Instrumentation & Measurement Magazine 24-2 - 82

Fig. 4. Example of modified Ys regions based on [12].

Because the locations of admittances Ys were not restricted, the
optimum locations of Ys appeared as four regions-A, B, C, and
D-on the Smith chart shown in Fig. 3. Conceptually, Ys in region A corresponds to a well-matched region that is helpful for
identifying the LNA gain and overall noise level; Ys from region
B isolates the input-referred noise voltage, vn, component; Ys
from region C isolates the input-referred noise current, in, component; and finally, Ys from region D produces a measurement
of correlation between vn and in. Furthermore, these regions can
be modified by selecting different sets of scaling factors in order
to increase frequency coverage of the method [12]. One of many
possible modifications to the regions is shown in Fig. 4.
In demonstrating that optimum admittances Ys for noiseparameter measurements do not have to form a constellation
of single points on the Smith chart, and that the optimum regions can be numerically modified to suit certain frequency
limitations of the matching network, the findings of [12] open
up the possibility of developing a broad-band approach to
measuring noise parameters.
In the past, the matching networks were implemented with
mechanical impedance tuners that relied on long transmission lines to provide the needed separation of Ys. As such, this
approach was very frequency dependent. However, new impedance generators have been designed that are capable of
maintaining Ys within optimum regions from [12] over large
frequency ranges, thereby allowing for concurrent noise-parameter measurements over very wide bands with only four
impedance generator states.

some radio astronomy systems require the use of lower noise
vLNAs, which are implemented via cryogenic cooling.
Verifying the performance of cryogenically cooled LNAs
(aka cryo-LNAs) is considerably more challenging than it is
for room-temperature vLNAs, as it is not possible to place the
measurement equipment near the LNA inside the cryogenic
dewars (or cryostats). Furthermore, the performance verification is relatively time consuming, as multiple lengthy cooling
and heating cycles are required to accomplish various calibration steps. For these reasons, and due to cryogenically cooled
receivers being a niche market, the literature contains few
studies documenting methods of measuring cryogenic noise
parameters [15]-[18]. However, the growing interest in quantum computing has helped to mitigate these challenges and
has led to increased interest in cryogenically cooled receivers.
As discussed above, at room temperature, Ys are commonly
generated with mechanical impedance tuners; however,
such tuners are too large to be used inside of measurement
cryostats. Furthermore, situating these tuners outside of the
cryostat restricts measurement accuracy due to the unknown
noise contribution of a cryogenic-to-room-temperature interconnect, whose insertion loss also restricts the attainable Y s.
As a result, the two main techniques for measuring noise parameters at cryogenic temperatures either entail the cooling of
large devices [17] or neglecting the error due to the unknown
noise of the interconnect [16]. An alternative approach for estimating noise parameters was proposed in [18]. This study
proposed the use of a 50Ω termination with noise parameters being estimated based on transistor small-signal models.
In [15], a custom-made tuner was designed and placed in the
same package as the transistor whose noise parameters were
measured.
The new approach proposed in [12], which enabled the required number of signal-source impedances to be reduced
to four, is particularly attractive for cryogenic noise parameter measurements because it avoids the need for large
mechanical tuners, replacing them with a small solid-state,
highly repeatable, impedance generator. A photo of the cryogenic measurement system is shown in Fig. 5. The wideband

Cryogenic Noise-Parameter
Measurements
The above-described methods are capable of providing measurements of vLNAs that are sufficiently accurate and reliable
to enable their installation on scientific instruments. However,
82	

Fig. 5. Photo of cryogenic noise-parameter measurement system.

IEEE Instrumentation & Measurement Magazine	

April 2021



Instrumentation & Measurement Magazine 24-2

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