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Transistor As Two-port Network

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In the last post, we saw bjt as a switch and different projects based on the concept of BJT as a switch. In this post, we will try to understand the concept of transistors as two-port networks.
First of all, we have to understand what is a two-port network to understand the transistor as a 2-port network.
Two-port Network:-
Any network with 4 nodes or 4 terminals is considered as a two-port network only if it satisfies the port condition 
Port Condition:-
If current entering from one terminal is leaving from some other terminal with the opposite direction but with equal magnitude then these two terminals combine to form the single port. So for a two-port network, we require 4 such terminals that satisfy the port condition.

As you can see above the transistor obeys port condition and therefore we can say that the transistor is like a two-port network.
There are total of 6 parameters for a two-port network but for analysis of transistor, we will be dealing with only one parameter that is an h-parameter. You can also go with g-parameter 
Since, 
h=1/g
Now the question arises why we are only using h-parameter for the analysis of transistors? 
So here is the answer to it.
Z-parameter:-
V1 = Z11*I1 + Z12*I2
V2 = Z21*I1 + Z22*I2
By using Z-parameters we can only get to know input and output impedances and we not at all interested in transfer impedances for the analysis of transistors.
Y-parameter:-
I1 = Y11*V1 + Y12*V2
I2 = Y21*V1 + Y22*V2
Similarly, by using Y-parameters we will only get input and output admittance and we not at all interested in transfer admittance
ABCD parameter:-
Vs = A*V + B*I
Is = C*V + D*I
By using ABCD parameters we can just find the source voltage and source current, which is not at all required for analysis of transistor.

But now let's talk about h-parameter 
V1 = h11*I1 + h12*V2.....(1)
I2 = h21*I1 + h22*V2.....(2)
Now, 
From equation (1)
if V2=0 (short-circuited) 
h11 = V1 / I1
And as we know voltage by the current is equal to the resistance. Therefore h11 is also known as input impedance (Zi)
if I1=0 (open circuited)
h12 = V1 / V2
So h12 provides reverse voltage gain(1\Av).
So if we took reciprocal of it then we will get the (Av)voltage gain (V2 / V1) of an amplifier.

Now, 
From equation (2)
If V2=0 (short circuited)
h21 = I2 / I1
So h21 parameter provides the current gain of the amplifier.
If I1=0 (open circuited)
h22 =  I2 / V2
So h22 provide output admittance of the amplifier
But if we take the reciprocal of it then we will get (Zo)output impedance (V2 / I2) of the amplifier.


So to study amplifier these 4 parameters plays an important role i.e. 
1) Input impedance (Zi).
2) Output impedance (Zo).
3) Voltage gain (Av). &
4) Current gain (Ai).

So in ac analysis or for small-signal analysis, the transistor model can be drawn as shown below. 

hie:-represents input impedance of transistor.
hre:-represents reverse voltage gain of the transistor.
hfe:-represents forward current gain of transistor it is also known as (b).
hoe:-represents open circuit or admittance of transistor.
(e) which is used in the above parameters represents that we are doing ac analysis of common emitter configuration.  
Now,
V1=Vin of the transistor which is in few millivolts while V2=Vce or output voltage which might be in volts but greater than Vin
Therefore h12=hre=V1/V2 is almost equals to zero (h12=hre=0).Thus it can be neglected.
Also,
I2=Ic or output current of the transistor is in few milli-amperes while the V2=Vce or output voltage which might be in volts
therefore h22=hoe=I2/I1 is almost equals to zero (h22=hoe=0).
So 1/hoe becomes very large. Thus it can be replaced by an open circuit.
So the approximate model of the BJT transistor can be drawn as shown below.
I hope you understood it. If you like it then please let me know in the comment section.



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