EXPONENTIAL TRANSMISSION LINE 



557 



not improved proportionally. This is easily remedied by completing 

 the impedance transforming network with the appropriate reactance 

 at the input. The resulting input impedance is shown in curve 3. In 

 the "pass" frequency range the maximum reactive component is of 



0.1 



0.5 ti 



2.0 i 



I 



3.0 : 



001 0-05 0.1 0-5 1.0 4" 



RELATIVE FREQUENCY f/fQ 



Fig. 1 — Input impedance characteristics of 1 : 2 exponential lines. Left ordinate 



scale refers to step-up line. Right ordinate scale refers to step-down line. 



Curve 1— Resistance termination. 



Curve 2 — With capacity equal to twice the electrostatic capacity of the line in series 

 with the same resistance, Zj = Zi.{\ — jfilf), for step-up line, or with an in- 

 ductance equal to twice the total inductance of the line in shunt with the 

 same resistance, Zi = Zi/(1 — jfi/f), for step-down line. 



Curve 3 — Termination as for curve 2 with inductance equal to twice the total induc- 

 tance of the line in parallel with input to the line, Zn = Zi/{1 — jfi/f), for 

 step-up line, or termination as for curve 2 with capacity equal to twice the 

 static capacity of line in series with input to the line, Za = Zi{\ — jfi/f). 



Curve 4 — Asymptotic value of impedance of capacity of line in parallel with termina- 

 tion for case 2 for step-up line, or asymptotic value of impedance of inductance 

 in series with termination for case 2 for step-down line. 



Curve 5 — Impedance of shunt inductance added at input for case 3 for step-up line, 

 or impedance of capacity added in series at input for case 3 for step-down line. 



the same order of magnitude as the deviation of the impedance from 

 the ideal. 



Besides its application as an impedance transforming network, the 

 exponential line may be used as a "resistance" load of constant known 

 impedance that has a high capability for dissipating power. As such 

 it is capable of dissipating more power in the same length of line than 



