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Expression 4.50 can be obtained by equating the ABCD parameters of the two circuits ?

How to derive expression 4.50 using the ABCD matrix for transmission line and π-circuit network ?

Note: Screenshots below are taken from Microstrip Filters for RF Microwave Applications, 2nd Edition

A

B

C

D

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    \$\begingroup\$ It's unclear what it is that you are asking for advice about. \$\endgroup\$ – Andy aka Jul 29 at 9:01
  • \$\begingroup\$ @Andyaka How to derive expression 4.50 ? \$\endgroup\$ – kevin Jul 29 at 12:50
  • \$\begingroup\$ @Andyaka I have edited the question \$\endgroup\$ – kevin Aug 14 at 3:53
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The following is the derivation process for expression 4.50

ABCD matrix for transmission line at Figure 4.7(a)

a

ABCD matrix for π-circuit network at Figure 4.7(b)

b

Comparing the two ABCD matrices above gives :

c

d

Applying trigonometry double angle formula :

e

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