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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 



V^i 



iV^ 



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

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

 to cutoff. The arrows are the vectors Zj — Zj"*" which are a measure of the magnitude 

 of the reflection. 



A. Step-up line. 



Curve 1 — Forward looking characteristic impedance, 



Zi+ = Zie-^^'''~'^^^'f\ f>fi, 



Zi^ = Zil- i(/i//)(l 4- y!\-Plim, /i > /; 



Curve 2 — Resistance termination, Zi = Zi; 

 Curve 3 — Capacity resistance termination, Zi = Zi{\ — jf\lf); 



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+ = Z;[+i(/>//)(l - Vl -/V/i^)], /i > /; 



Curve 6 — Resistance termination Z/ = Zj; 



Curve 7 — Inductance resistance termination Z; = Z;/(l — jfijf); 

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

 at twice the cutoff frequency and at infinite frequency. 



