February 1, 2002
Roberto Antonicelli, MSEE
2P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on
RF amplifiers: the S-parameter
approach
Contents
Input matching in LNA design:
methodologies and calculations
Sensitivity in high performance
amplifiers design: the tunability
factor
February 1, 2002
Roberto Antonicelli, MSEE
3P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on
Sensitivity in high
performance
amplifiers design:
the tunability
factor
February 1, 2002
Roberto Antonicelli, MSEE
4P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on Tunability curves
0 50 100 150 200 250 300 350 400
0
0,5
1,0
d = 0,3
T
un
a
bi
li
t
y
Tunability curves
d = 0,3
Max tunability
Min tunability
Max operative gainTu
na
bi
l
it
y
0 5 10 15
Tunabi li t y margin
Operative gain [dB]
The analysis of the tunability curves lets the
designer know immediately if a certain good
tunability is reachable together with the desired
operative gain.
February 1, 2002
Roberto Antonicelli, MSEE
5P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on Tunability zones
Max tunability
0.3 tunability
Min tunability
Minimum tunability curve: is the
set of points corresponding to the
minimum tunability (whatever it is)
over each constant gain circle
Maximum tunability curve: is the
set of points corresponding to the
maximum tunability for each gain
circle
0.3-tunability curve: is the set of
points corresponding to an exact
value of 0.3 tunability factor
February 1, 2002
Roberto Antonicelli, MSEE
6P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on Simulation results
The discrete
component
matching networks
perform the
desired tuning only
in proximity of the
targeted
frequency. At low
frequencies,
indeed, the gain
and the noise are
drastically bad.
0.01 0.51 1.01 1.51 2.01 2.51 3
Frequency (GHz)
Gain and Noise
5
10
15
20
0
2
4
6
8
10
DB(GMax) (L)
Dev001
DB(GT) (L)
LNA25
DB(NF) (R)
LNA25
DB(NFMin) (R)
Dev001
February 1, 2002
Roberto Antonicelli, MSEE
7P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on Tunability surface
Tunability surface. View z0x.
February 1, 2002
Roberto Antonicelli, MSEE
8P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on Tunable design
Tunability surface. View x0y.
9 dB
10 dB
0
1.
0
1.
0
-
1.
0
10
.0
10.0
-10.0
5.
0
5.0
-5.0
2.
0
2.
0
-
2.
0
3.
0
3.0
-3.0
4.
0
4.0
-4.0
0.
2
0.2
-0.2
0.
4
0.4
-0.4
0.
6
0.
6
-
0.
6
0.
8
0.
8
-
0.
8
Output Plane
Swp Max
2.5GHz
Swp Min
2.5GHz
-0.4
-
0.
6 -
0.
8
GPCIR[10,1,2]
Input matching
S[1,1] *
Output matching opt tun
By choosing 0.5 dB of
mismatch, we end up with:
°∠=Γ 293.0tunL
February 1, 2002
Roberto Antonicelli, MSEE
9P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on Performance of optimum tunable design
0.01 0.51 1.01 1.51 2.01 2.51 3
Frequency (GHz)
Gain and Noise opt tun
5
10
15
20
0
2
4
6
8
10
DB(GMax) (L)
DB(NFMin) (R)
DB(GT) (L)
DB(NF) (R)
The
transducer
gain is now
GT = 9.55 dB
Variation in
the gain due
to a ±10%
variation in the
load for the
optimum
tunability
circuit.
February 1, 2002
Roberto Antonicelli, MSEE
10P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on Tunability surface
February 1, 2002
Roberto Antonicelli, MSEE
11P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on Tunability contours
It comes evident that
only a small portion of
the entire output
reflection plane is
satisfying from the
tunability point of view.
February 1, 2002
Roberto Antonicelli, MSEE
12P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on Output reflection coefficient (I)
Output reflection plane
with the stability circle,
the constant operative
gain circles (16, 15 and
14 dB) and the tunability
contours at 3 GHz.
Let the wanted
transducer gain be
16 dB.
0
1.
0
1.
0
-
1.
0
10
.0
10.0
-10.0
5.
0
5.0
-5.0
2.
0
2.
0
-
2.
0
3.
0
3.0
-3.0
4.
0
4.0
-4.0
0.
2
0.2
-0.2
0.
4
0.4
-0.4
0.
6
0.
6
-
0.
6
0.
8
0.
8
-
0.
8
Output plane
Swp Max
3GHz
Swp Min
3GHz
16 dB
February 1, 2002
Roberto Antonicelli, MSEE
13P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on Input power matching (I)
The square symbol is
the complex and
conjugate of the input
impedance of the circuit
matched for the output.
Three constant
available gain circles
are illustrated, as well
as the mapped (and
distorted) output Smith
Chart.
0
1.
0
1.
0
-
1.
0
10
.0
10.0
-10.0
5.
0
5.0
-5.0
2.
0
2.
0
-
2.
0
3.
0
3.0
-3.0
4.
0
4.0
-4.0
0.
2
0.2
-0.2
0.
4
0.4
-0.4
0.
6
0.
6
-
0.
6
0.
8
0.
8
-
0.
8
Input plane
Swp Max
3GHz
Swp Min
3GHz
SCIR1
GAC_MAX[1,3]
Eqn *
SMAP[1,2] *
February 1, 2002
Roberto Antonicelli, MSEE
14P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on
0
1.
0
1.
0
-
1.
0
10
.0
10.0
-10.0
5.
0
5.0
-5.0
2.
0
2.
0
-
2.
0
3.
0
3.0
-3.0
4.
0
4.0
-4.0
0.
2
0.2
-0.2
0.
4
0.4
-0.4
0.
6
0.
6
-
0.
6
0.
8
0.
8
-
0.
8
Input plane
Swp Max
1.9GHz
Swp Min
1.9GHz
GACIR[15,0.25,6]
Device
NFCIR[3,0.25]
Device
Eqn
GMS2
dB 75.14Γ Input matching in
LNA design:
methodologies
and calculations
February 1, 2002
Roberto Antonicelli, MSEE
15P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on Input matching network
It is advisable
to work for a
gain of at least
half dB more.
Let us work
with 0.75 dB
more.
0
1.0
1.0
-
1.0
10.
0
10.0
-10.0
5.0
5.0
-5.0
2.0
2.0
-
2.0
3.0
3.0
-3.0
4.0
4.0
-4.0
0.2
0.2
-0.2
0.4
0.4
-0.4
0.6
0.6
-
0.6
0.8
0.8
-
0.8
Input plane
Swp Max
1.9GHz
Swp Min
1.9GHz
GACIR
14.75 dB
GACIR[15,0.25,6]
Device
NFCIR[3,0.25]
Device
February 1, 2002
Roberto Antonicelli, MSEE
16P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on Input reflection plane
The small circles
corresponds to all
tangency points
between noise and
available gain
contours.
Hence they
correspond to the
minimum noise figure
over any constant gain
circle.
0
1.
0
1.
0
-
1.
0
10
.0
10.0
-10.0
5.
0
5.0
-5.0
2.
0
2.
0
-
2.
0
3.
0
3.0
-3.0
4.
0
4.0
-4.0
0.
2
0.2
-0.2
0.
4
0.4
-0.4
0.
6
0.
6
-
0.
6
0.
8
0.
8
-
0.
8
Input plane
Swp Max
1.9GHz
Swp Min
1.9GHz
GACIR[15,0.25,6]
Device
NFCIR[3,0.25]
Device
Eqn
GMS2
dB 75.14Γ
February 1, 2002
Roberto Antonicelli, MSEE
17P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on Noise performances
Only 0.05 dB of
difference at the
frequency of
interest (1.9
GHz).
The plot shows
also the
unmatched case
(device plugged
in a 50 Ω
termination set).
0.1 0.6 1.1 1.6 2.1 2.6 3
Frequency (GHz)
LNA Noise
0
1
2
3
4
1.9 GHz
1.77 1.9 GHz
1.27
1.9 GHz
1.22
DB(NFMin)
Device
DB(NF)
LNA
DB(NF)
Device
February 1, 2002
Roberto Antonicelli, MSEE
18P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on Overall transducer gain
Effectively, the
system
presents a
very good
matching in all
the range
between 1 and
3 GHz,.
0.1 0.6 1.1 1.6 2.1 2.6 3
Frequency (GHz)
LNA Gain
-50
-25
0
25
50
1.9 GHz
14.75
1.9 GHz
15.1
DB(GT)
LNA
DB(GMax)
LNA
February 1, 2002
Roberto Antonicelli, MSEE
19P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on
0
1.
0
1.
0
-
1.
0
10
.0
10.0
-10.0
5.
0
5.0
-5.0
2.
0
2.
0
-
2.
0
3.
0
3.0
-3.0
4.
0
4.0
-4.0
0.
2
0.2
-0.2
0.
4
0.4
-0.4
0.
6
0.
6
-
0.
6
0.
8
0.
8
-
0.
8
Input plane
Swp Max
1.9GHz
Swp Min
1.9GHz
GACIR[15,0.25,6]
Device
NFCIR[3,0.25]
Device
Eqn
GMS2
dB 75.14Γ
Conclusions
ZS
ES
ZLSM1 M2
February 1, 2002
Roberto Antonicelli, MSEE
20P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on
Tunability analysis The sensitivity plays
a fundamental role in
the modern massive
run productions
because of its strong
impact on the final
yield as well as on
the required
performance in the
ASSP market.
�The tunability factor represents a
simple way of analysing the overall
sensitivity.
�Any parametric variation in the load affects
the transducer gain because of the output
mismatch and the input mismatch.
�The former is a direct consequence of
the parametric variation and can be
easily studied on the output Smith Chart.
�The latter is more complicated, since the
active device transfers those variations to
the input matching plane.
�The tunability factor express such
interactions with the device itself.
February 1, 2002
Roberto Antonicelli, MSEE
21P
ol
yt
ec
hn
ic
o
f B
ar
i -
E
ng
in
ee
ri
ng
F
ac
ul
ty
El
ec
tr
ic
al
a
nd
E
le
ct
ro
ni
cs
D
ep
t.
Numerical and Analytical Methodologies in
High-Frequency Low-Noise Amplifier Design
P
hD
in
E
le
ct
ro
ni
cs
E
ng
in
ee
rin
g
XI
II
Ed
iti
on
Noise optimisation methods An important role is
played, today, by CAD
tools, that simplify
enormously the design
phase from the system
pre-study to the layout
optimisation.
Often, most of the design time is
simulation time.
Reducing the simulation time is as
important as increasing the yield of a
product, since all of these factors are
directly related to the cost and,
therefore, to potential market slices.
The noise figure minimisation algorithm
constitutes the goal of the methodology
for single stage amplifiers, while for
multi-stage amplifiers the noise
measure replaces the noise figure,
giving more realistic results.
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