## So how well does my antenna have to be matched?

Friis equation illustration

Friis equation

I recently had some trouble matching an integrated antenna over the whole operating band, while sticking to the available space for mounting on a PCB? so? I got to wondering things like: ?what is the actual effect of return loss and gain on the communications range??

After spending some time musing about the Friis equation (above) – with the help of the Friis tool in Antenna Magus – I rediscovered why some general guidelines like ?- 10 dB is a good enough match and stick to lower frequencies for long distance communications?, are worth following.

I picked the following typical values:

Gt = Gr = 10 dBi, |S11|t = |S11|r = -20 dB, Pt = 1 W, Pr = 10 pW and Freq = 900 MHz.

and considered the effect of varying frequency, gain and |S11|t within this typical system. Note that the black marker on each graph represents the above-mentioned typical design case.

Relationship between return loss (|S11|) and range (R)

The above graph clearly shows why threshold for acceptable return loss is -10 dB. At -20 dB there is less than 2% reduction in range, at -10 dB and -6 dB the range is reduced to 5.5% and 14.5% respectively. In communication systems where maximal range is not such a strict specification 85.5% of the theoretical maximum range does seem like a reasonable trade-off, but if you can, it is definitely worth the effort to try get the extra meters!

Relationship between gain and range.

Next I plotted the relationship between antenna gain and range. The plot illustrates the communication engineers mantra: “for every 6 dBi increase in antenna gain, the range will double” – therefore range will increase from 80 km to over 2600 km when increasing the gain from 5 dBi to 40 dBi (equivalent to replacing a patch antenna with a large, high gain reflector antenna while changing nothing else in the system).

Relationship between frequency and range.

What about frequency? If we ignore all the pitfalls of propagation absorption and environmental effects, Frequency and Range are indirectly proportional to each other ? so doubling the frequency will halve the range. If one plots this relationship (as shown above) it is clear why long distance communication systems typically operate at lower frequencies.

So what did I learn from this exercise that helped me make some design choices?

1. I could increase my operating frequency so that I can use an electrically larger antenna that is easier to match. If, however, I need to increase the operating frequency by anything more than 10% to help me improve my reflection coefficient from -6 dB to -10 dB, the net result will be a reduction in range.
2. If I can design an antenna with similar size (and similar impedance), but with increased gain in the direction of interest, then I can achieve the same effect as improving the matching. The additional gain required in this instance is around 0.8 dB. For a low gain antenna like mine (with around 3 dBi gain) getting an additional 0.8 dB might be a challenge in the space I have. In another situation, optimising a higher gain antenna, like a 12 dBi horn – to get an extra 0.8 dB sounds a lot more doable.

I hope this exercise helped you (as it did me) put the different factors in a communication system in perspective.

Author: Robert Kellerman

### One Response to “So how well does my antenna have to be matched?”

1. mike says:

My longest wireless comunication is sattelite tv at 36,000 km and 11ghz…