Transmission Line Parameter Problems

Professional Engineer & PE Exam Forum

Help Support Professional Engineer & PE Exam Forum:


New member
Jan 1, 2023
Reaction score
New York
Hi all,

I'm trying to logic through the solutions to the two problems below. Problem A and problem B utilize the same system values. The only difference between the two is the distance of the transmission line, which affects how you calculate the ABCD parameters. My questions are:

1. Why does the solution to problem A consider the imaginary component of the shunt admittance whereas problem B ignores it? When I've calculated ABCD parameters in the past, I've always included the +90° phase angle in my calculation processes. I can see why one would want to exclude it from a long TL model problem because square rooting a complex number takes a few extra steps on your calculator (I'm using a TI-36X Pro). It also takes a few extra steps when calculating cosh (γl) and sinh (γl) because most calculators won't run the function straight up because of the presence of a complex number. I swear my TI-84 plus silver edition could do both without the extra steps, but you can't use that calculator on the test.

2. Why do both solutions assign a phase angle of 0° to the impedance? Shouldn't it be -36.87° since the power factor is provided as 0.80 leading? Again, an impedance with a phase angle of 0° and a shunt admittance with a phase angle of 0° make for easy plug and chug when a long TL model problem comes across your plate.


  • Problem A.JPG
    Problem A.JPG
    31.4 KB · Views: 0
  • Problem A Solution.JPG
    Problem A Solution.JPG
    48 KB · Views: 0
  • Problem B.JPG
    Problem B.JPG
    34.1 KB · Views: 0
  • Problem B Solution.JPG
    Problem B Solution.JPG
    50.8 KB · Views: 0