Power and how many people can hear you

Fairly regularly on this reflector there is a discussion on the value of higher transmitter power. Someone points out that doubling the power is half-an-S-unit which is of little value to the receiver; and the response comes that it is very valuable to stations near the limit of detection.
I have some quantitative results from two WSPR experiments that Ken VE6AGR and I did recently.
We set up two WSPR transmitting stations in Calgary. Ken’s station was kept constant from day-to-day, and Ian’s station was reduced in power each day, running at 200mW, 100mW, 50mW, 20mW, and 10mW. We ran the experiment on both 20m and on 40m. On 20m the power reduction was conveniently done in the late evening when the band had closed and we were not being heard anywhere. On 40m the power was reduced in the morning when the spot-rate was nearly zero. The two WSPRlite devices were re-started simultaneously, so the transmission from both units were synchronized at all times.
We calculated for each power-level the average range of all spots received, the number of spots that were received, and the number of periods where transmissions were made but no-one heard them.
For each parameter, at each power level, the result of Ian’s station was divided by the result of Ken’s constant reference station. The results for 40m are shown graph. The results for 20m are similar.

In summary for WSPR transmissions, we found that doubling the power of transmission caused the number of stations reporting to (approximately) double as well.
So this observation does suggest that when struggling to make 4 contacts under marginal conditions, doubling of power is a useful way to significantly increase your chance of being heard.


I’d been using my 13cms transverter today and that needs the 817 power turning to 500mW. Then I went onto 40m CW. I worked the 1st 5 stations on 500mW till I noticed and upped the steam pressure to all 5W! Didn’t seem to make much difference to be honest :slight_smile:

Interesting. To a first approximation, doubling the number of reporting stations means doubling the area covered, suggesting that the increase in range you get from doubling power is 41%.

It makes sense that a 3db increase in power will increase the S:N ratio at every receiver by that amount. So if there were a number of receivers in which the signal was previously -30 db S:N, it will now be -27 db S:N, which may be the borderline of reception on WSPR. (Adjust to suit whatever you think the borderline is. )

However there is no evidence that the increase in reports received was due to an increase in range. It could equally well reflect the number of receivers for which the signal increased past the WSPR noise floor to produce a -27 or better S:N.

However the inverse square law does predict an increase in range from doubling power.

This is a valid “intuitive” result, I think.

Andrew VK1DA/VK2UH

When Ken and I first did this experiment, we were surprised at how little the range of the stations hearing us changed. (the blue line in the graph of the first post). I think that the range is determined primarily by the geometry of the path between the stations, (the directionality of the antenna, the height of the refraction layer in the ionosphere, etc.).

And I think that Andrew is correct, the increase in the number of spots with power is a result of the increase in the S/N ratio at receivers in the same range.

I don’t think the inverse square law applies to prediction of range over the surface of the earth, (see comment about geometry of the path). Increasing the power does not change the geometry, unless it is large enough that a second skip becomes possible.
Certainly our results do not show a 1.42 increase in range from a doubling of power.


Agree re inverse square law. That works as a model only in space, when there is nothing like the ionosphere muddying the water. Even tropospheric bending and ducting on vhf and uhf fails to obey the inverse square law.

Your point about the increased power making the second (or subsequent) hop possible is a good one. Perhaps we should say that the second hop was always there but too far down below the noise (say, -36 db s:n) to be detected. The fourth and subsequent hops are there too but are too weak to be detected.

As you increase the power you should see a widening circle of receiving station start to detect the signal as it emerges above the minimum detectable by WSPR. With enough power you would see the skip zones narrowing too. You’d also see the third reflection start to become apparent etc. More power does increase the range but only in multiples of the skip distance.

The studies of propagation using wspr and low powered transmitters have demonstrated to mnay people the basics of propagation and that can only be a good thing.

What wspr has done is to allow receivers to look below the noise and observe signals that were always there but were not previously detectable. This would have been science fiction in past years. I’m looking forward to WSPR type detection getting 10 db more sensitive.

73 Andrew VK1DA/VK2UH

Increasing the power could be visualised as similar to the google earth flooding simulation, where you change the flooding elevation to observe what land is visible above the flooding level.

Hi all,
I think this is a very interesting analysis. However, as for the implications for SOTA activations, e.g. whether it makes sense to carry an amplifier and additional batteries, I think we should take into account that WSPR is designed for weak signal detection, whereas most SOTA CW QSOs require a signal way above minimum SNR. In other words, if you increase your WSPR signal just a little bit, you might be above the threshold for detection and reporting for a host of additional stations.

I doubt that the same holds for the willingness of chasers to work you on a summit: While some people can work weak CW around 0 dB SNR, the majority of my SOTA QSOs takes place in an SNR “comfort zone” of likely 10 dB or more - only a handful reports are less than 559, and I typically neither give or get 11x and very few 22x reports while on a summit. It is simply too noisy and distracting there.

Just my 2 cents.

73 de Martin, DK3IT

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