Instrumentation & Measurement Magazine 24-2 - 79

Noise-Parameter Measurements
of Very-Low-Noise Amplifiers
at Ambient and Cryogenic
Temperatures
Alexander Sheldon and Leonid Belostotski

R

adio-telescope receivers are developed to sense
very weak astronomical signals. The sensitivity
of a radio telescope is inversely proportional to
its noise temperature, which is largely dependent on the
amount of noise generated in the receiver low-noise amplifier (LNA). In addition, a radio telescope sensitivity is
also proportional to its collecting area; however, it is very
costly to enhance sensitivity by increasing the collecting
area. Given the high costs associated with increasing the
collecting area, the development of methods of reducing
LNA noise becomes critical to optimizing the operation
of radio telescopes. Such LNA-noise reduction techniques
must first be verified via laboratory measurements and
then subsequently verified using field measurements on
the telescope.
This article reviews noise-parameter measurements of radio-frequency (RF) circuits, such as astronomy-grade LNAs,
operating from a few hundred MHz to many GHz. The prevalent noise sources in this frequency range include thermal
noise and shot noise, which both feature a white power spectrum. Although this article focuses on thermal noise, also
known as Johnson or Nyquist noise, the same discussions are
applicable for shot noise.
Since thermal noise is a random Gaussian process, it is
not possible to measure signal amplitudes. As a result, the
mean-square values of amplitudes or noise powers are measured instead. The available noise power, PAV, delivered to a
conjugately matched load by a passive network in thermal
equilibrium at a physical temperature, Tn, is
 hf


PAV hfB  e kbTn  1   kbTn B





where kb is Boltzmann's constant, h is Planck's constant, f
is the measurement frequency, and B is the measurement
bandwidth. The approximation is valid for low frequencies,
f << kbTn/h, with the errors in noise power being due to the approximation of ∼0.4% at 50 GHz at Tn=290 K.
April 2021	

When weak signals and the inevitable accompanying
noise propagate through a receiver, their signal-to-noise ratios (SNRs) are reduced due to noise originating in the receiver
circuitry. Therefore, the ability to accurately measure SNR
degradation and to mitigate its impact on sensitivity is critical for applications that strive for high sensitivity. To quantify
SNR degradation, noise factor is introduced as the ratio of the
SNR at the input, SNRin, to the SNR at the output, SNRout, as
F ≡ SNRin/SNRout. However, measuring the noise factor, F, of active circuits is challenging, as the equipment required to do so
also contains high-gain receivers that generate noise at powers
that are sometimes orders of magnitude higher than the measured quantity.
Noise-factor (or equivalently, noise figure, NF = 10log(F),
or noise temperature, T = T0(F-1), where T0=290 K) measurements are obtained by determining the noise power at the
LNA output, and then comparing it to a known standard, such
as a noise source [1]. The noise source is typically connected
at the LNA input. When the noise source is turned OFF (also
known as in a " cold " state) and is in a thermal equilibrium
with the LNA at temperature Tc, its output noise power is described as kbTcB. The LNA output noise power is composed of
the noise from the noise source and the LNA itself. The noise
source is then turned ON to its " hot " state, which is associated with noise represented by temperature Th, and the LNA
again outputs another level of noise power. These two noisepower measurements and their corresponding Tc and Th can
then be used to determine the LNA noise factor and gain. Often, the LNA cannot measure the output noise power; in such
cases, a receiver is used to obtain this measurement, although
the receiver will contribute its own noise to measurements. To
account for this added noise, the receiver noise factor is measured first following the same above-described procedure.
Several simplifying assumptions are made in this measurement process. For example, it is assumed that the amount of
noise power emanating from the noise source is not dependent
on its reflection coefficients in either the hot or cold state; that
the LNA and receiver noise are independent of their drivingport impedances; and that the bandwidth of the measurement

IEEE Instrumentation & Measurement Magazine	79
1094-6969/21/$25.00©2021IEEE



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