No discussion about antennas would be complete without a word or two about
** SWR.**
The Standing Wave Ratio will be explained somewhere much later in this site,
but I suspect that you have the idea from somewhere that the SWR must be
1:1 for a perfect antenna. Actually, that is **not true.****not** match a vertical antenna.

The formula for non-reactive SWR has two possible formulas. Choose the one that gives you an answer that is greater than 1.

Lets find the SWR of a 50 Ohm coax hooked to a 36 Ohm vertical antenna.
I will use both of the formulas to show you what happens if you choose
the wrong one.

SWR = Z coax / Z load = 50 Ohms / 36 Ohms = 1.38, which is more than 1.

In this example, you should choose the answer which is greater than 1,
which is 1.38.
This will become 1.38 to 1 or can be written 1.38:1. 1.38 is almost 1.4, so I will
say that this SWR is 1.4 to 1.**The conclusion here is that a perfect vertical antenna with a perfect ground
connected to a perfect 50 Ohm coax will have a SWR of 1.4 to 1. **

The efficiency of a vertical antenna system with extra resistance in it will be
lower than a perfect system. Lets do the math again.

Remember when we looked at both of those graphs, and found that 55 radials each 0.288 wavelengths long would give us 80% efficiency? You can use the 36 Ohms and the 80% to find out what the total resistance is in the whole system. You can use the formula for efficiency and turn it around (transpose it) to find that total resistance, then use that total resistance in the SWR formula.

Efficiency = 36 Ohms / the Total resistance . . . so, Total
Resistance = 36 Ohms / 0.8 = **45 Ohms**
Calculating the SWR of an 80 % efficient antenna looks like this.....

80 %? That really does not look good, **but it is not as bad as it looks.**

dB = 10 times log 10 (power ratio)

where the power ratio is 0.8. (because 80% is equal to 0.8)

Decibels = -.969

Actually, you might want to know the value of efficiency VS. decibels so you can make a better estimation of how many radials you really need. This information comes from the same two graphs at the Stepper web site found on another page in this web site.

90% | -.457 dB | 120 radials | 0.40 wl | 1.25 : 1

80 % | -.969 dB | 45 radials | 0.24 wl | 1.11 : 1

70 % | -1.54 dB | 22 radials | 0.16 wl | 1.02 : 1

60 % | -2.21 dB | 7 radials | 0.06 wl | 1.20 : 1

50 % | -3.01 dB | 4 radials |0.03 wl | 1.44 : 1

40 % | -3.97 dB | no info | no info | 1.8 : 1

30 % | -5.23 dB | no info | no info | 2.4 : 1

20 % | -6.99 dB | no info | no info | 3.6 :1

10 % | -10.0 dB | no info | no info | 7.2: 1

You can see that at 50% efficiency an automotive 50 Watt transmitter will be putting out 25 Watts which beats any standard handheld transmitter at UHF or VHF. Using the formulas for efficiency and SWR as shown above, the SWR for a 50% efficient antenna is 1.44, which looks pretty good for an automobile system. While this system is not very good at all, the operator will possibly think that her/his system is doing fine because everyone says the signal gets into the repeater "full quieting".

I hope you can see that a poor antenna can do a OK job and the operator will
never suspect that the antenna is not really doing all it can do. In fact, the
operator is likely to think the antenna is quite good. ** This is where bad
information gets its start and intelligent people get the wrong idea !**

Go to the NOISE section. Some Vert. antenna noise theory.. From W8JI's serious lab.