One of the things we do when we restore a receiver is perform a sensitivity
test. There is great rivalry among receiver nuts about which is the most
sensitive. Presumably that has something to do with pulling the weakest
signals out of the ether.
John Bertrand Johnson (who is known by the Eponym "Johnson Noise") described
thermal noise as follows:
"This is a fluctuating voltage generated by an electric
current flowing through a resistance in the
input circuit of an amplifier, not in the amplifier itself.
The motion of charge is a spontaneous and random flow of the
electric charge in the conductor in response to the heat
motion of its molecules. The voltage between the
ends of the conductor varies and is impressed upon the
input to the amplifier as a fluctuating noise." From "Electronic
Noise: The First Two Decades," IEEE Spectrum,
Volume 8, pp42-46, Feb. 1971. Johnson first reported quantitative
observations of this noise in the 1927-28 time frame (See his article
in Physics Review, V29 (1929), p367, and V32 (1928) p97
The point is that if your receiver front-end is not operating at
a temperature of absolute zero, the electrons bouncing around in the
wires, coils, resistors, and capacitors produce a noise voltage. Nyquist
in a companion paper (Physics Review, V29 (1929), p614) derived
a formula to calculate this noise voltage as follows:
You can calculate this and make a cute little table from it.
The point of this is that many of the measurements you see people talk about are
physically impossible. If we take the input impedance of a receiver to be 100 ohms
(see below for the "real" story), then there is already a .0376 microvolt potential
at the input. For a signal to be 10 dB greater than that, it would have to be .119
microvolts (10 dB is a factor of about 3.16).
Thus, any claim of receiver sensitivity that is lower than .12 microvolts
is bogus. It has to be. Any plausible sensitivity rating would have to be several
times larger than this theoretical lower bound. So, when someone tells you that their
receiver has a .5 microvolt input sensitivity, that is nothing to sneeze at (if it
was measured properly). If they tell you it has a .06 microvolt sensitivity, they
are giving you a value that violates fundamental laws of physics. Sorry.
R in Ohms
Dallas Lankford on Receiver Sensitivity Measurement
This note appeared in the R-390 email reflector on QTH. It is the most
cogent discussion of receiver sensitivity I have ever seen. I reproduce
it here (with permission) with minor typographical corrections:
"There has been a lot of confusion about how to measure the AM sensitivity of
an R-390A. Unfortunately the manuals have contributed to this confusion.
The 1970 Navships 0967-063-2010 manual has a sensitivity measuring procedure
on pages 4-2 and 4-3 which involves setting the signal generator (URM-25D)
to minimum output. This is equivalent to the method of turning the signal
generator on and off which is used at several web sites to find the 10 dB
S+N/N ratio. However, the Navships manual does not mention a 10 dB S+N/N
ratio, but rather a 10 dB rise, which it is. What the Navships and web
sites measure is the 10 dB S+N1/N2 where N1 is the
noise due to the signal and receiver, and N2 is the no-signal receiver noise.
Also, the 50 ohm
impedance of the signal generator is not matched to the 125 ohm nominal
(100 - 300 ohms) antenna input impedance (through a UG-636A/U and UG-971/U)
of the R-390A. Consequently, the signal generator reading is not the number
of microvolts that appears across the R-390A antenna input. The Army manual
TM 11-5820-358-35 gives a Sensitivity Test, not a procedure for measuring
the 10 dB S+N/N ratio. The earlier Army manual TM 11-856A in paragraph 166
has what it calls an AM Sensitivity measurement procedure. However, there
are at least two things wrong with it: (1) a DA-121/U attenuator (8.9 dB)
two way match (52.2 ohms to 128.8 ohms) is used between the URM-25D and
R-390A, and (2) the 0.8 volt noise indication in step (f.) is not maximized
with the antenna trimmer, nor is its value checked after the signal
generator is adjusted for 2.5 volts, as it must be.
Here is a correct method for measuring the AM sensitivity of an R-390A.
I measured the real component of the R-390A antenna input impedance by
connecting a 250 ohm 2 watt Clarostat composition pot in the signal path,
and used a UG-971/U (twinax to C) and UG-636AU (C to BNC). The 10X scope
probe was connected across the 636. The 25D was set to some convenient
value that could bee seen on the scope. The signal was peaked (as seen on
the scope) using the 390A antenna trimmer. The pot was adjusted so that the
scope read half the open circuit voltage (the voltage from the antenna input
side of the pot when disconnected from the antenna input). The value of the
pot was read using an accurate voltmeter, call this value R1. The R-390A
antenna input resistance is R = R1 + 50 at that frequency.
I may have gotten the high end numbers a little too high previously. My
scope method is probably not all that accurate because there is quite a bit
of uncertainty as to the half the open circuit voltage. A true RMS
voltmeter might be better. Now I am getting 180 - 220 ohms for the high
values. Previously I got up to 300 ohms. The low values still come in
around 90 - 100 ohms. Low values were found at 1.001, 1.999, and 3.999 MHz.
High values were found at 1.5, 4.5, and 5.5 MHz.
I used a TEK 2465B (cal traceable to NIST), and a rebuilt (by me) URM-25D
(cal by me using my 2465B and a precision 50 ohm terminator).
I used 2 feet of RG-58A/U to connect the 25D to the 390A, and a BNC T
connector adapter with a short stub coming out of one of the females of the
BNC T for clipping the 10X probe to. I measured the voltage across the 390A
antenna input (UG-971/U and UG-636A/U) to get a correction factor to
multiply the 25D reading by. Then I measured the S+N/N ratio as if the
impedances were matched (which they weren't).
My method for measuring sensitivity for a 10 dB S+N/N ratio involves turning
the modulation ON and OFF (NOT turning the signal generator ON and OFF or
tuning the R-390A away from and back to the signal generator). I could use
a volt meter on the diode load, but it is more convenient and about as
accurate to use the LINE LEVEL meter. I adjust the meter and signal
generator repeatedly if necessary, peaking the ANT TRIM at each resetting of
the signal generator output level, until the meter reads 0 VU with
modulation on, and the meter reads -10 with modulation off.
At 4.5 MHz, with the antenna input resistance measured as 187 ohms, using
the 4 kHz BW, and a correction factor of cf= 1.57 (cf = 2R/(R + 50), where R
is the measured antenna input resistance of the R-390A at the frequency
where the measurement is being taken), with AGC off, and 30% modulation, I
got a reading of 0.5 microvolts on the 25D for a 10 dB S+N/N ratio. Using
the correction factor, the voltage across the UG-636A/U was deduced to be
0.785 microvolts. So the input power was P = (0.785)^2 x E-12/187 = 3.3 x
E-15 watts, or -114.8 dBm. The sensitivity looks a lot better when you
convert it to dBm. If you had a 50 ohm receiver with a -114.8 dBm
sensitivity for a 10 dB S+N/N ratio, that would be 0.41 microvolts. Not
shabby. Note that this is also quite close to the uncorrected 0.5 microvolt
I also used a broadband matching transformer and got a slightly better
sensitivity, namely -115.2 dBm. This suggests that matching with a
broadband transformer does not change the results very much.
My R-390A was a bit weak at the top end of the 4 MHz band, coming in at -109
dBm at 3.9 MHz. Maybe I need to go in there an up the 2 pF coupling
capacitor in the double tuned circuit between the RF amp and MIXER? We'll
Coincidentally, late last night I received an e-mail copy of John Wilson's
May 2002 Short Wave Magazine article, "Simply The Best?" In the article
John has a detailed discussion of why it is incorrect to turn the signal
generator off and on, (or, equivalently, detune and retune the signal
generator or receiver) when measuring the 10 dB S+N/N ratio. This would be
a nice article to have on someone's web site if SWM would approve.
There is one
more thing I need to post for the group on R-390A sensitivity.
I recently discovered that at 900 kHz
the R-390A antenna input impedance is considerably below 100 ohms, namely
only about 28 ohms. That came as quite a surprise to me, and I wanted to
measure it again and look for other similar frequencies."
Dallas Lankford, 2002