Many thanks to Scott (KK4Z) who shares the following post from his blog KK4Z.com:
QRO SCHMURO
There is always a lot of talk about QRP vs QRO, 5 watts vs 10, ad nauseam. So today I thought I would run the numbers and see what the real deal is. First we need a few definitions. An S-unit in general terms is the minimum change in signal strength to be just noticeable (k3wwp.com). In more technical terms it equates to approximately 6 db in change. The decibel (dB) is a logarithmic number. Each 10 dB represents a factor of 10 difference. This may be a little out there for some so we will cut right to the shortcut. There are two types of logarithms. For calculating dB, use the common logarithm which is base 10. To see if your calculator uses the right one. Punch in 100 and then log. The answer should be 2 which equates to 10 to the second power which equals 100. This is not a technical paper but an entry way to see how changing the power levels affect the signal level of your transmitting signal. As you guessed, it is not linear.
Let me introduce an equation:
Where Power P1 is the power you wish to evaluate and reference power P2 is your starting power. Let’s take going from 5 watts to 10 watts. The equation would look like this:
We take 10 and divide it by 5 which give us 2. Then we hit the log function on our calculator which gives us 0.301. Multiply that by 10 and you have about 3 dB in gain or about one half of an S-unit (remember 1 S-unit is equal to 6 dB). Let’s do one more by hand and tackle the QRP/QRO debate. How many S-units will increasing power from 5 watts to 100 watts give you? The equation looks like this:
Take the 100 and divide by 5 to give you 20 and then hit the log function to give you 1.301. Multiply by 10 for 13.01 dB. Divide 13.01 by 6 dB and you have 2.17 S-units. Going back to our definition that one S-unit is the minimum change in signal strength to be just noticeable shows that going from 5 watts to 100 watts is not that great of a change.
Let’s let the other shoe drop. What about going from 5 watts to 1500 watt? That will give you 4.13 S-units of gain vs 1.96 S-units going from 100 watts to 1500 watts?
This gives you a fairly easy equation to help you evaluate your needs based upon empirical data. Running 20 watts over 5 gives you 1 S-Unit. Using less power means less drain on the battery for longer operation. This is only part of the equation. Propagation, antenna, mode used, and station efficiency all play a part. Have fun and maybe don’t toss the QRP radio yet. 🙂
The mathematical evidence behind what we QRP ops already know!
Takes me back to school and college days – last time I used a log table mathematically! Only log tables since have been for sitting my QRP rigs on when operating. 😉 dit dit
Richard M0RGM
Interesting and takes me back to the day when that was ‘easy’ and the math was right there…….
Thanks again for sharing and yes, letting us confirm what we already may know.
73
wb8yxf.com
I like S-meter readings. But some use dBm for levels, give receiver sensitivity in dBm. Have never used it. I prefer uV specs, hi.
I do use dB in many calculations such as a transmitter spurious emission spec, is important for repeater work, defines the transmitter wide band noise. Good transmitters are 80db down. Duplexers are another where dB is important, how much isolation one gets. Few Ham rigs are this good and why Ham gear makes lousy repeaters.
At Field Day used band pass filters to separate the transmitters on different bands. All transmitters have wide band noise where a 20m xmt can generate noise on 40m (FCC spec for HF is -40db, VHF -60db). The filters I have give over 50 db of attenuation on adjacent bands. Would be important if looking for such filters.
Most S-meters today do not seem to be calibrated, 1 S-unit is probably not really 6db, but can be relative. I do use my S-meter for RST reports, a S-5 will get you 559, any thing over S9 is 599. I wish others would do the same. I hate it when I get “”UR 599 pls rpt all””.
73, ron, n9ee
On 5 vs 10W, I have made calls to a station with 5W, got no response, turned up to 10W and did get a response. I have done this many times.
I do think the difference between 5 & 10W does improve things for QRP.
73, ron, n9ee
The minimum change in signal strength which is just noticeable is not one S-unit, it is one decibel
(or your receiver or ear is nearly deaf ! )
73 Rolf DL3AO
It’s close, but not exact. Bell labs coined the decibel based on the power ratio, but chose that particular ratio because it was pretty close to the previously used unit of measurement (Miles of standard cable) that *was* based on the minimum detectable difference.
You are right though, an S unit is much more than the minimum detectable difference. An S unit is more useful as a course measure from weak to strong signal. We don’t really care about a minimum detectable difference between signals, but the difference between no copy, weak, and easy copy, for example.
I always cringe when I read articles like this to justify QRP. As Rolf says, we don’t hear in S-units.
If the premise of this article were true, hams wouldn’t go to such (expensive) lengths to improve their antenna systems, often by as little as 2 or 3 dB.
One thing that hams could do a lot more of is playing with that tx power knob in a QSO. If you are communicating easily at 50w, what does 5w sound like? What about 1w? That is the best way to learn. Also do this with a websdr so you can hear it yourself.