Handbook, chapter 6. Decibels, power and sensitivity
The first thing you want to do when a contact will not come off is add power. The second thing, which is worth doing instead, is to work out what that power will actually buy.
A hundred watts against five is not «twenty times better». It is thirteen decibels, and to the other station's ear a little over two S-points. The difference between «barely readable» and «solid copy», but not between «no contact» and «a contact».
See what each extra watt costs
The upper scale is what the other station sees if with your five watts they heard you at S5. The lower one is what each further step costs.
The first steps are cheap: five watts to ten is three decibels, that is half a point, and it is simply a different transceiver. The last ones cost obscenely: to add another three after four hundred watts you need a kilowatt amplifier, a separate mains feed and patient neighbours — and the needle moves the same half a point.
The scale is logarithmic not because that is convenient to compute, but because hearing is like that and so is propagation. Doubling the power is always exactly three decibels: from one watt to two and from five hundred to a thousand alike. The other station's ear responds the same way to both doublings; your wallet does not.
The S scale: one point is six decibels
The meter in a transceiver is graduated in points from S1 to S9, and above that in decibels over nine: «S9 + 20». By the IARU recommendation (Region 1, 1981) one point equals six decibels, and S9 on the short waves is 50 microvolts into fifty ohms, that is −73 dBm.
On VHF, from 144 MHz upwards, that same nine is by agreement 20 dB lower — −93 dBm. The reason is simple: there the band noise is lower and the signals weaker, so otherwise the whole scale would bunch into the first two points. There is one consequence for the operator, but an important one: points on HF and on VHF cannot be compared; they are different scales with the same numbers.
Hence the conversion worth being able to do in your head: double the power, add half a point. The whole difference between QRP and a full transceiver is a little over two points.
Six decibels to a point is a recommendation, not what is inside your set. Real S meters are graduated however the manufacturer pleased: the same signal reads differently on different transceivers, and the lower part of the scale is usually compressed more than the upper. So «five nine» on the air is a courtesy, not a measurement.
What is worth trusting is the difference between readings on the same set, not the number itself.
Three numbers worth knowing by heart
+1 dB = ×1.25 — the smallest difference still audible
+3 dB = twice
+6 dB = four times, and that is exactly one S-point
+10 dB = ten times
Everything else adds up from there, and that is the whole point of decibels: multiplication turns into addition. The antenna gave +6, the cable took −2, the amplifier added +10 — together +14 dB, and you can do it on paper rather than with a calculator.
The thirteen decibels from the opening are exactly 10 + 3: ten times and then twice, which is precisely those hundred watts from five.
The decibel formula depends on what you are comparing. For powers it is 10·lg of the ratio, for voltages and currents 20·lg. The reason is that power is proportional to the square of voltage, and a square under a logarithm is what puts the two in front of it.
In practice: doubling the power is 3 dB and doubling the voltage is 6 dB. It is the same doubling of the signal, simply measured two ways, and confusing them gives an error of exactly a factor of two.
Why the receiver matters more than the amplifier
Here is the conclusion of the chapter, and it contradicts your first instinct.
Three decibels on transmit is twice the power. They are audible only there, at the other station, and they cost money.
Three decibels on receive is half the noise. They are audible here, at your end, and they come free: switch off the switching power supply that hums across the whole band, move the antenna away from the wiring, fit a decent feeder.
And above all: a contact takes two. You can shout with a kilowatt, but if you cannot hear the reply there is no contact. So in a shack where the choice lies between an amplifier and a better antenna, the antenna wins twice over: it adds the same decibels on transmit and on receive.
dB, dBm and dBi are three different things
Confusing them costs mistakes in calculations, so they are worth separating straight away:
| Notation | What it is |
|---|---|
| dB | a ratio. Simply «how many times», written as a logarithm. On its own it means nothing |
| dBm | absolute power relative to one milliwatt. 30 dBm = 1 W, 50 dBm = 100 W |
| dBi | antenna gain relative to an isotropic radiator — an imaginary point that shines equally in all directions |
| dBd | the same, but relative to a half-wave dipole. 1 dBd = 2.15 dBi |
You may add dBm and dB — the result is dBm. You may not add dBm to dBm: that is like adding two temperatures.
A dipole by itself has a gain of 2.15 dB over an isotropic point — simply because it does not shine towards its own ends. So the same piece of metal can be called «7 dBd» or «9.15 dBi», and the second sounds more impressive.
The rule is simple: if the specification says a bare «dB» with no letter, it is almost always dBi, because that makes the number bigger. Two antennas can only be compared in the same units.
An antenna amplifies nothing — there is no source of energy in it. It redistributes: what was added in the wanted direction was taken from the others. So a Yagi with 10 dBi of gain does not «add power», it simply does not spend it on the sky and on the neighbour behind.
The mW ↔ dBm calculator converts power both ways and has a table of familiar levels.
Next — chapter 7, modulation: how a voice turns into a radio wave.