited, i.e. V1 = 0,
I1 = Y12 V2 and I2 = Y22 V2
Calculation:
The given equations are:
I1 = 4I2 and V2 = 0.25 I2
⇒ I2 = 4V2 ⇒ Y22 = 4
I1 = 4 (4V2) = 16 V2
⇒ Y12 = 16The y-parameters for the network shown in the figure can be represented by
Answer (Detailed Solution Below)
Two Port Networks Question 15 Detailed Solution
Download Solution PDFConcept:
Y parameter:
I1 = V1 Y11 + V2 Y12
I2 = V1 Y21 + V2 Y22
\({I_1} = \frac{{{V_1} - {V_2}}}{Z}\)
\({I_1} = \frac{{{V_1}}}{Z} - \frac{1}{Z}\;{V_2}\) ...1)
\({I_2} = - \frac{1}{Z}\;{V_1} + \frac{1}{Z}\;{V_2}\) ...2)
\(\left[ y \right] = \left[ {\begin{array}{*{20}{c}} {\frac{1}{Z}}&{ - \frac{1}{Z}} \\ { - \frac{1}{Z}}&{\frac{1}{Z}} \end{array}} \right]\)
Calculation:
For the given question Z = 5 Ω
\(\therefore \left[ y \right] = \left[ {\begin{array}{*{20}{c}} {\frac{1}{5}}&{ - \frac{1}{5}} \\ { - \frac{1}{5}}&{\frac{1}{5}} \end{array}} \right]\)