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Before somebody tells me there's something wrong with programs
LINE_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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