Transmission Line Input Impedance - ITTC

1/26/2005 Transmission Line Input 1/9 Jim Stiles The Univ. of Kansas Dept. of EECS Transmission Line Input Impedance Consider a lossless line, length A, terminated with a load ZL. Let s determine the Input Impedance of this line! Q: Just what do you mean by Input Impedance ? A: The Input Impedance is simply the line Impedance seen at the beginning (z= A) of the Transmission line, : ()()()inVzZZzIz= == == AAA Note Zin equal to neither the load Impedance ZL nor the characteristic Impedance Z0 ! 0 and ininLZZZZ I(z) 0,Z + V (z) - + VL - A ZL IL z= A0z=1/26/2005 Transmission Line Input 2/9 Jim Stiles The Univ. of Kansas Dept. of EECS To determine exactly what Zin is, we first must determine the voltage and current at the beginning of the Transmission line (z= A). 000jjLjjLV(z) V eeVI(z)eeZAAAAAA + +++ = =+ = = Therefore: ()()0jjLinjjLVzeeZZIzee+ + = + == = AAAAAA We can explicitly write inZ in terms of load ZL using the previously determined relationship: 00 LLLZZZZ =+ Combining these two expressions, we get: ()()()()()()()()00000000jjLLinjjLLjjjjLj jjjLZZeZZeZZZZeZZeZeeZeeZZeeZee + + + + + + ++ =+ ++ = + AAAAAA AAAA AA Now, recall Euler s equations: cossincossinjjejej + =+= AAAAAA 1/26/2005 Transmissio

1/26/2005 Transmission Line Input Impedance.doc 6/9 Jim Stiles The Univ. of Kansas Dept. of EECS 3. L 0 ZZ= If the load is numerically equal to the characteristic impedance of the transmission line (a real value), we find that the input

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