Extra credit 10 points optional With these values for Z1 and

Extra credit (10 points, optional) With these values for Z1 and Y2 for the equivalent T-network of a transmission line, the two systems are totally equivalent. The input impedance Z can be calculated for this T-network: Question () 5 points. Write the input impedance for this network using your knowledge from circuit analysis Question (iij5 points. Use the following trig identities for hyperbolic functions to simplify your expression for Z, Compare with equation (0) from problem 1. 2 -sinh-cosh?yl-sinh2

Solution

i) INPUT IMPEDANCE

Z_I=(Z₁/2)+(1/Y₂₊(1/Z₁/2))

= (Z₁/2)+(Z₁/(2+Y₂Z₁))

Z_I =Z₁[(4+Z₁Y₂)/(4+2Z₁Y₂)]

if we consider Z_L

Z_I =(Z₁/2)+{(Z₁+2Z_L)/(2+Y₂Z₁+2Z_LY₂)}