March 1969 Electronics World
Table of Contents
Wax nostalgic about and learn from the history of early electronics. See articles
from
Electronics World, published May 1959
 December 1971. All copyrights hereby acknowledged.

I was first introduced to the
concept of receiver noise figure at the start of my engineering career in 1989 at General
Electric Aerospace Electronics Systems Division (AESD) in Utica, New York. During my
four years in the U.S. Air Force (1978 to 1983) working on airport surveillance and precision
approach radars, I do not recall having ever heard the term noise figure or noise temperature.
We did signal to noise and signal sensitivity measurements as part of the normal maintenance,
but the terms never arose. Ditto for my courses at the University of Vermont. We never
did cascade parameter calculations for noise figure, intercept points, compression points,
etc. That is primarily the realm of practicing design engineers, evidently. Maybe I was
asleep in class at tech school (Keesler AFB, Mississippi) and UVM the day(s) it came
up.
I would be remiss without taking the occasion of this article to promote my
Wireless System Designer software that provides an incredible level of RF system
design calculations for a mere $45. That price doesn't even amount to a single hour of
your company's billing time for your work.
LowNoise Receiver Performance Measurements
By Lee R. Bishop / U. S. Air Force
Noisefigure measurements are easy to make; it's an efficient, simple, and accurate
method of determining receiver performance.
During the past decade, lownoise receivers have become practical devices and are
widely used in commercial and military communications systems.
Fig. 1  Thermally agitated electrons cause noise in receiver input
circuits. Johnson noise reduces signal intelligibility.
However, the literature which describes their performance continues to confuse many
engineers and technicians. In this article, two of the most meaningful receiver sensitivity
terms"noise figure" and "effective noise temperature" (ENT)  have been related and
the problems involved in gauging the actual sensitivity of a receiver rated with a "negative"
noise figure shown. The hot/cold body standard technique, a testing procedure specifically
designed to measure the noise figure or ENT of lownoise receivers, is also discussed.
Both noise figure and ENT are currently used by engineers to indicate the performance
of lownoise radiofrequency amplifiers. Most engineers prefer to use ENT for the extremely
low noise devices and noise figure for conventional receivers (for example, those with
noise figures greater than 6 decibels).
Noise Figure
The noise figure of a receiver represents a comparison between an actual receiver
and its theoretically perfect counterpart. The term "noise figure" was first used in
1940 by radar engineers making receiver sensitivity measurements. They found that a receiver's
bandwidth had a disturbing effect on sensitivity readings: the narrower the bandwidth,
the better the reading. But when sensitivity was measured using gas or thermal noise
generators, the bandwidth did not affect the readings; low receiver gain showed up as
an abnormal noise figure.
The noise figure of a network is defined by the IEEE as the ratio of the total noise
power available at the output port when the input termination is at 290° Kelvin to
that portion of the total available noise power produced by the input termination and
delivered to the output by the primary signal channel. It will become apparent from the
discussion clarifying this definition that noise figures below zero decibels are automatically
excluded. Therefore, the "perfect" amplifier has a noise figure of 0 dB.
Fig. 1 illustrates the case of the perfect receiver with its input network at a temperature
of 290° K (63° F). The resistance (R), which represents the impedance of the
feed, generates a noise voltage called Johnson noise. This noise results from the random
motion of thermally agitated free electrons. Although this noise voltage has an infinitely
wide bandwidth, we are only interested in the signals which fall within the receiver's
bandwidth because only these noise voltage signals pass through the amplifier and register
on the power meter. It is only this noise with which the incoming signals have to compete.
When a perfect receiver is matched to an input network, the input noise power (in
watts) can be expressed as:
noise power input = kBT
(1)
where k is Boltzmann's constant (1.38 X 10^{23} joule/degree Kelvin), B is
noise bandwidth of the amplifier in Hz, and T is 290° K.
The noise bandwidth of the network is not the same as the halfpower bandwidth normally
given in performance specifications; rather, it is somewhat wider and normalized at the
network's center frequency. In some cases, it is quite close to the 3dB bandwidth, but
sometimes it is as much as 1.57 times the halfpower figure. However, as long the receiver
is tested with very wide thermal or gas noise sources, this difference is of no great
concern.
Fig. 2  This graph can be used to convert effective noise temperature
measurements to their true noise figure value.
A power meter hooked to the output of a perfect receiver as shown in Fig. 1 would
read a power N_{1} equal to kBTG, where G is the power gain of the receiver.
However, a receiver contributes noise of its own (ΔN) so that an actual receiver's
output (N_{2}) is kBTG + ΔN. Specifically, the term noise figure (F) is
a ratio that compares a receiver with its ideal counterpart and is equal to the noise
power output from an actual receiver with its input network at 290° K, divided by
the noise power output from an ideal receiver with its input network at 290° K. Or,
F = N_{2} / N_{1} = (kBTG + ΔN) / kBTG
(2)
Expressed in decibels, the noise figure is:
f =10 log_{10} F
(3)
If the device under test were perfect, ΔN would be zero and the receiver's noise
figure would reach the limit of unity or 0 dB.
Effective Noise Temperature
The effective noise temperature is more difficult to determine. When a receiver's
inputnetwork temperature is raised above 290° K, the random noise generated by the
network increases and the output noise power rises to a new value of N_{2}. The
ENT is the number of degrees that the input network's temperature had to be raised before
the receiver's output reached the new value of N_{2}.
When the expression for N_{2} in equation (2) is resolved into thermal components,
the equation has the following form:
F = [KBG (T + T_{e})] / KBTG
(4)
Component T is the noise from the receiver's input network (at 290° K) and T_{e}
is the internally generated amplifier noise or ENT:
If the receiver contributed no noise of its own, T_{e} would be zero and F
would again be unity or 0 dB. When the kBG terms of equation (4) are cancelled, we are
left with a simple expression for noise figure in terms of ENT:
F = (T + T_{e}) / T = 1 + T/T_{e}
(5)
Fig. 3  Measurement errors are greater at the lower noise figure
values. This graph is used when the input network behaves as though it were operating
at other than 290° Kelvin. In the example, a 5dB measurement is corrected to read
6 db.
ENT is an absolute quantity in degrees Kelvin defined by the relationship T_{e}
= (F  1)T. It is emphasized at this point that ENT is not the physical temperature of
the receiver's input network; it is an apparent temperature that is representative of
an amplifier's internally generated noise. Fig. 2 is a graph for converting ENT ratings
to noise figure and vice versa.
Measuring Errors
We have excluded negative values from our definition of noise figure and have, until
now, assumed that all networks behave as though they were at 290° K. Quite frequently,
however, a network acts as though it were at a lower temperature. The result is an abnormal
noise figure which, by conventional measuring techniques, is difficult to distinguish
from an acceptable noise figure measurement. If, for example, the input circuit behaved
as though it were at a temperature lower than 290° K and the amplifier itself contributed
little noise, the quantity of noise proportional to kBTG + ΔN, which conventional
techniques measure, is small. On the other hand, the quantity kBTG, which conventional
techniques calculate, will be considerably greater than its true value, If the amplifier's
true noise figure is low enough and the network's temperature deviation from the assumed
290° K is large enough, the calculated value almost equals the measured values.
The magnitude of the measurement error depends upon the true noise figure. Measurement
errors increase rapidly as lower noise figure values are reached. Fig. 3 is a graph of
the equation used to correct the values of noise figures. In the example shown on the
graph, the 5dB noise figure measurement was made while the input network behaved as
though it were operating at 100° K. The correction is +1 dB so that the true noise
figure, referenced to 290° K, is 6 dB.
Hot/Cold Body Standards
Hot/cold body standards enable the previously described measurement difficulties to
be overcome. While not suitable for the amateur or small shop owner, they enable the
manufacturer to test his products and assign them a proper noise figure or ENT.
Hot/cold body standards use two resistive elements, one immersed in liquid nitrogen
at 77.3° K and the other in a temperaturecontrolled oven at 373.1° K. The noise
power (in watts) from either resistor equals kBT, where T is the temperature of the particular
resistor in degrees Kelvin and k and B are the quantities described in equation (1) .
The testing procedure is illustrated in Fig. 4.
(6)
where To is 290° K, T_{1}, is 77.3° K, T_{2} is 373.1°
K, and Y is N_{2}/N_{1}. By measuring N_{1} when the receiver's
input network is at a known temperature (T_{1}) and measuring N_{2} when
it is terminated at T_{2}, the corrected noise figure can be calculated directly
by equation (6).
Other Errors
Fig. 4  Accurate noise figure measurements can be obtained by switching
a receiver between an input network immersed in liquid nitrogen and a network in a temperaturecontrolled
oven.
Although hot/cold body standards were specifically developed to clear up the problems
that arose when lownoise amplifiers were tested by conventional methods, they have,
unfortunately, also been used as a means to further improve noise figure specifications.
In examining the literature, one can find examples of noise figures specified as the
ratio of ENT to the nitrogen bath temperature. Such ratings are usually presented as
negative noise figures. AnĀother practice, even more misleading because it yields a positive
noise figure, is that of specifying noise figure as the ratio of the nitrogen bath temperature
plus ENT to the bath temperature.
A further difficulty, not necessarily associated with the hot/cold body standards,
is the tendency of some experimenters to specify noise figures based on reference temperatures
other than 290° K.
Noise figure and ENT are equivalent ways of describing lownoise receiver performance.
For absolute comparisons to be made between devices, however, both terms must be referenced
to the standard temperature of 290° K.
Posted January 8, 2018
