IEEE Solid-States Circuits Magazine - Spring 2020 - 27

The regression analysis result-
e
- d in
Pdc [mW] 0.16 # Tcas [K] 0.55
	
L [nm] 0.5
(2)
- 14.2 [GHz],

25

FOM new =

L [nm] # ^f0 [GHz] + 14.2h
,
Tcas [K] 1.1 # P dc [mW] 0.32
(3)

15
10

0
0.1

1
16 nm
45 nm
180 nm
500 nm

10
Frequency (GHz)
22 nm
28 nm
55 nm
65 nm
200 nm 240 nm
Envelope

32 nm
90 nm
250 nm

100
40 nm
130 nm
350 nm

FIGURE 5: The proposed FOMnew versus center frequency.

35

B

30
25
20

2

where the right-hand and left-hand
sides of (2) are squared and the scaling factor identified in (2) is dropped
but its units are retained in (3) to
make FOM new dimensionless.
The result of the regression analysis and the suggested FOM enable a
few interesting observations. One
such observation is that the FOM is
only marginally dependent on frequency when the center frequency
is much lower than 14.2 GHz. We
speculate that this is likely because
many low-frequency LNAs avoid
large, low-Q inductors by employing
shunt feedback and common-gate
circuits. Since the noise in these circuits is not significantly determined
by the transistor itself, noise temperature becomes less dependent on
frequency. For other low-frequency
topologies, where the transistor noise

	

20

5

FOMnew (dB)

where L is the minimum technology
feature size. This expression shows
how, in a typical CMOS LNA, performance parameters relate to f0. In (2),
the units of the scaling factor, 13.8,
are such that the units on the righthand side of (2) are in GHz. Interestingly, the regression analysis showed
that an offset of 14.2 GHz improves
the regression R2 value from about
0.5 to 0.75. This was already highlighted with trend lines in Figure 1,
where, below 20 GHz, the noise-figure trend slope increases relative to
that at lower frequencies.
Since the right-hand side of (2) is
equivalent to the left-hand side, we
suggest that, for a typical CMOS LNA,
the ratio of the operating frequency
[right-hand side of (2)] to the left-hand
side of (2) is expected to be constant.
Based on this, we use the result of the
regression analysis to suggest the following core FOM to replace FOM0:

FOMnew (dB)

f0 [GHz] ~13.8

15

0.1

1
16 nm
45 nm
180 nm
500 nm

10
Frequency (GHz)
22 nm
28 nm
55 nm
65 nm
200 nm 240 nm
Envelope

32 nm
90 nm
250 nm

100
40 nm
130 nm
350 nm

FIGURE 6: The proposed FOM Bnew versus center frequency.

is very low, the passives are mostly
responsible for the frequency-independent noise generated in the LNAs.
LNA noise becomes more transistor-dominated at frequencies above
14.2 GHz, w ith com mon-source
LNAs being used more frequently in
this range. For these LNAs, noise temperatures T ? g m f 20 /f 2T [19], [20]-
where gm is the MOSFET transconductance and f T is the frequency of
unity current gain-are expected

to guide the dominant trend. With
fT . g m /2rC gs, g m ? I dc /L ? Pdc /L ,
and C gs ? L, we can surmise that the
expression f 20 L2.5 /T Pdc will remain
constant for CMOS common-source
and source-degenerated LNAs. This
expression closely resembles the relationships between the terms in (3), only
with L and Pdc raised to a higher power.
It is likely that velocity saturation, the
dependence of minimum noise temperature on power consumption [21],

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IEEE Solid-States Circuits Magazine - Spring 2020

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