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.
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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.
Low-Noise Receiver Performance Measurements

Fig. 1 - Thermally agitated electrons cause noise in receiver
input circuits. Johnson noise reduces signal intelligibility.
By Lee R. Bishop / U. S. Air Force
Noise-figure measurements are easy to make; it's an efficient, simple, and accurate
method of determining receiver performance.
During the past decade, low-noise receivers have become practical devices and
are widely used in commercial and military communications systems.
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
low-noise receivers, is also discussed.
Both noise figure and ENT are currently used by engineers to indicate the performance
of low-noise radio-frequency 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 half-power 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 3-dB
bandwidth, but sometimes it is as much as 1.57 times the half-power 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 N1 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 (N2) 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 = N2 / N1 = (kBTG + ΔN) /
kBTG
(2)
Expressed in decibels, the noise figure is:
f =10 log10 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
input-network 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 N2.
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 N2.
When the expression for N2 in equation (2) is resolved into thermal
components, the equation has the following form:
F = [KBG (T + Te)] / KBTG
(4)
Component T is the noise from the receiver's input network (at 290° K) and
Te is the internally generated amplifier noise or ENT:
If the receiver contributed no noise of its own, Te 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 + Te) / T = 1 + T/Te
(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 5-dB measurement is corrected
to read 6 db.
ENT is an absolute quantity in degrees Kelvin defined by the relationship Te
= (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 5-dB 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 temperature-controlled 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, T1, is 77.3° K, T2 is 373.1°
K, and Y is N2/N1. By measuring N1 when the receiver's
input network is at a known temperature (T1) and measuring N2
when it is terminated at T2, 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 temperature-controlled oven.
Although hot/cold body standards were specifically developed to clear up the
problems that arose when low-noise 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. Another 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 low-noise receiver performance.
For absolute comparisons to be made between devices, however, both terms must be
referenced to the standard temperature of 290° K.
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