The ABCD constants of this series impedance are\(\left[\begin{array}{ll} 1 & 8 \\ 6 & 3 \end{array}\right]\,\)Which of the following represents the B parameter?

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  1. 1
  2. 8
  3. 3
  4. 6

Answer (Detailed Solution Below)

Option 2 : 8
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Concept:

ABCD Parameter:

We know that the ABCD parameter of the transmission line

\(\left[ {\begin{array}{*{20}{c}} {{V_1}}\\ {{I_1}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} A&B\\ C&D \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{V_2}}\\ { - {I_2}} \end{array}} \right]\ \)

A = D

AD – BC = 1

\(\left[{\begin{array}{*{20}{c}} A&B\\ C&D \end{array}}\right]\)\(\left[\begin{array}{ll} 1 & 8 \\ 6 & 3 \end{array}\right]\)

So, B = 8

Conditions of reciprocity and symmetry in terms of different two-port parameters are:

Parameter

Conditions of reciprocity

 Conditions of symmetry

Z

z12 = z21

z11 = z22

Y

y12 = y21

y11 = y22

T(ABCD)

(AD – BC) = 1

A = D

h

h12 = -h21

(h11h22 – h12h21)

= 1

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