z Parameters And h Parameters Of Two Port Networks
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z Parameters And h Parameters Of Two Port Networks (a) What is a one-port network?
(b) What is a two-port network?
(c) What are z parameters?
(d) What are h parameters?
(e) Figure 1.2 is a two-port network. Find:
(i) the voltage-gain ratio, V2/V1, in terms of the z parameters.
(ii) the current-gain ratio, I2/I1 in terms of the h parameters.
(iii) the current-gain ratio, I2/I1, in terms of the z parameters.

The strings: S7P3A32 (force - push).

The math:
Pj Problem of Interest is of type force (push). (a) A pair of terminals constitute a port: if there is an identifiable voltage across the terminals and the current into one terminal is the same as the current out of the other terminal.
Figure 1.1(a) consists of two one-port networks (A and B). Network, A is a one-port network when viewed from from the left of terminals 1, 2. Network B is a one-port network when viewed from the right side of terminals 1,2.

(b) Figure 1.1(b) is a two-port network if currents I1in and I1out are equal; and currents I2in and I2out are equal. The four variables V1, V2, I1 and I2 (only two of which can be independent) characterize the network.

(c) z parameters are the shortened name of open circuit impedance parameters. They are the coefficients of the dependent currents of a two-port network given that both voltages V1 and V2 are independent and the linear network contains no independent sources. In other words, the coeffiecients in the following equations:
V1 = z11I1 + z12I2 -------(1)
V2 = z21I1 + z22I2.-------(2)
Where z11 = V1/I1 (I2 is assumed = 0)
z12 = V1/I2 (I1 is assumed = 0)
z21 = V2/I1 (I2 is assumed = 0)
z22 = V2/I2 (I1 is assumed = 0)

(d) h parameters are the shortened name of hybrid parameters. As the name suggests, they are the coefficients of a dependent voltage and a dependent current. In other words, a voltage source and a current source are independent while the other voltage and current are dependent. So, h parameters are the coefficient in the following equations given that V1 and I2 are independent and V2 and I1 are dependent:
V1 = h11I1 + h12V2 -------(3)
I2 = h21I1 + h22V2.-------(4)
Where h11 = V1/I1 (V2 is assumed = 0)
h12 = V1/V2 (I1 is assumed = 0)
h21 = I2/I1 (V2 is assumed = 0)
h22 = I2/V2 (I1 is assumed = 0) (ei) Consider V2 and RL of figure 1.2:
By Ohms Law, -V2/RL = I2
From equation (2), I2 = (V2 - z21I1)/z22-------(5)
From equation (1) I1 = (V1 - z12I2)/z11 = (V1 - z12)(-V2/RL))/z11-------(6)
Replacing I1 in (5) by its value in (6), we have:
-V2/RL = [V2 - z21((V1 - z12)(-V2/RL))/z11)]/z22-------(7)
So, (z21z12/RL))/z11)]/z22)V2 - V2/z22 - V2/RL = -(z21/z11z22)V1
So, (z21z12/RLz11z22)V2 - V2/z22 - V2/RL = -(z21/z11z22)V1
So,V2/V1 = z21RL/(z11RL + z11z22 - z12z21).

(eii) Consider V2 and RL of figure 1.2:
By Ohms Law, -V2/RL = I2
Let V1 and I2 be the independent variables, then, equation (4) holds:
I2 = h21I1 + h22V2
Since V2 = -I2RL, we have
I2 = h21I1 - h22I2RL
So, I2/I1 = h21/(1 + h22RL).

(eiii) Consider V2 and RL of figure 1.2:
By Ohms Law, -V2/RL = I2
From equation (2), I2 = (V2 - z21I1)/z22 -------(5)
Substitute V2 = -I2RL in (5), we have:
I2 = (-I2RL - z21I1)/z22
So, I2(z22 + RL) = - z21I1)
So, I2/I1 = - z21/(z22 + RL).

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