Table of Contents
ToggleAim
To calculate and verify Y-parameters of two-port network.
Apparatus
Breadboard, Batteries or DC regulated power supply, Resistors, Digital multimeter, Connecting wires, Alligator clips.
Theory
Y parameters (also known as admittance parameters or short-circuit parameters) are properties used in electrical engineering to describe the electrical behaviour of linear electrical networks.
For any two-port network, input voltage V_{1}and output voltage V_{2}can be expressed in terms of input current I_{1}and output current I_{2}respectively.
The Y parameter for a two-port network is defined as
[ I ] = [ Y ] [ V ]
where [ Y ] is the admittance matrix, [ I ] and [ V ] are the current and voltage matrix.
From the above matrix form representation of two port network, it is clear that there are four admittance parameters i.e. Y_{11}, Y_{12}, Y_{21}and Y_{22}.
From the above matrix, we get,
I_{1}= Y_{11}V_{1}+ Y_{12}V_{2} …(1)
I_{2}= Y_{21}V_{1}+ Y_{22}V_{2} …(2)
- Assuming the output of the two-port network to be short circuited, therefore V_{2}= 0
Now putting V_{2}= 0 in (1), we get
I_{1}= Y_{11}V_{1}
∴Y_{11}= (I_{1}/ V_{1})
Similarly putting V_{2}= 0 in (1), we get
I_{2}= Y_{21}V_{1}
∴Y_{21}= (I_{2}/ V_{1})
- Again, assuming input port of the two-port network to be short circuited, the input voltage will be zero. i.e. V_{1}= 0
Now putting V_{1}= 0 in (1), we get
I_{1}= Y_{12}V_{2}
∴Y_{12}= (I_{1}/ V_{2})
Similarly putting V_{1}= 0 in (2), we get
I_{2}= Y_{22}V_{2}
∴Y_{22}= (I_{2}/ V_{2})
Thus, there are four Y parameter for a two port or four terminal network. Their values are tabulated below.
Y_{11} | (I_{1}/ V_{1}) | Condition: Output port of the two-port network is short circuited i.e. V_{2}= 0 |
Y_{21} | (I_{2}/ V_{1}) | |
Y_{12} | (I_{1}/ V_{2}) | Condition: Input port of the two-port network is short circuited i.e. V_{1}= 0 |
Y_{22} | (I_{2}/ V_{2}) |
Significance of Different Y Parameter
- Since Y_{11}is the ratio of input current and voltage when the output port is short circuited, therefore it is known as input driving point admittance.
- Y_{22}is the ratio of output current and voltage when input port is short circuited, therefore it is called output driving point admittance of the network.
- Y_{12}is the ratio of input current and output voltage when input port is short circuited, therefore it is called reverse transfer admittance.
- Y_{21}is the ratio of output current and input voltage when output port is short circuited, therefore it is called forward transfer admittance.
Circuit Diagram
[Recommended values: R_{1}= 2KΩ, R_{2}= 450Ω, R_{3}= 1kΩ, V_{1}= 10V and V_{2}= 5V OR chose any resistor between 200Ω to 2KΩ and DC supply beween 5V to 12V]
Procedure
- Connect the circuit as shown in figure 2.
- First short the output port (port 2) and supply 10V to input port (port 1). Measure output current and input current using multi-meter.
- Secondly, short circuit input port and supply 5V to output port. Measure input current and output current using multi-meter.
- Calculate the values of Y-parameters using respective formulas (Shown in calculation section).
- Switch ‘OFF’ the supply after taking the readings.
Precautions
- Before circuit connection working condition of all the components must be checked.
- All the connection should be tight.
- Ammeter must be connected in series while voltmeter must be connected in parallel to the components (resistors).
- The electrical current should not flow the circuit for long time, otherwise its temperature will increase and the result will be affected.
Observation table
When output port is short circuited | When input port is short circuited | ||||
V_{1} | I_{1} | I_{2} | V_{2} | I_{1} | I_{2} |
Calculations
For Practical Values:
(a) When output is short circuited i.e. V_{2} = 0
Y_{11}= I_{1}/V_{1} = ____S
Y_{21} = I_{2}/V_{1} = ____S
(b) When input is short circuited i.e. V_{1} = 0
Y_{12} = I_{1}/V_{2} = ____S
Y_{22} = I_{2} /V_{2 }= ____S
For Theoretical Values:
[Use any method to calculate Y-parameters]
Y_{11} = ____S
Y_{22}= ____S
Y_{12}= ____S
Y_{21}= ____S
Result
Parameter→ | Y_{11} | Y_{12} | Y_{21} | Y_{22} |
Theoretical | ||||
Practical |
Conclusion
Calculated and practical values of Y-parameters are found to be nearly equal hence Y-parameters are verified.
Video Tutorial on Y-Parameters
Video Tutorial "To verify Y-parameters of two-port network"
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