September 1976 QST
Table of Contents
Wax nostalgic about and learn from the history of early electronics. See articles
from
QST, published December 1915  present (visit ARRL
for info). All copyrights hereby acknowledged.

Whether you are new to the subject
of noise figure or are just looking for a quick review, this "Hot and Cold
Resistors as UHF Noise Sources" article in a 1976 issue of QST magazine
is a good source. Author Benjamin Lowe, K4VOW, does a nice job of explaining the
concept of electrical noise, and then presenting equations governing the
calculation of noise factor and noise figure. Actual numerical examples are
provided to demonstrate how the formulas work. Using this method, you can
make a fair measurement of the noise figure of a receiver without the need for
expensive test equipment.
Hot and Cold Resistors as UHF Noise Sources
Using the Gaussian Distribution of White Noise Generated by CarbonFilm Devices
That Are Subjected to a Thermal Gradient in a PseudoLaboratory Environment for
Ascertaining the Ability of Quiescent Amplifiers to Resolve LowEnergy Quantum.
How's that again?
By Benjamin L. Lowe,* K4VOW/WA5UVM
Here is a method for obtaining an accurate measurement of the noise performance
of your preamplifier. The equipment needed is inexpensive (if you don't have an
oven and a freezer, you can get them and split the cost with the household budget).
If your wife will not let you into the kitchen, she can make the measurements, even
without a cookbook.
When a requirement exists to determine the noise figure of an amplifier, it is
difficult to obtain an absolute measurement for very lownoise devices. Simple diode
noise generators allow the amateur, as well as other designers, to adjust equipment
for minimum noise, but the question eventually arises, "How good is the noise figure?"
This is a valid question in determining the system capability.
Popular automatic noisefiguremeasurement systems, which are practically standards
in today's electronic industry, can yield errors in the order of 0.5 to 1 dB in
some cases, such as 432MHz preamplifier measurements. It is not meant here to fault
such equipment, because very good measurements were obtainable on vacuumtube amplifiers
that had noise figures of 5 to 10 dB. However, a 1dB error in the measurement of
an expected 1.5 dB noisefigure device can certainly produce disappointing results.
This can readily be seen by observing the decrease in the signaltonoise ratio
for a 2.5 dB noise figure preamplifier in a system when a 1.5dB noise figure is
expected. The resulting signaltonoise ratio decreases about 2 dB at 432 MHz,
which is disastrous when only a 3dB ratio might be expected in the first place!
It may be beneficial to make a few comments in laymen's terms on what the noise
figure is and why it is important. For any receiver system to produce signals through
its audio amplifier, a signal must be applied to the detector that is strong enough,
or has enough energy, to operate the detector and, hence, be converted from an rf
or if signal into an audio signal. In order to produce this necessary signal at
the detector, the incoming energy at the antenna terminals must be amplified many
times. This is accomplished by the use of preamplifiers, mixers, if amplifiers,
and sometimes a second or third if stage. Different frequencies are used in obtaining
the required gain in order that the gain at anyone frequency is not so great that
the receiver oscillates.
Unfortunately, the devices that provide this amplification also generate noise.
At vhf and uhf this noise is usually greater than the atmospheric noise presented
to the receiver by the antenna. Hence, the noise generated by the amplifying stages
is the limiting factor that must be overcome by the signal. Minimizing this noise
reduces the required incoming signal for a given signaltonoise ratio. The noise
figure is simply a measurement of the noise generated, or added, by the amplifiers.
The following expression is generally used in calculating noise figure.
NF = 10 log F_{T} = 10 log (F_{1} + F_{2}^{1}/G_{1}
+ F_{3}^{1}/G_{1}G_{2}+ etc.)
where
NF = noise figure, total
F_{T} = total noise factor
F_{1} = noise factor of the first amplifier stage
F_{2} = noise factor of the second amplifier stage
G_{1} = gain of the first amplifier stage
G_{2} = gain of the second amplifier stage
It can be seen that most of the total amplifier noise is generated a the first
stage if the gain of the first stage is high enough. This is why a lownoisefigure
preamplifier is so important.
How Can Noise Figure Be Accurately Measured at Home?
In this section the the technique for measuring noise figure is described. For
those who are interested, the theory of this approach is discussed in the following
section.
As is mentioned earlier, any device that amplifies also generates noise. Along
with this principle, any device which is at a temperature above absolute 0,
T = 273 °C, also generates noise. While it is difficult to measure noise power
at low levels, the temperature can be measured. Therefore, a relationship is determined
(given in the next section) between the noise figure and the temperature, or equivalent
temperature, of a device. This principle is now applied to apparatus for noisefigure
measurements that are available to most hams. The scheme utilized here is to adjust
the temperature of two resistors to known values, apply the noise power generated
from each resistor to the preamplifier stage under test, and determine the noise
figure from the resulting increase in noise at the receiver's audio output. Note
that the noise power generated by the resistors depends on the temperature of the
resistors, not the resistance value. Resistor values close to 50 Ω are used,
since this will eventually be the source impedance applied to the preamp by the
antenna. The apparatus required to do this are: (1) an oven, such as found in a
kitchen, (2) a freezer, (3) a thermometer, (4) a receiver for the frequency under
consideration and (5) a VTVM or VOM. Additionally, two 49.9 Ω resistors and
two 152.5cm (5foot) feed lines are needed that will withstand the operating temperatures
to be used. (The XYL is going to be overjoyed to see this ham project headed for
the kitchen!)
A procedure which can be followed is to connect the two resistors to the two
feed lines with as short a lead as possible to minimize the SWR. The freezer is
set to 17.8 °C (0 °F) and allowed to stabilize at that temperature. Of course,
the thermometer is used to measure this temperature. The test setup is shown in
Fig. 1. Using one of the specified resistors, the resistor and 30.5 cm (1 foot)
of feed line are placed inside the freezer. This allows 122 cm (4 feet) of feed
line to be outside the freezer to connect to the preamp. Also, a resistor with 30.5 cm of feed line is placed in the oven, leaving 122 cm outside the oven for connection
to the preamp. The room temperature, which is the temperature of the feed lilies
external to the freezer and the oven, is assumed to be +21 °C (70 °F), T_{1}.
It is necessary to operate the receiver in its linear range, i.e. the rf and
af gain controls in the linear region and the AVC "off." Also, it is best to connect
the VOM or VTVM to a highimpedance point, such as the headphone output, in order
to obtain a readable voltage level with the receiver gain set in the linear region.
Now place the thermometer in the oven with the hot resistor and begin increasing
the oven temperature. The preamplifier is switched back and forth between the hot
and cold resistors (noise sources), and the noise voltage is observed on the VOM
until the noise from the hot resistor is 1 dB greater than the noise from the cold
resistor. Most VOMs have a dB scale which can be used, or the "hot" voltage level
should be 1.12 times the "cold" voltage level (20 log 1.12 = 1 dB). When the 1dB
increase in noise power at the receiver output is achieved with the oven temperature
stable, quickly remove the thermometer and record the temperature, T_{2}.
Be sure to use heat pads (pot holders) because the thermometer is going to be hot.
From the graph shown in Fig. 2, use the oventemperature reading to determine the
amplifier noise figure.
Fig. 1  Noisefiguremeasurement test setup.
Fig. 2  Noise figure vs. "hot" resistor temperature.
Fig. 3  Attenuator values.
Several points should be noted about this test procedure. One is that precision
carbonfilm resistors, type RN55C with a value of 49.9 ohms, are used for two reasons:
(1) the value changes only about 0.5 ohm at 150 °C, thereby maintaining a good match,
and (2) the maximum operating temperature rating of 175 °C (34°F) for the
resistors is above the expected oven temperature preventing destruction of the resistor.
Other resistors meeting the same criteria can be used. A similar point concerns
the type of coax used to connect the resistors to the preamp. Type RG188A/U semirigid
can be used up to 200 °C, and its attenuation characteristic, 23 dB/100 ft. (100
ft. = 30.48 meters), is used in deriving the chart in Fig. 2. For resolving any
questions about the linearity of the receiver or the accuracy of the VOM, attenuators
can be placed between the converter and receiver in the test setup shown in Fig. 1. In this case a given VOM reading could be established with the preamp connected
to the "cold" resistor and a 3 dB attenuator between the converter and the receiver.
When "hot" resistor measurements are made the attenuator is changed to 4 dB, and
the "hot" resistor is heated until the original meter reading is obtained. 3 dB
and 4 dB attenuators for 50 Ω are shown in Fig. 3 and can be constructed with 1/4watt
carboncomposition resistors.
Even this method isn't completely foolproof, because a receiver input SWR of
2:1 could change the difference in attenuation between the 3 and 4dB attenuators
to 0.9 dB. The attenuation factor is only completely accurate for matched systems.
Theory and Calculations
Since not all amateurs will want to produce identical test setups as just described,
the method of deriving the graph in Fig. 2 may be of interest. The output noise
power from a system with gain and with a source impedance at some temperature is
given as
N_{1} = GK (T_{1} + T_{e}) B_{n}
where N_{1} = output noise power for temperature T_{1}
G = system gain
K = Boltzmann's constant (1.38 X 10^{23} joules/degree Kelvin)
T_{1} = temperature of the source impedance
T_{e} = equivalent input temperature of the amplifying device
B_{n} = the noise bandwidth
Note that the noise power from the input impedance, assumed to be resistive,
is
N_{1} = K T_{1} B_{n} and the equivalent input noise
power for the amplifier is
N =K T_{e} B_{n}
By increasing the temperature of the input resistor to T_{2} the output
noise power becomes
N_{2} = GK (T_{2} + T_{e}) B_{n}
Now, suppose we wanted to measure a difference between the output powers of 1
dB. Hence,
10 log N_{2}/N_{1} = 1 dB
and
N_{2}/N_{1} = 126 = [GK (T_{2} + T_{e}) B_{n}]/[GK (T_{1} + T_{e}) B_{n}]
yielding
T_{e} = (T_{2}  1.26 T_{1})/0.26
Also, a power ratio of 1.26:1 is a voltage ratio of 1.12:1. T_{2}
and T_{1} would be the temperatures of the hot and cold resistors if we
could connect our amplifier directly to the resistors. But, since we must use a
length of feed line that has some loss, the equivalent temperature including that
feed line must be determined. The type of line chosen, so as not to melt, is RG188A/U
semirigid coax. This cable has a loss factor of 23 dB/100 ft. (0.755 dB/m) at 432 MHz. Now, it is assumed that 152.5 cm (5 ft.) will be used to connect the resistor
to the input of the preamp. Furthermore, it is assumed that 30.5 cm (1 ft.) will
be inside the freezer or the oven at the same temperature as the resistor, and the
remainder, 122 cm (4 ft.) will be outside the oven at room temperature, 21.1 °C (70 °F or 294.1 °K). Now we can determine the equivalent noise temperature
of the resistor as viewed looking through the coax. This temperature, now defined
as T_{1}, is
T_{1} = T_{r1} + T_{e1} + T_{e2}/G_{1}
where
T_{r1} = the resistor temperature in °K
T_{e1} = the equivalent temperature of the 30.48 cm (1 ft) of line in
the temperature chamber
T_{e2} = the equivalent temperature of the 122 cm (4 ft) of line outside
the temperature chamber
G_{1} = the gain (in this case, the loss) of feed line in the temperature
chamber
Also T_{e1} = (L_{1}  1)T_{L1}
where
L_{1} = the feedline loss for 30.48 cm
T_{L1} = the actual temperature of the length L_{1} in °K
and
T_{e2} = (L_{2}  1)T_{L2}
where
L_{2} = the feedline loss for 122 cm
T_{L2} = the actual temperature of the length L_{2} in °K
A calculation is now made to determine one point for the curve in Fig 2. The
resistor temperature, T_{r1}, and the 30.48cm feedline loss is 0.23 dB
= 1.055 = L_{1}.
So,
T_{e1} = (L_{1}  1) T_{L1} = (1.055  1) 255.2 °K
T_{e1} = 13.88 °K
and
T_{e2} = (L_{2}  1) T_{L2} = (1.236  1) 294.1 °K
= 69.41 °K
for
T_{L2} = 21.1 °C=70 °F
So
T_{1} = 255.2 °K + 13.88 °K + 1.055 (69.41 °K) = 342.33 °K
Similarly, for the hot resistor at a temperature of 93.3 °C = 200 °F and
feed line connected to that resistor
T_{2} = 366.3 °K + (1.055  1)
366.3 °K + 1.055 (1.236 
1)
294.1 °K = ( 459.7 °K
 (1.26) (342.33 °K) )/0.26
Knowing T_{1} and T_{2}, the equivalent noise temperature for
a 1dB increase in output noise power is
T_{e} = 459.7 °K
T_{e} = 109.1 °K
From this temperature the noise figure is calculated from:
T_{e} = (F  1) T_{0}
where
F = noise factor
T_{0} = 290 °K, IEEE definition
For
T_{e} = 109.1 °K
F= T_{e}/T_{0} +1 = 109.1 °K/290 °K +1 = 1.38.
and
NF = 10 log F = 1.39 dB
where
NF = noise figure
If an error in the measurements of the temperature was made (for example, the
"cold" resistor was actually 2.77 °C (5 °F) lower than measured and the "hot"
resistor was 2.77 °C (5 °F) higher than measured), the resulting noisefigure
error would be in the order of 0.2 dB. It is felt that most amateurs can make temperature
measurements at least this accurate, and consequently, obtain a noisefigure reading
very close to the actual noise figure.
* Stanford Research Institute, 306 Wynn Dr., Huntsville, AL 35805
Posted October 8, 2020
