How important is a low VSWR

 

It is the generally accepted view amongst the more knowledgeable, that a low VSWR is unimportant when considering which antenna to put up.

I do not of course include resonant antennas such as beams or vertical’s that are designed to provide a good match to coaxial cable.   Walt Maxwell in his book reflections states, “too low a SWR can kill you”, this dramatic statement does not imply that we will shuffle off this mortal coil when the meter drops to 1:1, but refers to how a good antenna can become no more than a dummy load if we pursue the holy grail of a 1:1 VSWR reading without considering the implications.

 

You will forgive me I hope, if I repeat the words of many who have gone before, in saying it is very difficult to find a better and more versatile antenna than a reasonable length doublet fed with open wire feeder all the way back to the transmitter.  The difficulty with such an antenna is that we need a magic box to bridge the gap between the end of that open wire feeder and the ubiquitous SO239 socket on the back of almost every transceiver.

 

This is the crux of the problem; we must separate the antenna where the object is to provide an efficient radiator preferably in some desired direction, from the matching which is the task of transferring the power from the transmitter to the antenna with as little loss as possible and a correct match for the PA.

 

In spite of all the hype that we hear on the amateur bands there is very little to choose between the various popular designs, if height and length are of the same order.          For any single wire antenna the radiation pattern depends on its length in wavelengths and height above ground.  The main exception is the  “V”  inverted or otherwise, because of it having a vertical component to its radiation, some low angle radiation is gained at the expense of some of the normal horizontal pattern.

 

The same cannot be said of methods of feeding the antenna; I will show that some methods can lose a very large proportion of the transmitters output, and at the same time showing a very low VSWR. In fact it is a general rule that the more efficient an antenna / feeder combination, the more difficult it is to find a good match. Since this is the opposite to what we might intuitively believe, it is worthy of a more detailed explanation.

 

The lowest VSWR is obtained with a dummy load! However a length of corroded low quality coax makes an excellent dummy load. This is where a low VSWR reading should not be regarded as a sign that all is well, but rather should be treated with suspicion, even when using a resonant antenna such as a half wave dipole where we would expect to see a low reading, moving the transmit frequency away from the resonant frequency the reading should rise steeply, if it lingers near the bottom of the scale be suspicious!

 

 

VSWR and feeder attenuation

 

The VSWR at the antenna feed point is frequently impossible to measure, but can give an indication of whether a design is behaving as expected.

If we know the matched loss of the feeder and the VSWR at the bottom then it is possible to calculate the probable VSWR at the antenna end.

 

If we set (VF + VR) = 1 then since   (VF + VR) / (VF  – VR) = VSWR

 

then   (VF  –  VR) =  (1 / VSWR),           since VF  =  1 – VR  and  VR =  1 – VF

 

2VF  = 1 + (1 / VSWR)               and          2 VR = 1 – (1 / VSWR)

 

The forward part of the wave at the bottom of the feeder is: -

 

VFG = 0.5 + (1/(2*VSWR))

 

and the reflected part is: -

 

VRG = 0.5 – (1(2*VSWR))

 

You will note that whatever the value of VSWR, when added together these two equations always add up to 1 as we initially defined.  These are the relative amplitudes of the forward and reverse waves for that value of VSWR at the generator.  As we move towards the load, the amplitude of the forward wave reduces due to the feeder loss and the amplitude of the reflected wave increases since we are moving closer to it’s source with less loss.

 

The factor “M” by which the reflected wave must be multiplied and the forward wave divided can be obtained from the loss figure for the length of feeder used.

         

M = 10(dB/20)

 

(where dB is the loss in dB for the length of feeder)

(dB is divided by 20 because these are voltage ratio’s)

 

we can now evaluate expressions for the relative amplitudes of the forward and reflected waves: -

 

VFL  =  VFG / M      and    VRL =  VRG * M

 

The value of VSWR at the load end of the feeder is: -

 

VSWRL  =    VFL + VRL

                            VFL - VRL

 

We can if we wish use this computed value of the load VSWR and the calculated figure for the matched line loss to calculate the actual feeder loss in the next section.

 

 

 

Actual feeder attenuation under VSWR conditions

If we know (whether calculated or measured) the feed impedance of the antenna and the matched line loss of the feeder, we can calculate the actual loss.

 

As before the relative amplitude of the forward and reflected waves can be calculated from the VSWR at the load.

The actual voltage (VFL + VRL), which we previously assigned the value of 1, can be calculated for an arbitrary load power of 1watt
.  V2 = P * R

 

hence   V = (P* R)-2   for P = 1watt and R = VSWR * Z0

 

VFL=(0.5+(1/(2*VSWRL))) * (VSWRL * Z0)-2

 

VRL=(0.5–(1/(2*VSWR))) * (VSWRL * Z0)-2

 

This time however we must multiply the amplitude of the forward wave by M and divide the amplitude of the reflected wave by M              “M = 10(dB/20)

 

VRG=(0.5+(1/(2*VSWRL)))*(VSWRL*Z0)-2 / M

 

VFG =(0.5– (1/(2*VSWR)))*(VSWRL*Z0)-2 * M

 

Power is V2/ R                (where R is Z0)
 



Fig. 1  curves of SWR at transmitter
        against SWR at load
 
 
 

 

 


Forward power is    (0.5 + (1/(2*VSWRL))) 2  * VSWRL / M2          

 

Reflected power is   (0.5 –  (1/(2*VSWR))) 2  * VSWRL * M2 

 

The power from the transmitter is Forward power - reflected power = Ptx

 

The power to the load is declared to be 1watt so the loss due to the feeder is: -

                                      10*log10 (Ptx)

 

The accuracy of these figures depends on how accurately we can measure the VSWR at the generator end

and how close the actual feeder loss is to the published value.

 

 

Looking at the Smith Chart

 

Phillip H. Smith of Bell Telephone Laboratories developed the Smith chart and an account was published in the American magazine ELECTRONICS in January 1939, subsequently an improved version appeared in January 1944.

 

 

 

 

This simplified view of a Smith chart shows how the main axes of a normal graph have been curved into circles and arcs. As is normal practice with the Smith chart it has been normalised so that the characteristic impedance Zo = 1, for Zo other than 1, all the figures are multiplied by Zo. One rotation of the chart corresponds to a half wavelength of transmission line; (the wavelength scale around the edge has been omitted for clarity) to find the transforming effect of a transmission line first you plot the load impedance on the chart, then draw a circle centred the centre of the chart that passes through that point, this is a circle of constant SWR. Moving clockwise around the chart for the length of the line, remember one rotation is a half wavelength; continuing to rotate adds one half wave for every complete rotation. You can then read off the impedance that the generator will see from the new position on the chart.  Even in these days of computers where transformations like this can be calculated in much less than a second, the Smith chart is a powerful visual tool. If the transmission line has loss, then reducing the diameter of the SWR circle as it rotates can show this.