Instrumentation & Measurement Magazine 24-7 - 50

Biases and Uncertainties of RF
Noise Power Measurements
Brett T. Walkenhorst, Ryan T. Cutshall, and Daniel R. Frey
I
n this paper, we explore various methods of measuring
noise power in RF systems. We discuss some of the systems
commonly used to make such measurements, then
analyze each system's architecture to obtain the measurement
bias and uncertainty for six different combinations of noise
models (real and complex noise) and methods of averaging
(linear power, magnitude, and logarithmic). Equipped with
this knowledge, users can correct for post-measurement biases
and determine the number of averages required to yield a desired
uncertainty level.
Introduction
The impact of noise on RF systems is a universal issue.
Whether in communications, radar, telemetry, or remote sensing,
noise has the potential to disrupt our measurements and
cause uncertainty in the resultant data. In order to understand
the impact of noise, it is often desirable to measure the
noise power in the environment or in an RF system. It is common
to characterize RF components and systems by their noise
figure (when an antenna is not involved) or gain over temperature
(G/T) (when an antenna is involved) using methods
such as the cold source method (also known as the direct noise
method) and the Y-factor method [1]-[4]. These methods require
one or more measurements of noise power at the output
of a device under test.
Noise power measurements in RF systems are sometimes
conducted without a thorough understanding of the bias and
uncertainty associated with such measurements. Many books
and journal articles have analyzed the uncertainties associated
with noise figure, noise temperature, and noise power measurements
[3], [5]-[7]. All of these measures rely on some form
of non-coherent averaging to estimate noise power. Some of
the methodologies perform this averaging at multiple stages.
In modern instrumentation, such as modern spectrum analyzers,
there are different options on how the instrument
performs this averaging. Each method has a different impact on
the bias and uncertainty of the reported noise power, depending
on the instrument's architecture. The goal of this paper is to
analyze and summarize these biases and uncertainties, which
50
Noise Theory
For many electrical devices, noise at RF frequencies (e.g., 3
kHz to 300 GHz) is typically dominated by thermal noise,
sometimes called Johnson-Nyquist noise [1], [8]. The voltage
representation of this noise can be modeled as a zero-mean stationary
Gaussian process, often denoted as [9]:
Xt
The variance, 2
rX
 
  2


2
X t kTB

0, .
(1)
X , is equal to the noise power, given by [10]
P 2 nX E,r
will then enable the user to conduct such tests with greater
confidence. When properly understood, the biases can be
removed, and the uncertainty bounds can give the user an understanding
of the accuracy of their noise power measurement.
This paper begins with a brief discussion of noise theory.
We then look at different methods of directly measuring
RF noise power and the instruments associated with these
methods. We derive equations used to compute the biases
and uncertainties associated with each of these measurement
methods, and we present Monte Carlo simulation results that
support the results of the derivations.
(2)
where k is Boltzmann's constant, T is the effective noise temperature
of the system, B is the equivalent noise bandwidth,
and E[·] indicates the expected value operator.
In some systems and frequencies, flicker noise dominates,
but this noise may also be modeled as Gaussian [11]. Thus, the
Gaussian model will be applied to all RF noise, and the variance
of that Gaussian process is what we seek to measure in an
RF noise power measurement.
If this noise process is sent through a Hilbert transform
and recombined to yield the complex envelope of an ideal inphase/quadrature
(I/Q) mixdown, whether implemented in
analog or digital circuitry, the result will be [12]:
Xt Xt jXt e
2
c rr

IEEE Instrumentation & Measurement Magazine
1094-6969/21/$25.00©2021IEEE
 

1
 
ˆ
 
jtc
,
(3)
October 2021
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