A reader of On the concept of that P=Pfwd-Prev asked if / how the scenario discussed could be modeled in SimSmith.
SimSmith uses different transmission line modelling to what was used in that article, but a SimSmith model of RG58A/U allows illustration of the principles and it will deliver similar results.
Let’s explore the voltage maximum and minimum nearest the load to show that VSWR calculated from the magnitude of reflection coefficient is pretty meaningless in this scenario.
Above is the basic model. I have created two line sections, one from the load to the first voltage maximum, and another to the first voltage minimum where I have placed the source. I have set Zo to the actual Zo of the line as calculated by SimSmith (56.952373-j8.8572664Ω), effZ as SimSmith calls it, so the Smith chart relates to the real transmission line.
You will note that the load is outside the chart, it is because of the load value and the chart reference (56.952373-j8.8572664Ω). It also happens that the complex reflection coefficient Γ is 1.06∠98°, that’s fine.
See how the path follows a smooth spiral inwards due to the line attenuation, reaching the point of the first voltage maximum.The voltage maximum occurs where 1+Γ reaches a maximum, it also corresponds to the point that is the greatest distance from the left hand extremity of the chart. At this point, Γ1=0.810∠1.7° and 1+Γ1=1.810∠0.761°.
Continuing on, we reach a voltage minimum where 1+Γ is minimum, in this case Γ2=0.501∠-173° and 1+Γ2=0.5064∠6.925°.
Just a small side task, let’s calculate the two way voltage gain of that last 421m section of line from the spiral. It is |Γ2|/|Γ1|=0.501/0.810=0.6185, and the one way voltage gain OWVG is 0.6185^0.5=0.7865.
Ok, now let’s calculate the ratio of the nearby voltage maximum to the voltage minimum, the VSWR. VSWR=|1+Γ1|/|1+Γ2|*OWVG=1.810/0.5064*0.7865=2.811. (This reconciles with the displayed value for V at each end of T1.)
You will note that SimSmith calculates the VSWR at the input end to be 3.009, and half way between the minimum and maximum it shows 4.708 (see graphic), and 9.5 at the voltage maximum.
None of the SimSmith calculated VSWR figures give a hint of the VSWR as measured above. The problem is not SimSmith’s calculations, it is that the assumptions on which calculating VSWR do not apply in this scenario (as discussed at On negative VSWR), the user does need to understand transmission lines to know what figures are valid in the scenario at hand.
- Setting generator Zo to the cable Zo is done by inserting the formula G.Zo=T1.effZ; into the Plt box.
- Calculating 1+Γ can be done with a hand calculator, but you may find this online calculator convenient:
- There appear to be defects in SimSmith’s handling of a complex chart reference (eg some arcs appear wrongly scaled).
- An eagle-eye questioned that the length of T1 is not exactly 90°. We commonly talk of the distance between voltage maximum and minimum being 90°, but that is exactly correct only when Zo is purely real.