Aim
To calculate and verify Yparameters of twoport 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 shortcircuit parameters) are properties used in electrical engineering to describe the electrical behaviour of linear electrical networks.
For any twoport 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 twoport 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 twoport 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 twoport 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 twoport 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 twoport 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 multimeter.
 Secondly, short circuit input port and supply 5V to output port. Measure input current and output current using multimeter.
 Calculate the values of Yparameters 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 Yparameters]
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 Yparameters are found to be nearly equal hence Yparameters are verified.
Video Tutorial on YParameters
Video Tutorial "To verify Yparameters of twoport network"
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