At HF it's all very simple.

To summarise -

The S-meter is essentially a 50-ohm power or wattmeter.

It is correctly calibrated with a 50-ohm signal generator with its
open-circuit volts set to 100 microvolts. The S-meter should then read S9.

Therefore, at the standard S9, the input to the receiver is 50 microvolts
across 50 ohms, corresponding to a power input of 50 picowatts.

The standard S-unit = 6 dB.

So for each change of one S-unit the input voltage halves (or doubles).

At S-zero the input voltage is 50/512 = 0.1 microvolts, which is roughly
equal to the the internal noise level of a good receiver with a bandwidth of
a few KHz.. Theoretically this is about the noise level you should get when
the antenna is disconnected.

At S9 + 40dB the input voltage is 50*100 microvolts = 5 millivolts.

Some S-meters may indicate as high as S9 + 60dB. The input voltage is then
50 millivolts which is about the overload point of a very good receiver.

So the whole scale is calibrated logarithmically, with S9 being about
half-way along it, and with 54 dB below S9 and 40 or 60dB above S9. The
input voltage range is from from 0.1 microvolts to 5 or 50 millivolts.

==============================

However, all meters have indicating errors. The problem arises because of
the difficulties and great expense in designing and manufacturing receivers
with an agc meter system which can accommodate a signal level range of 54 +
60 = 114 dB. Economics invariably rules the roost.

(It helps to have very high receiver gain and attenuators at or near the
receiver input.)

Fortunately modern receivers all tend to have errors of the same sort and
sign. So amateurs using different manufacturer's receivers will exhange very
similar signal strength reports.

These errors congregate at the very small signal end of the range. Meter
calibration begins to go wrong at around or below S4 or S5. Meter readings
of, say, S1 or S2 may actually be appropriate to power levels of S3 or S4.
A meter reading of S-zero may be appropriate to a power level of S2 or S3.

That is, at very small signal levels the S-meter underestimates signal power
level. But it's not of great consequence. At HF, to which the foregoing
applies, signals are usually below the noise and QRM levels anyway.
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Reg.