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network [24], which led to the so-called " Y-factor " method
developed later [25]. In the same year, the IRE derived the
relationship between the noise factor and its four noise parameters [26]. Since then, different algorithms were developed to
obtain noise factors and/or noise parameters [27]-[66], and
in general, they can be divided into two categories. The first
category involves forward and reverse noise measurements
based on the concept of noise waves [27]-[45]. The wave-based
approach was first introduced by the pioneering work of Penfield in 1962 [27]. Such wave-based representation allows the
use of the scattering parameters, which are widely used in
the microwave frequency range. Wave-based noise parameters represent the intrinsic noise behavior of a noisy two-port
network. They do not necessarily depend on the reflection coefficient seen by the input of the two-port. However, since the
requirement of reverse noise measurements increases the system calibration complexity, they have not been widely applied
in practice in commercial noise measurement systems.
In the second category, only forward measurements are
conducted to obtain a noisy two-port network's noise powers
or noise factors at different source admittances (or impedances). In this category, two approaches were developed. In the
first approach, four (or more) noise factors at different source
admittances are obtained first, using the Y-factor method.
This approach requires the noise powers measured in both
hot and cold states at each source admittance. The four noise
parameters are then obtained by solving the linearized noise
equations with algorithms to take care of the experimental
errors and the uncertainties in noise factors and source admittances [46]-[62]. On the other hand, the second approach
solves the noise parameters using the power equation. The
noise power is expressed as a function of source admittance
with noise parameters as the coefficients. The noise factors are
then calculated based on the noise parameters obtained from
the power equation [63], [64]. This approach is the foundation

of the so-called " cold-only " method in which the noise power
in the hot state is only measured during the system calibration but not in the measurement of a device-under-test (DUT)
[63]-[66]. The noise factors (and noise parameters) [21]-[26],
the measurement techniques [46]-[66], and the noise correlation matrices [67] form the foundation for the noise system
calibration and noise parameter de-embedding described later
in this paper.
This paper presents the thermal noise measurement and
characterization of nanoscale MOSFET as an example. The algorithms presented are general, and people can apply them
to the noise measurement and characterization of other devices such as bipolar junction transistors (BJT). This paper will
present the noise measurement system, device characterization techniques, and noise source implementation for circuit
designs.

Noise Measurement System
System Setup
To avoid the impact of low-frequency noise in transistors on
the thermal noise measurement, people usually characterize the transistors in the gigahertz (GHz) range through its
noise parameters - the minimum noise factor NFmin (or minimum noise figure in dB), the equivalent noise resistance Rn in
ohm, and the optimized source admittance Yopt = Gopt + j ยท Bopt
in siemens (or mho). To obtain these noise parameters, I use a
high-frequency noise measurement system, as shown in Fig. 2.
It consists of a noise source, a vector network analyzer (VNA),
a noise figure analyzer (NFA), a microwave tuner at the source
(input) side, a low-noise amplifier (LNA) at the receiver side,
and other peripheral components (e.g., a personal computer,
microwave cables, and tuner controllers). The source tuner
varies and provides different source impedances for a device-under-test (DUT), and the LNA boosts the noise signal

Fig. 2. The high-frequency (HF) noise measurement system for thermal noise characterization consists of: (a) a probe station, a noise source, a source tuner, a low
noise amplifier (LNA), input and output HF switches, a programmable dc power supply; (b) a tuner controller, a switch driver, a vector network analyzer (VNA), and a
noise figure analyzer (NFA).
April 2021	

IEEE Instrumentation & Measurement Magazine	61



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