IEEE Solid-States Circuits Magazine - Spring 2021 - 27

vn,b
B
CBE
vbe
+
_
in,b
in,c
vn,b
2 = 2qIB∆f
2 = 2qIC∆f
2 = 4kTaRB∆f
E
in,b
in,c
vn,b
vn,c
vn,e
(a)
2 = 2qIB∆f
2 = 2qIC∆f
2 = 4kTaRB∆f
2 = 4kTaRC∆f
2 = 4kTaRE∆f
(b)
FIGURE 4: Equivalent noise models for a SiGe HBT. (a) A simplified small-signal equivalent noise model employed in [41]. (b) An improved
small-signal noise model typically used in cryogenic LNA design. In both cases, the small-signal noise models can be completely determined
without the need for any noise measurements.
deep cryogenic temperatures (i.e.,
)
T 15K
a # was not provided by these
initial studies. Since on-wafer techniques
for cryogenic noise measurements
of the required accuracy were
(and still are) not available, there was
still an open question as to how one
could develop the simulation models
necessary to systematically design
cryogenic SiGe LNAs optimized for
operation at 15 K or below. The first
attempt to answer this question
was reported in 2007 [41]. The basic
idea proposed in this article was
to extract a simplified small-signal
noise model of the form depicted in
Figure 4(a) by combining room temperature
process design kit (PDK)
parameter values with parameters
extracted via cryogenic dc characterization
of the transistors.
In a SiGe HBT, the relevant sources
of noise are the independent thermal-noise
processes associated with
physical resistances and the partially
correlated shot-noise processes associated
with the base and collector currents
[45]. However, at frequencies
well below /f 3t
(i.e., where a cryogenic
LNA would operate), the effect
of shot-noise correlation is minimal
and can be ignored [46], meaning
that all noise sources can be
assumed to be uncorrelated. Thus,
the noise model is fully determined
by the small-signal model and dc currents.
Further, the hypothesis of this
initial work was that the only significant
changes occurring to the model
pa rameters with cryogenic cooling
would be attributed to DCb and
g ,m
whose values can be extracted
from dc measurements.
Following this hypothesis, the
dc currents of a SiGe HBT from the
Global Foundries (then IBM) BiCMOS8HP
process were characterized
cryogenically and used to compute
the low-frequency limit of TMIN
encouraging preliminary results,
we combined our experimentally
obtained model parameters (,IB
and g )m with room temperature
I ,C
PDK values of the remaining components
(,CBE
C ,CB and )RB
small-signal model to design a simple
discrete transistor cascode amplifier.
As presented in Figure 5, the meafor
this
transistor. Doing so, it was found
that the low-frequency value of TMIN
was below 1 K over a wide range of
current densities. Following these
sured gain and noise agreed well
with the simulation, va l idat ing
our simple modeling approach for
amplifiers operating in the low-gigahertz
frequency range. Moreover, the
amplifier achieved a noise temperature
of about 2 K at 1 GHz while dissipating
Vce = 1.06 V, Ic = 6.4 mA, Ib1 = 1 µA, lb2 = 1.1 µA,
Vb1 = 1.12 V, Vb2 = 1.4 V
11
10
9
8
7
6
5
4
3
2
1
0.5
1
Gain
Noise
33
30
27
24
21
18
15
12
9
6
3
1.5
2
Frequency (GHz)
FIGURE 5: The measured and modeled gain and noise temperature of the discrete transistor
cascode amplifier reported in [41]. (Source: [41]; reprinted with permission.)
IEEE SOLID-STATE CIRCUITS MAGAZINE
SPRING 2021
27
2.5
3
and used this
E
gmvbe
in,c
RB
CCB
vn,b
C
B
in,b
gbe CBE vbe gmvbe
+
_
~
RE
vn,e
in,c
RB
CCB
RC
vn,c
C
gm = gm exp {-j2πf }
~
Noise (K)
Gain (dB)
IEEE Solid-States Circuits Magazine - Spring 2021

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