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				 Gamma.  Before somebody tells me. 
 
			
			Before somebody tells me there's something wrong with programsLINE_ZIN and INPUT_Z  I'd better put in a few words of explanation.
 
 First of all there's nothing wrong with the programs. Both are
 correct.
 
 They both calculate the reflection coefficient Gamma for a given line
 and given load impedance at a given frequency. One does it for coaxial
 lines and the other for balanced-twin and open-wire lines.
 
 But, believe it or not, under certain load conditions the reflection
 coefficient Gamma can exceed unity. Indeed, at a sufficiently low
 frequency, Gamma can approach 1+Sqrt(2) = 2.414
 
 With program LINE_ZIN enter the following -
 
 Freq = 0.2 MHz
 Conductor diameter = 0.2 mm
 Conductor spacing = 10 mm
 Line length = 119.25 metres
 Velocity factor = 1.00
 Load resistance = 0.00 ohms
 Load reactance = + 552.6 ohms
 
 From which we get -
 
 Zo = 552.6 ohms
 Gamma = 1.084
 Angle of Gamma = -90.0 degrees
 SWR at load end = 24.8
 SWR at input end = Infinity
 
 With program INPUT_Z  enter the following -
 
 Frequ = 0.2 MHz
 Zo = 50 ohms
 Line length = 100 metres
 Inner conductor diameter = 0.73 mm (RG-58)
 Velocity factor = 0.66
 Load resistance = 0.00 ohms
 Load reactance = +50.00 ohms
 
 From which we get -
 
 Gamma = 1.109
 Angle of Gamma = -90.0 degrees
 SWR at load end = 19.3
 
 The reason for the abnormally high values of Gamma, and the SWR at the
 input end being higher than the SWR at the load end, is that the line
 impedance Zo is not purely resistive. It has a negative angle.  Zo =
 Ro - jXo.
 
 There is a resonance between -jXo and + jXload which causes the
 reflected wave to be greater than the incident wave. Hence Gamma
 exceeds unity.  The effect is not present when jXload is negative.
 
 Gamma has a maximum value when +Xload = Zo  as can be found by varying
 Xload on either side of Zo.
 
 At some distance back from the load the extraordinary high value of
 SWR occurs (as demonstrated with program LINE_ZIN) due to that point
 taking the place of the end of the line when Zo is purely resistive.
 
 The true value of Zo = Ro+jXo can be found by making the line long
 enough such that attenuation exceeds about 35 or 40 dB. Line input
 impedance is then becomes equal to Zo.
 
 It is the fact that Zo is never purely resistive which causes errors
 when using the Smith Chart.  Errors which the user can be entirely
 unaware of.  Coax lines are more prone to error than higher impedance
 balanced-twin lines.
 
 The reason why both programs stop at 200 KHz has nothing to do with
 the foregoing.  It is due to skin effect not being fully operative at
 lower frequencies which complicates calculations.
 There are other programs which go down to audio and power frequencies.
 ----
 Reg, G4FGQ
 
 
 
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