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BELL SYSTEM TECHNICAL JOURNAL 



teristic impedance of a non-dissipative exponential line looking toward 

 the high impedance end as a function of frequency. At infinite fre- 

 quency the characteristic impedance is a resistance equal to the 

 nominal characteristic impedance but as the frequency is decreased the 

 phase angle of the characteristic impedance changes so that its locus 



\/^ 



Fig. 2 — Impedance diagram comparing the forward looking ciiaracterlstic imped- 

 ance with various terminal impedances. The numbers give the frequency relative 

 to cutoff. The arrows are the vectors Zi — Zj+ which are a measure of the magnitude 

 of the reflection. 



A. Step-up line. 



Curve 1 — Forward looking characteristic impedance, 

 Zi+ = Zie-^ sin-Hfiin^ f > y,^ 



Zi+ = Zti- j(/i//)(i + Vi -f/fi'n /i > /; 



Curve 2 — Resistance termination, Zi = Zi\ 

 Curve 3 — Capacity resistance termination, Zi = Z;(l — jf^/f); 



Curve 4 — Capacity, resistance and inductance termination adjusted for no reflection 

 at twice the cutoff frequency and at infinite frequency; 



B. Step-down line. 



Curve 5 — Forward-looking characteristic impedance, 



Zi+ = Zie+''^'"- ^f^lf\ f>fi 



Zi+ = Z;C+i(/,//)(l - Vl -Mrn 



Curve 

 Curve 



6 — Resistance termination Zi = Zr, 

 7 — Inductance resistance termination Zi = Z;/(l 

 Curve 8 — Inductance, resistance and capacity termination adjusted for no reflection 

 at twice the cutoff frequency and at infinite frequency. 



i/i//); 



