1. The document discusses key concepts in amplifier design using the scattering matrix (S-parameters) model. It defines concepts like transducer power gain, operating power gain, available power gain, and stability circles. 2. Operating power gain and available power gain are represented by circles on the Smith chart known as the operating power gain circle and available power gain circle respectively. These circles define the range of stable input/output impedance values that produce constant gain. 3. Several tests for stability are described, including Rollett's K-factor test and stability circles. Unilateral and bilateral cases are also distinguished, with the unilateral case requiring one port to be matched.

1. IV
(rfsys.ntut@gmail.com)
April 2014

2. 1
(Advanced Design System, ADS)
I ADS II DCS
1900 III
IV
ADS

3. 2
1.1
ADS
1.2
1.
1.1 (
) sE sZ
(
) LZ
( 50 ) sΓ
LΓ [ ]S 1.2 1.1 inΓ
inΓ
outΓ outΓ
in s
∗
Γ = Γ out L
∗
Γ = Γ
2. inΓ outΓ
inΓ outΓ 1.3
Transistor
[S]
2a
2b
1a
1b
Port 1 Port 2
+
−sE
sZ
outΓ
LZ
inΓ
sΓ LΓ
1.1

4. 3
s o
s
s o
Z Z
Z Z
−
Γ =
+
L o
L
L o
Z Z
Z Z
−
Γ =
+
Source reflection coefficient:
Load reflection coefficient:
1 11 1 12 2b S a S a= +
2 21 1 22 2b S a S a= +
Transistor:
+
−sE
sZ
sΓ
LZ
LΓ
Transistor
[S]
1.2
1.3 inΓ
outΓ inΓ
outΓ sΓ LΓ [ ]S
( )
sΓ LΓ [ ]S
inΓ [ ]S LΓ outΓ [ ]S sΓ
in s
∗
Γ = Γ out L
∗
Γ = Γ
Transistor
[S]
outΓ
LZ
inΓ
LΓ
12 21
11
221
L
in
L
S S
S
S
Γ
Γ = +
− Γ
Transistor
[S]+
−sE
sZ
outΓinΓ
sΓ
Find input reflection coefficient:
12 21
22
111
s
out
s
S S
S
S
Γ
Γ = +
− Γ
Find output reflection coefficient:
1.3 inΓ outΓ

5. 4
3.
1.4 AVSP
(Available power)
in s
∗
Γ = Γ AVSP
inP in s
∗
Γ = Γ inP AVSP
in s
∗
Γ ≠ Γ
AVSP
in AVSP P≠ in s AVSP M P= sM (Source
mismatch factor) sM 1 ( dB )
AVNP
(Available power from network) AVNP
in s
∗
Γ = Γ
AVNP ( LP )
out L
∗
Γ = Γ
AVNP LP out L
∗
Γ ≠ Γ
AVNP
L AVNP P≠ L L AVNP M P= LM (Load
mismatch factor) LM 1 ( dB
)
1sM =
1LM =
Transistor
[S]+
−sE
sZ
LZ
PAVNPAVS PLPin
Ms
interface interface
ML
inΓ
sΓ
outΓ
LΓ
1.4

6. 5
4.
1.5 pG
(Operating power gain)
pG
(Power amplifier, PA)
pG PA TG
TG
TG
AG AG (Low noise amplifier, LNA)
AG
• The power gain L
p
in
P
G
P
=
• The transducer power gain L
T p s
AVS
P
G G M
P
= =
• The available power gain AVN T
A
AVS L
P G
G
P M
= =
p TG G>
A TG G>
• When the Input and output are matched: p T AG G G= =
From the amplifier input to load
From the source to load
1.5
pG PA
1.6 ( LΓ ) LΓ inΓ
inΓ ( s in
∗
Γ = Γ )
inΓ
1E
oZ
oZ
Transistor
oG
Output
matching
LG
Input
matching
sG
sΓ LΓ
1.6 ( PA )

7. 6
AG LNA 1.7
( sΓ ) sΓ outΓ outΓ
( L out
∗
Γ = Γ )
1E
oZ
oZ
Transistor
oG
Output
matching
LG
Input
matching
sG
sΓ LΓoutΓ
1.7 ( LNA )
sΓ LΓ [ ]S 1.8
2
2
212 2
22
11
1 1
L
p
in L
G S
S
− Γ
=
− Γ − Γ
• The Power Gain Gp
• The Transducer Power Gain GT
2 2 2 2
2 2
21 212 2 2 2
22 11
1 1 1 1
1 1 1 1
s L s L
T
s in L s out L
G S S
S S
− Γ − Γ − Γ − Γ
= =
− Γ Γ − Γ − Γ − Γ Γ
• The Available Power Gain GA
2
2
212 2
11
1 1
1 1
s
A
s out
G S
S
− Γ
=
− Γ − Γ
1.8
5.
1
1.2
<1sΓ <1LΓ inΓ outΓ 1inΓ <
inP 1outΓ <
( 1 )
1inΓ >
( 1outΓ >

8. 7
Transistor
[S]+
−
sE
sZ
outΓ
LZ
inΓ
sΓ LΓ
12 21
11
221
L
in
L
S S
S
S
Γ
Γ = +
− Γ
12 21
22
111
s
out
s
S S
S
S
Γ
Γ = +
− Γ
1sΓ <
12 21
22
11
1
1
s
out
s
S S
S
S
Γ
Γ = + <
− Γ
1LΓ <
12 21
11
22
1
1
L
in
L
S S
S
S
Γ
Γ = + <
− Γ
and
( )22 11 12 21
2 2 2 2
22 22
L
S S S S
S S
∗∗
− ∆
Γ − =
− ∆ − ∆
( )11 22 12 21
2 2 2 2
11 11
s
S S S S
S S
∗∗
− ∆
Γ − =
− ∆ − ∆
11 22 12 21S S S S∆ = −
• Stability Circles include
and
where
• Stable Condition:
Output Stability Circle Input Stability Circle
1.9
)
inΓ outΓ 1
( ) (
) ( )
inΓ outΓ 1
1.9 1inΓ = 1outΓ =
1.10 LΓ inΓ 1
11S 0LΓ =
11in SΓ = 0LΓ = LΓ Case (1)
11 1S <
Case (2) 11 1S >
1.11
Rollet’s
condition( K- Test) -test

9. 8
LC
LC
Lr
1inΓ =
11 1S <
12 21
11
221
L
in
L
S S
S
S
Γ
Γ = +
− Γ
0LΓ =
LC
LC
0LΓ =
Lr
1inΓ =
• Criteria: virtually make , then and0LΓ = 11in SΓ =L oZ Z=
-planeLΓ -planeLΓ
Case (1): 11 1S >Case (2):
stable region stable region
Output
stability circle
Output
stability circle
1.10
12 21
22
111
s
out
s
S S
S
S
Γ
Γ = +
− Γ
22 1S < 22 1S >Case (1): Case (2):
• Criteria: virtually make , then and0sΓ = 22out SΓ =s oZ Z=
stable region stable region
-planesΓ -planesΓ
0sΓ =0sΓ =
sC sC
sC
srsr
sC
1outΓ = 1outΓ =Input
stability circle
Input
stability circle
1.11
6. (Unilateral Transducer Power Gain)
1.8 TG sΓ
LΓ [ ]S inΓ outΓ inΓ outΓ
LΓ sΓ

10. 9
inΓ outΓ
12S 0 (Bilateral case) 12S 0
( )
12 0S = (Unilateral case)
1.12 inΓ 11S outΓ 22S
U(Unilateral figure of merit)
12S ( )
11S
1E
oZ
oZ
Transistor
oG
Output
matching
LG
Input
matching
sG
sΓ LΓ22S
=12 0S
2 2
2
212 2
11 22
1 1
1 1
s L
TU s o L
s L
G S G G G
S S
− Γ − Γ
= =
− Γ − Γ
2
2
11
1
1
s
s
s
G
S
− Γ
=
− Γ
2
21oG S=
2
2
22
1
1
L
L
L
G
S
− Γ
=
− Γ
(dB) (dB) (dB) (dB)TU s o LG G G G= + +
• Unilateral Transducer Power Gain GTU
• The term Gs and GL represent the gain or loss produced by the matching
or mismatching of the input or output circuits.
2 2 2 2
2 2
21 212 2 2 2
22 11
1 1 1 1
1 1 1 1
s L s L
T
s in L s out L
G S S
S S
− Γ − Γ − Γ − Γ
= =
− Γ Γ − Γ − Γ − Γ Γ
12 21
11
221
L
in
L
S S
S
S
Γ
Γ = +
− Γ
• Transducer Power Gain GT
Unilateral condition
12 0S = 11in SΓ =
1.12 (Unilateral case)

11. 10
1.12 12 0S =
sG oG LG
21S 20 dB
20 dB sG
dB LG dB
sG dB
LG dB
sG oG LG
7. (Bilateral Transducer Power Gain)
6 Unilateral 12S
( 0)
12S 0(
)
Bilateral
(Operating power gain) (Available power gain) 4
8. (Operating Power-Gain Circle)
pG 1.8 inΓ
1.9 pG inΓ
pG 1.13
2
21p pG S g= ⋅ pg
(Normalized gain factor) 0 1 1pg =
pG 21S pg pG
pg pg
LΓ
( LΓ ) pG 1.6

12. 11
( )2 2
21 2
212
211
22
22
1
1 1
1
L
p p
L
L
L
S
G S g
S
S
S
− Γ
= = ⋅
 − ∆Γ
 − − Γ
 − Γ
 
• Unconditionally stable bilateral case:
( ) ( )
2 2
2 2 2 2 2 2
22 11 11 22 2
1 1
1 1 2Re
L L
p
L L L L
g
S S S S C
− Γ − Γ
= =
− Γ − − ∆Γ − + Γ − ∆ − Γ
2 22 11C S S∗
= − ∆
Gp and gp are the functions of the device
S parameters and ΓL. The values of ΓL that
produce a constant gp are shown to lie on
a circle, known as an operating power-
gain circle.
L p pC rΓ − =
( )
2
2 2
221
p
p
p
g C
C
g S
∗
=
+ − ∆ ( )
2 2
12 21 12 21
2 2
22
1 2
1
p p
p
p
K S S g S S g
r
g S
− +
=
+ − ∆
Center Radius
where
• Operating Power-Gain Circle:
1.13
pg 0 1 0.5pg =
LΓ 0.5pg = LΓ
0.5pg = ( 1pg = )
3 dB −3 dB
0.6pg = LΓ
0.8pg = LΓ
1pg = LΓ
0 pg pg
1.13
( )
1.14
1.13 1pg = ( ,g optΓ ) 1.14
,maxpG ( ,max 11.38 dBpG = )
,g optΓ 9 dBpG =
2.38 dB 2.38 dB 0.578pg = − =
9 dBpG = LΓ
9 dBpG = LΓ 1.15

13. 12
optΓ optΓ pg pg pg
optΓ ( 4.38 dB 0.364pg = − = )
( ,g optΓ , ,maxpG ) 1.15
gp = 0 dB
gp = −2.38 dB
ΓL -Plane
Γg,opt
1.14
gp = 0 dB
gp = −4.38 dB
ΓL -Plane
Γg,opt
Γopt
Maximum output power
1.15

14. 13
( )2 2
21 2
212
222
11
11
1
1 1
1
s
A a
s
s
s
S
G S g
S
S
S
− Γ
= = ⋅
 − ∆Γ
 − − Γ
 − Γ
 
• Unconditionally stable bilateral case:
( ) ( )
2
2 2 2 2 2
21 22 11 1
1
1 2Re
sA
a
s s
G
g
S S S C
− Γ
= =
− + Γ − ∆ − Γ
1 11 22C S S∗
= − ∆
Ga and ga are the functions of the device
S parameters and Γs. The values of Γs that
produce a constant ga are shown to lie on
a circle, known as an available power-gain
circle.
s a aC rΓ − =
( )
1
2 2
111
a
a
a
g C
C
g S
∗
=
+ − ∆ ( )
2 2
12 21 12 21
2 2
11
1 2
1
a a
a
a
K S S g S S g
r
g S
− +
=
+ − ∆
Center Radius
• Available Power-Gain Circle:
where
1.16
9. (Available Power-Gain Circle)
AG 1.8 outΓ AG
outΓ AG 1.16
2
21A aG S g= ⋅
ag 0 1 1ag = ag
sΓ ( sΓ )
AG 1.7
( 1.14 1.15 sΓ ,g optΓ
,a optΓ pG AG optΓ sΓ )
10.
(

15. 14
) ( )
1.17
9 dBpG = A C D
B ( ) A C
D C
D A C D
ΓL -Plane
Unstable region
Stable region
Output stability circle
A
B
C
D
1.17
1.3
1.
Gonzalez Microwave Transistor Amplifier Analysis and Design
Example 3.3.2 800 MHz 11 0.65 95S = ∠ −
12 0.035 40S = ∠ 21 5 115S = ∠ 22 0.8 35S = ∠ − K
(Maximum stable gain, MSG)
20 dB 18 dB 16 dB

16. 15
2.
amp1900 Data Display circles.dds Data Display
1111 0.65 95S a S= = ∠ − 1212 0.035 40S a S= = ∠
2121 5 115S a S= = ∠ 2222 0.8 35S a S= = ∠ − 1.18
CL rL C rs
( circle( ) ) ADS
l_stab_circle(S,points) s_stab_circle(S,points)
S points
l_stab_circle_center_radius(S, “x”) s_stab_circle_center_radius(S, “x”)
(x center) (x radius)
l_stab_region(S) s_stab_region(S)
ADS
stab_fact() mu() mu_prime() U
unilateral_figure() 1.19
Eqn S11a=polar(0.65,-94)
Eqn S12a=polar(0.035,40)
Eqn S21a=polar(5,115)
Eqn S22a=polar(0.8,-35)
Eqn Delta=S11a*S22a-S12a*S21a
Eqn CL=conj(S22a-Delta*conj(S11a))/(abs(S22a)**2-abs(Delta)**2)
Eqn rL=abs(S12a*S21a/(abs(S22a)**2-abs(Delta)**2))
Eqn Sa={{S11a,S12a},{S21a,S22a}}
Sa
Sa(1,1) Sa(1,2) Sa(2,1) Sa(2,2)
0.650 / -94.000 0.035 / 40.000 5.000 / 115.000 0.800 / -35.000
CL
1.310 / 47.706
rL
0.457
Eqn In_stable_circle=s_stab_circle(Sa,51)
indep(In_stable_circle) (0.000 to 51.000)
In_stable_circle
indep(Out_stable_circle) (0.000 to 51.000)
Out_stable_circle
(0.000 to 0.000)
CL
Cs
Eqn Cs=conj(S11a-Delta*conj(S22a))/(abs(S11a)**2-abs(Delta)**2)
Eqn rs=abs(S12a*S21a/(abs(S11a)**2-abs(Delta)**2))
Cs
1.815 / 120.890
rs
1.057
Eqn Out_stable_circle=l_stab_circle(Sa,51)
Eqn Cs_cal=s_stab_circle_center_radius(Sa,"center")
Eqn rs_cal=s_stab_circle_center_radius(Sa,"radius")
CL_cal
1.310 / 47.706
rL_cal
0.457
Eqn CL_cal=l_stab_circle_center_radius(Sa,"center")
Eqn rL_cal=l_stab_circle_center_radius(Sa,"radius")
Cs_cal
1.815 / 120.890
rs_cal
1.057
Eqn In_stable_region=s_stab_region(Sa)
Eqn Out_stable_region=l_stab_region(Sa)
In_stable_region
Outside
Out_stable_region
Outside
Draw the stability circles: see Example 3.3.2 in Gonzalez’s Textbook
Transistor parameter Make Sa as a “Matrix”
Calculate CL, rL, Cs, and
rs by equations
You can also calculate CL, rL, Cs, and rs
by ADS build-in functions.
Input stability circle
Output stability circle
1.18

17. 16
Eqn K=stab_fact(Sa) K
0.556
Mu_load
0.853
Mu_source
0.757
Eqn U=unilateral_figure(Sa)
U
0.438
Eqn Mu_load=mu(Sa)
Eqn Mu_source=mu_prime(Sa)
Numerical Stability Factors and Unilateral Figure
1.19
Eqn Gmax1=10*log((abs(S21a)/abs(S12a)))
Gmax1
21.549
Gmax2
21.549
Eqn Gp_circle_20dB=gp_circle(Sa,20,51)
cir_pts (0.000 to 51.000)
Gp_circle_20dB
Gp_circle_18dB
Gp_circle_16dB
indep(Out_stable_circle) (0.000 to 51.000)
Out_stable_circle
Eqn Gmax2=max_gain(Sa)
Eqn Gp_circle_18dB=gp_circle(Sa,18,51)
Eqn Gp_circle_16dB=gp_circle(Sa,16,51)
Constant Operating Power-Gain Circles:
Maximum stable gain (MSG)
Calculate MSG using
built-in function
Use gp_circle() function to get constant
gain circles.
1.20
3.
ADS gp_circle()
1.20 max_gain() MSG
Gmax2 MSG Gmax1 Gmax1 Gmax2
MSG MSG
MSG MSG
21.549 dB gp_circle(Sa, 21.549, 51) Sa
21.549 51
51 21.549 23 25 28 ADS
( )

18. 17
gp_circle()
1.21 gp_circle(Sa, [20, 18, 16], 51)
20 dB 18 dB 16 dB gp_circle(Sa, , 51, 3, 2)
MSG 2 dB 3 gp_circle()
Eqn Gp_circles=gp_circle(Sa,[20,18,16],51)
indep(Out_stable_circle) (0.000 to 51.000)
Out_stable_circle
cir_pts (0.000 to 51.000)
Gp_circles
Eqn Gp_circles_step=gp_circle(Sa, ,51,3,2)
indep(Out_stable_circle) (0.000 to 51.000)
Out_stable_circle
cir_pts (0.000 to 51.000)
Gp_circles_step
Assign constant-gain sequence
to get a series of circles
Constant Operating Power-Gain Circles:
Draw 3 circles every 2 dB lower
than MSG.
1.21
Eqn Ga_circle_20dB=ga_circle(Sa,20,51)
Eqn Ga_circle_18dB=ga_circle(Sa,18,51)
Eqn Ga_circle_16dB=ga_circle(Sa,16,51)
cir_pts (0.000 to 51.000)
Ga_circle_20dB
Ga_circle_18dB
Ga_circle_16dB
indep(In_stable_circle) (0.000 to 51.000)
In_stable_circle
Constant Available Power-Gain Circles:
Use ga_circle() function to get constant
gain circles.
1.22

19. 18
4.
ADS
ga_circle() 1.22
5.
S_Param
1.23 1.24
Data Display
Ideal amplifier behavioral model
MuPrime
MuPrime2
MuPrime2=mu_prime(S)
MuPrime
MuPrime
MuPrime1
MuPrime1=mu_prime(S)
MuPrime
Mu
Mu1
Mu1=mu(S)
Mu
GaCircle
GaCircle1
GaCircle1=ga_circle(S,[20,18,16],51)
GaCircle
GpCircle
GpCircle1
GpCircle1=gp_circle(S,[20,18,16],51)
GpCircle
L_StabCircle
L_StabCircle1
L_StabCircle1=l_stab_circle(S,51)
LStabCircle
S_StabCircle
S_StabCircle1
S_StabCircle1=s_stab_circle(S,51)
SStabCircle
S_Param
SP1
Step=1.0 MHz
Stop=800 MHz
Start=800 MHz
S-PARAMETERS
Amplif ier2
AMP1
S12=polar(0.035,40)
S22=polar(0.8,-35)
S11=polar(0.65,-95)
S21=polar(5,115)
Term
Term2
Z=50 Ohm
Num=2
Term
Term1
Z=50 Ohm
Num=1
You can just use the measuring components in S_Param palette within schematic.
1.23
cir_pts (0.000 to 51.000)
GaCircle1
indep(S_StabCircle1) (0.000 to 51.000)
S_StabCircle1
cir_pts (0.000 to 51.000)
GpCircle1
indep(L_StabCircle1) (0.000 to 51.000)
L_StabCircle1
Constant Operating Power-Gain Circles
Output Stability Circle
Constant Available Power-Gain Circles
Output Stability Circle
1.24

20. 19
1.4
ADS

21. 20
2.1
(Infineon) SiGe BJT BFP640ESD
2.4 GHz ~ 2.5 GHz 13 dB 1.5 dB
2.2
1.
Johnson Nyquist
Johnson
Noise ( )
(mean-square) (root-mean-square)
(Available noise power) NAP kTB=
k (Boltzman’s constant) ( )23
1.38 10 J K−
× T B
NAP kTB= kT (Power spectrum
density, PSD) B PSD W/Hz( dBm/Hz)
B NAP
PSD
(White noise) 2.1 PSD kT
( PSD )

22. 21
PSD (dBm/Hz)
Frequency (Hz)
Bandwidth B (Hz)
kT
2.1
2. ( )
NAP kTB= ( )o
17 C 290 K= 1 Hz
( )21
4 10 W 174 dBm−
× = −
PSD 174 dBm Hz− 2.2
PSD (dBm/Hz)
Frequency (Hz)
−174
2.2 ( )290 K
(Spectrum analyzer, SA) SA
(Resolution bandwidth, RBW)
RBW
RBW SA NAP kTB= B
PSD( 174 dBm Hz− ) B
(
) SA
(Noise floor) RBW
SA RBW 1 Hz SA
174 dBm− ( 1Hz) RBW 1 kHz
174 dBm 30 dB 144 dBm− + = − ( 1 kHz 1 Hz 1000 )
144 dBm 1 kHz− 1 kHz RBW 10

23. 22
kHz 144 dBm 10 dB 134 dBm− + = − ( 10 kHz 1 kHz 10
) RBW 100 kHz 134 dBm 10 dB 124 dBm− + = − (
100 kHz 10 kHz 10 ) 2.3 y P dBm
P (dBm)
Frequency (Hz)
−174
Noise Floor of Spectrum Analyzer
−144
−134
−124
30 dB
10 dB
10 dB
Noise floor@RBW = 1 Hz
Noise floor@RBW = 1 kHz
Noise floor@RBW = 10 kHz
Noise floor@RBW = 100 kHz
2.3 ( )290 K RBW
RBW
SA
2.4 SA RBW
1 kHz 144 dBm 1 kHz−
2.5 SA
2.6
RBW 1 kHz A 136 dBm− B
127 dBm− A 136 dBm− B
127 dBm− ( SA RBW
RBW 1 kHz ) SA

24. 23
P (dBm)
Frequency (Hz)
Noise Floor of Spectrum Analyzer
−144
−136
Noise floor@RBW = 1 kHz
Noise floor@RBW = 1 kHz
Only white noise
White noise + other noise
2.4
P (dBm)
Frequency (Hz)
Spectrum Analyzer
−136
Noise floor@RBW = 1 kHz
above floor: measurable
below floor: unmeasurable
2.5
P (dBm)
Frequency (Hz)
Spectrum Analyzer A
−136
Noise floor@RBW = 1 kHz
P (dBm)
Frequency (Hz)
Spectrum Analyzer B
−127
Noise floor@RBW = 1 kHz
2.6
3. ( )
2.7
80 MHz
95 dBm− 80 dBm−

25. 24
(Signal-to-Noise Ratio, SNR) 15 dB
15 dB
SNR
SNR (
)
−174 dBm/Hz
noise
B = 80 MHz
Noise floor = −95 dBm
2.7
4.
p-n
(Shot noise Schottky noise) (Flicker noise
Pink noise 1 f noise) (Popcorn noise Burst noise Bistable
noise random telegraph signals, RTS) BJT
FET ( FET )
FET
BJT

26. 25
5.
NAP kTB=
2.8
R NAP kTB=
2
, 4n rmsv kTBR= , 4n rmsv kTBR=
( )2
, 4n rmsv B kTR= 2
V Hz ( ), 4n rmsv B kTR=
V Hz 2.9
R
Thermal noise source
(Noisy resistor) R
+
−
,n rmsv
R Matched load
Noise-free resistor
Noise source
2
,
1
2
n rms
NA
v
P kTB
R
 
 
 = =
2
, 4n rmsv kTBR=Mean-square open-circuited noise voltage:
For a 1 kΩ resistor over 1 Hz bandwidth: , 4 4 nVn rmsv kTR= ≃
At room temperature
For a 50 Ω resistor over 1 Hz bandwidth: , 4 0.9 nVn rmsv kTR= ≃
Thus, said, the rms-noise spectral density:
For a 1 kΩ resistor over 1 Hz bandwidth: , 4 4 nV Hzn rmsv kTR= ≃
For a 50 Ω resistor over 1 Hz bandwidth: , 4 0.9 nV Hzn rmsv kTR= ≃
Or, said, the mean-square noise spectral density:
For a 1 kΩ resistor over 1 Hz bandwidth:
2 2
, 4 16 nV Hzn rmsv kTR= ≃
For a 50 Ω resistor over 1 Hz bandwidth: 2 2
, 4 0.81 nV Hzn rmsv kTR= ≃
2.8
R
Thermal noise source
(Noisy resistor) R
+
−
,n rmsv
Noise-free resistor
R,n rmsi
Noise-free resistor
2
, 4n rmsv kTBR=
2
,2
,
4
4n rms
n rms
v kTB
i kTGB
R R
 
= = = 
 
Thevenin’s Equivalent Circuit Norton’s Equivalent Circuit
2.9

27. 26
6.
oN 0 eqN kT B=
oN ( )eq oT N kB=
eqT K 2.10
(Cold) (Hot)
For one-port components to acts as noise sources under impedance matched condition:
o
eq
N
T
kB
=
eqT
2.10
(Input-referred noise) aG
2.11
0N 0 K(
iN 0) oN
2.11
oN oN iN aG
i o a eqN N G kT B= = eq i o aT N kB N G kB= =
eqT

28. 27
aG aG
o a eqN G kT B=
i o
eq
a
N N
T
kB G kB
= =
i eqN kT B=
2.11
7. (Y )
o a i a eqN G N G kT B= =
oN
2.11 0 K
0 (
)
(Excess noise ratio, ENR)
ENR 0 290 KT =
ENR (
0 290 KT = ) 0 290 KT =
0 290 KT =
0 290 KT = 21
0 4 10 JkT −
= ×
ENR
( ) ( ) ( ) ( )0 0 0 0dB 10log 10log 10log 290 290s s sENR N N N T T T T     = − = − = −     
0 0N kT B= 0 290 KT = sN sT B
ENR B
ENR B
ENR ( ) ENR 20 dB
40 dB
ENR ENR

29. 28
ENR ENR
ENR
ENR 6 dB ENR
16 dB 16 dB 15 dB
ENR 25 dB
Y 2.12
( ) ( ) Y
Y eqT
Y
Y-factor Method
Noise source ON
Noise source Off
1 1a a eqN G kT B G kT B= +
2 2a a eqN G kT B G kT B= +
11 1 2
2 2
1
1
eqON
eq
Off eq
T TN N T YT
Y T
N N T T Y
+ −
= = = ≥ ⇒ =
+ −
, ,a eqG T B
2.12 Y
8. F NF
F(Noise factor)
NF(Noise figure) NF F dB ( )10log dBNF F=
aG
iN a iG N
oN

30. 29
a iG N addN _o a i o addN G N N= +
_o addN eT ( )
_o add a eN G kT B= _i add eN kT B=
iN 290 K 0iN kT B=
oN ( )0 _ 0o a a i add a eN G kT B G N G kB T T= + ⋅ = +
( )o a iF N G N=
( ) ( ) ( ) ( )0 0 01 1 290a e a e eF G kB T T G kBT T T T= + = + = + F 1 o a iN G N=
F 1 o a iN G N>
1.2F = 1 a iG N
0.2 a iG N
F dB NF ( ) ( )10log 1.2 0.79 dBNF = =
a iG N 0.79 dB (
0 dBNF = )
F (Signal-to-noise ratio,
SNR)
( )
_ _
0
_
1 1
i i
a i a i add i addi i i e
o a io a i i
o a i o add
S S
G N G N NSNR N N T
F
S G SSNR G N N T
N G N N
+
= = = = = + = +
+
2.13 −60 dBm
−100 dBm SNRi 40 dB 20
dB 20 dB −40 dBm −80 dBm
−72 dBm 8 dB 8 dB
SNR SNRo 32 dB
( ) ( )dB dB 40 32 8 dBi oNF SNR SNR= − = − =

31. 30
P (dBm)
Frequency (Hz)
−100
−60
SNRi = 40 dB
P (dBm)
Frequency (Hz)
−80
−40
SNRo= 32 dB
−72
Gain = 20 dB
NF = ?
NF = 8 dB
Amplifier
2.13 SNR
9.
( )
2.14 ADS
( ) ( )
2 2 2
min min
n n
s opt s opt s opt
s s
R R
F F Y Y F G G B B
G G
 = + − = + − + −  
s s sY G jB= + : Source admittance
opt opt optY G jB= + : Optimum source admittance for minimum F (or NF)
minF : Minimum noise factor
nR : Equivalent noise resistance
Noise factor of a two-port amplifier
Constant Noise Circle
0
11
1
s
s
s
Y
Z
− Γ
=
+ Γ
0
11
1
opt
opt
opt
Y
Z
− Γ
=
+ Γ
( )
( )
2
min 22
0
4
1 1
s optn
s
s opt
R
F F
Z
Γ − Γ
Γ = +
− Γ + Γ
2.14

32. 31
2.3
1. (Datasheet)
(Infineon) SiGe BJT
Infineon BFP640 BFP640
BFP640ESD BFP640
BFP640ESD ADS BFP640ESD
BFP640 ADS Datasheet
BFP640
(Reference design)
(Datasheet)
Datasheet
2.15
BFP640ESD (SiGe)
21 dBm 6 mA 1.5 GHz 2.4 GHz
0.65 dB 0.7 dB
2.15 Infineon BFP640ESD SiGe BJT abstract

33. 32
2.16 Datasheet
4.7 V 180 50 mA
Datasheet Maximum Ratings 2.17
2.4 GHz VCE=3 V IC = 6 mA
0.7 dB (Associated gain, Gass) 20 dB
( , 6 mA) ( , 30 mA)
18 dB 20 dB 21 dB 23
dB 2.4 GHz
20 dB ( )
1 dB
23 dB 23 dB
( )
(
) Datasheet
IC
(
) Datasheet 2.4 GHz
0.7 dB
0.3 dB 0.4 dB
BFP640ESD Datasheet Datasheet
Datasheet

34. 33
2.16 BFP640ESD
2.17 BFP640ESD
2.
ADS BFP640ESD Infineon
BFP640ESD_spar10GHz_noisepar10GHz_spice10GHz_ADS_MWO.zip
s2p SPICE AWR MWO
BFP640ESD_MWO.sch Agilent ADS bfp640esd_ADS.dsn
ADS bfp640esd_ADS.dsn

35. 34
2.4
1. (Project)
(1) LNA24G
(2) 2.18 Copy Design dsn /network
(3) /network bfp640esd_ADS.dsn 2.19
Symbol Symbol
Library
(4) I-V Curve
Copy the transistor model to your project
2.18 bfp640esd_ADS.dsn
bfp640esd_ADS
X1
Use “Design Parameters…” to assign a symbol for this transistor
2.19 bfp640esd_ADS.dsn (symbol)

36. 35
2.
(1)
2.4 GHz ADS
(2) Bias_MinNF.dsn 2.20
I-V Curve 2.4 GHz ( )
NFmin
(3) IBB 0 µA 100 µA 10 µA -
VCE 0 V 4 V 0.2 V IBB
VCE I-V Curve( )
(4) Z0 50 50 2.21
dataset datadisplay
S_Param
SP1
Freq=2.4 GHz
CalcNoise=yes
S-PARAMETERS
Options
Options1
Tnom=25
Temp=16.85
OPTIONS
VAR
VAR2
Z0=50
VCEstep=0.2 V
VCEmax=4 V
VCEmin=0 V
IBBstep=10 uA
IBBmax=100 uA
IBBmin=0 uA
Eqn
Var
VAR
VAR1
Rload=50
IBB=0 A
VCE=0 V
Eqn
Var
DC
DC1
Step=VCEstep
Stop=VCEmax
Start=VCEmin
SweepVar="VCE"
DC
ParamSweep
Sweep2
Step=VCEstep
Stop=VCEmax
Start=VCEmin
SimInstanceName[6]=
SimInstanceName[5]=
SimInstanceName[4]=
SimInstanceName[3]=
SimInstanceName[2]=
SimInstanceName[1]="SP1"
SweepVar="VCE"
PARAMETER SWEEP
Term
Term2
Z=50 Ohm
Num=2
Term
Term1
Z=50 Ohm
Num=1
DC_Feed
DC_Feed2
DC_Block
DC_Block2
DC_Block
DC_Block1
DC_Feed
DC_Feed1
bfp640esd_ADS
X1
BFP640ESD
I_Probe
IC
V_DC
SRC1
Vdc=VCE
ParamSweep
Sweep1
SweepVar="IBB"
SimInstanceName[1]="Sweep2"
SimInstanceName[2]="DC1"
SimInstanceName[3]=
SimInstanceName[4]=
SimInstanceName[5]=
SimInstanceName[6]=
Start=IBBmin
Stop=IBBmax
Step=IBBstep
PARAMETER SWEEP
I_DC
SRC2
Idc=IBB
Ideal chokes and bypass caps.
DC-biasing voltage
Collector current probing
DC-biasing base current
Frequency is 2.4 GHz and turn on
“CalcNoise” to consider noise
Use “Options” to set Temp=16.85 according
to the standard definition and the room
temperature Tnom.
Set the ranges and steps
you like to run
2.20 (2.4 GHz)

37. 36
S_Param
SP1
Freq=2.4 GHz
CalcNoise=yes
S-PARAMETERS
VAR
VAR2
Z0=50
VCEstep=0.2 V
VCEmax=4 V
VCEmin=0 V
IBBstep=10 uA
IBBmax=100 uA
IBBmin=0 uA
Eqn
Var
Pass the variable Z0 to the dataset
2.21 Z0 dataset
(5) Datadisplay
dB(S21[0]) NFmin[0] 2.22
IBB VCE S21 NFmin S21[0]
NFmin[0] [0] 2.4 GHz
0 S21[0] NFmin[0] 2.4 GHz S21
S21[0] NFmin[0]
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
-20
-15
-10
-5
0
5
10
15
-25
20
IBB=0.000
IBB=10.0u
IBB=20.0uIBB=30.0uIBB=40.0uIBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u
VCE
dB(S21[0])
m1
m1
VCE=
dB(S21[0])=19.172
IBB=0.000050
1.800
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
2
4
6
8
10
0
12
IBB=0.000
IBB=10.0uIBB=20.0uIBB=30.0uIBB=40.0uIBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u
VCE
NFmin[0]
m2
m2
VCE=
NFmin[0]=600.9052m
IBB=0.000010
1.200000
BJT OFF BJT OFF
S21 is around 15 dB to 20 dB
Minimum NF is around 0.6 dB to 1 dB
2.22 S21 NFmin
(6) 2.22 BJT S21 15 dB 20 dB
0.6 dB 1 dB VCE 1 V
S21 NF ( )
( )
I-V Curve
S21 NF
(7) 2.23 IC VCE maker m3 I-V Curve
m3

38. 37
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
5.00m
10.0m
15.0m
20.0m
0.000
25.0m
IBB=0.000
IBB=10.0u
IBB=20.0u
IBB=30.0u
IBB=40.0u
IBB=50.0u
IBB=60.0u
IBB=70.0u
IBB=80.0u
IBB=90.0u
IBB=100.u
VCE
IC.i,A
m3
m3
VCE=
IC.i=5.406418m
IBB=0.000020
2.800000
Eqn frequency=SP.freq[0,0,0]
Eqn ICindex=find_index(IC[VCEindex],m3)
Eqn VCEindex=find_index(DC.VCE[0,::],indep(m3))
Eqn IC=-SRC1.i
Eqn DC_power=m3*indep(m3)
Eqn NFmin_at_bias_pt=NFmin[ICindex,VCEindex,0]
Collector DC current
Find index for the swept variable VCE and ICE
according to marker "m3" x-axis.
Minimum noise figure at the m3 bias point.
DC power comsumption when biased at marker "m3" (base current is ignored)
Basic information at the bias point m3.
These equations are used to find out the DC
consumption power and the minimum NF
according to the biased-point
I-V Curves
Put a maker “m3” to select a biased-point
indep(m3)
3.0000
m3[0]
5.4174 m
DC_power[0]
16.252 m
...min_at_bias_pt
651.19 m
frequency
2.400 G
DC pow er (W)ICVCE NFmin@biased-point
List a table and move maker “m3,” and you will see
the parameters varies for different biased-point.
2.23 m3
(8) NFmin 2.24 Maker m3
VCE( 3-V) VCE IC
NFmin 2.25 maker m3 ( VCE ) NFmin
m3 ( VCE) NFmin (
)
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
5.00m
10.0m
15.0m
20.0m
0.000
25.0m
IBB=0.000
IBB=10.0u
IBB=20.0u
IBB=30.0u
IBB=40.0u
IBB=50.0u
IBB=60.0u
IBB=70.0u
IBB=80.0u
IBB=90.0u
IBB=100.u
VCE
IC.i,A
m3
m3
VCE=
IC.i=2.902361m
IBB=0.000010
3.000000
2.00m
4.00m
6.00m
8.00m
10.0m
12.0m
14.0m
16.0m
18.0m
0.000
20.0m
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0.4
2.0
IC
NFmin,dB
NFmin versus IC, at VCE (set by m3)
I-V Curve
Eqn VCEindex=find_index(DC.VCE[0,::],indep(m3))
Write an equation to find the index of VCE
according to the marker m3
NFmin v.s. IC at a specified VCE
2.24 NFmin
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
5.00m
10.0m
15.0m
20.0m
0.000
25.0m
IBB=0.000
IBB=10.0u
IBB=20.0u
IBB=30.0u
IBB=40.0u
IBB=50.0u
IBB=60.0u
IBB=70.0u
IBB=80.0u
IBB=90.0u
IBB=100.u
VCE
IC.i,A
m3
m3
VCE=
IC.i=5.406418m
IBB=0.000020
2.800000
I-V Curves
Move the maker “m3” and observe the
variation of NFmin for different biased-points.
2.00m
4.00m
6.00m
8.00m
10.0m
12.0m
14.0m
16.0m
18.0m
0.000
20.0m
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.4
2.2
IC
NFmin,dB
2.00m
4.00m
6.00m
8.00m
10.0m
12.0m
14.0m
16.0m
18.0m
0.000
20.0m
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.4
2.2
IC
NFmin,dB
2.00m
4.00m
6.00m
8.00m
10.0m
12.0m
14.0m
16.0m
18.0m
0.000
20.0m
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.4
2.2
IC
NFmin,dB
2.00m
4.00m
6.00m
8.00m
10.0m
12.0m
14.0m
16.0m
18.0m
20.0m
0.000
22.0m
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.4
2.2
IC
NFmin,dB
(1) Move “m3” vertically to keep VCE constant (IBB or IC varies)
(2) Move “m3” horizontally to keep IC constant (VCE varies)
2.25 NFmin ( m3 )

39. 38
(9) m3 VCE NFmin IC
VCE NFmin IC IC NFmin
VCE VCE IC NFmin
(10) NFmin 2.24
IBBstep 1 uA NFmin
(11) 2.26 m3
K µ K 1
( MSG) µ
1 ( MSG) µ
1 ( MAG) µ
dB(S_11)
-6.7279
dB(S_12)
-23.460
dB(S_21)
17.996
dB(S_22)
-7.0302
Transistor S-parameter at bias point m3
Use these equations to find S-parameters, stability factor, and maximum available gain at
certain biased-point.
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
-10
-5
0
5
10
15
20
-15
25
IBB=0.000
IBB=10.0u
IBB=20.0u
IBB=30.0uIBB=40.0uIBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u
VCE
MAG,dB
Maximum Available Gain versus IBB and VCE
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
-25
-20
-15
-10
-5
-30
0
IBB=0.000
IBB=10.0u
IBB=20.0u
IBB=30.0uIBB=40.0uIBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u
VCE
dB(S12)
dB(S12) versus IBB and VCE
m1
VCE=
dB(S21[0])=15.888
IBB=0.000010
2.000
Transistor dB(S21) versus IBB and VCE
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
-20
-15
-10
-5
0
5
10
15
-25
20
IBB=0.000
IBB=10.0u
IBB=20.0uIBB=30.0uIBB=40.0uIBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u
VCE
dB(S21)
m1
m1
VCE=
dB(S21[0])=15.888
IBB=0.000010
2.000
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
-14
-12
-10
-8
-6
-4
-2
-16
0 IBB=0.000
IBB=10.0u
IBB=20.0u
IBB=30.0u
IBB=40.0u
IBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u
VCE
dB(S11[0])
IBB=0.000
IBB=10.0u
IBB=20.0u
IBB=30.0u
IBB=40.0u
IBB=50.0u
IBB=60.0u
IBB=70.0u
IBB=80.0uIBB=90.0uIBB=100.u
dB(S22[0])
dB(S11) and dB(S22) versus IBB and VCE
You can also observe the swept S21, S12, S11, S22, and MAG
2.00m
4.00m
6.00m
8.00m
10.0m
12.0m
14.0m
16.0m
18.0m
0.000
20.0m
-15
-10
-5
0
5
10
15
-20
20
IC
dB(S21)
dB(S21) versus IC, at VCE (set by m3)
You can also observe how the dB(S21) varies with
respect to the biased current IC at certain VCE
K
0.6776
Stability Factor
MuL
0.7081
MuL
0.7081
Characteristics Impedance
Z0[0,0,0]
50.0000
Eqn MAG=max_gain(S) Maximum available/stable gain at all frequencies
Eqn S_11=S_bp(1,1)
Eqn S_12=S_bp(1,2)
Eqn S_21=S_bp(2,1)
Eqn S_22=S_bp(2,2)
Eqn K=stab_fact(S_bp)
Eqn S_bp=S[ICindex,VCEindex,0]
S-parameters at the bias point specified by marker m3.
Stability factors at the bias point m3.
Eqn MuL=mu(S_bp)
Eqn MuS=mu_prime(S_bp)
MAG[ICindex,VCEindex,0]
20.7283
Max Avaliable/Stable Gain (dB)
2.26 m3
3.
(1) ADS 2.27
Pgain_assoc (Associated power gain)

40. 39
(2) 2.27 m3
NFmin_at_bias_pt source
Sopt_at_bias_pt Zopt
Zload_wSopt Pgain_assoc_at_bias_pt
Eqn S_22p_at_bias=S_22p[ICindex,VCEindex]
Eqn Zload_wSopt=zopt(conj(S_22p_at_bias),Z0[0,0,0])
Eqn S_22p=S22[0]+(S12[0]*S21[0]*Sopt[0])/(1-S11[0]*Sopt[0])
Eqn GammaL_wSopt=conj(S_22p_at_bias)
S_22p : ref lection looking into the output of the dev ice,
when the source is optimal f or minimum noise f igure.
GammaL_wSopt is the complex conjugate of S22_p, and
is the optimal load ref lection coef f icient when Sopt is the source
ref lection coef f icient. Zload_wSopt is the corresponding impedance.
Output Conjugately Matching Impdeance Calculation (when input is noise matched)
Eqn Zopt=zopt(Sopt_at_bias_pt,Z0[0,0,0]) Source impedance for minimum noise figure at the bias
point specified by marker m3.
Eqn Sopt_at_bias_pt=Sopt[ICindex,VCEindex,0]
Source reflection coefficient for minimum noise figure
at frequency specified by marker m3. Sopt is the s-parameter
for optimum noise performance.
Optimum reflection coefficient(impedance) for minimum noise at the bias point m3.
Eqn Pgain_assoc_at_bias=Pgain_assoc[ICindex,VCEindex]
Eqn Pgain_assoc=pwr_gain(S[0],zopt(Sopt[0],Z0[0,0,0]),zopt(conj(S_22p),Z0[0,0,0]),Z0[0,0,0])
Transducer power gain with the source reflection coefficient Sopt for minimum noise figure, and the load
then conjugately matched. zopt() is just used to convert a reflection coefficient to an impedance.
Matching for Noise Figure
NFmin_at_bias_pt
0.6512
Minimum Noise Figure (dB)
Sopt_at_bias_pt
0.2799 / 57.8169
Soure Ref lection Coef f . f or NFmin
Zopt
59.0670 + j30.3691
Zopt f or NFmin
Zload_wSopt
31.8982 + j31.7136
Conjugate Matched Load
(f or input matched to NFmin)
Zopt Zload_wSopt
DUT*
Pgain_assoc_at_bias
18.6761
Power Gain (dB)
at this noise matched condition
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
-10
-5
0
5
10
15
20
-15
25
IBB=0.000
IBB=10.0u
IBB=20.0u
IBB=30.0u
IBB=40.0u
IBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u
VCE
Pgain_assoc
m4
m4
VCE=
Pgain_assoc=18.676
IBB=0.000020
3.000
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
5.00m
10.0m
15.0m
20.0m
0.000
25.0m
IBB=0.000
IBB=10.0u
IBB=20.0u
IBB=30.0u
IBB=40.0u
IBB=50.0u
IBB=60.0u
IBB=70.0u
IBB=80.0u
IBB=90.0u
IBB=100.u
VCE
IC.i,A
m3
m3
VCE=
IC.i=5.417352m
IBB=0.000020
3.000000
Use these equations to find the matching result (associated gain) for minimum NF at certain
biased-point.
Example: Move maker m3 to VCE=3V, IBB=20uA
Move maker m4 to VCE=3V, IBB=20uA
You can find the associated gain is 18.676 dB
You can list out all parameters of interest, such as Nfmin,
optimum source reflection coefficient and impedance,
conjugate matched load impedance, and the associated
gain for this minimum NF matching at biased-point m3.
2.27 m3
(3) (
) 2.28 ADS m3
Smith Chart
( 50
) K<1
m3
(4) 2.29 page

41. 40
Eqn GammaS_at_bias_pt=sm_gamma1(S_bp)
Eqn GammaL_at_bias_pt=sm_gamma2(S_bp)
Zsource and Zload are the source and load impedances to present to
the device for simultaneous conjugate matching, at the bias point m3.
These are not defined and return 0 if K<1.
Simultaneous conjugate match source and load reflection coefficients
at bias point m3. These are not defined and return 0 if K<1.
Eqn Zsource=sm_z1(S_bp,Z0[0,0,0])
Eqn Zload=sm_z2(S_bp,Z0[0,0,0])
Input/Output Simultaneously Conjugate Matched (input is NOT noise matched)
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
5.00m
10.0m
15.0m
20.0m
0.000
25.0m
IBB=0.000
IBB=10.0u
IBB=20.0u
IBB=30.0u
IBB=40.0u
IBB=50.0u
IBB=60.0u
IBB=70.0u
IBB=80.0u
IBB=90.0u
IBB=100.u
VCE
IC.i,A
m3
m3
VCE=
IC.i=5.417352m
IBB=0.000020
3.000000
K
0.6776
Stability Factor
Matching for Gain Zsource Zload
DUT*
max_gain(S_bp)
20.7283
Max Avaliable Gain (dB) Zsource
50.0000
Zload
50.0000
Simultaneous Match
(0.000 to 0.000)
Sopt_at_bias_pt
GammaS_at_bias_pt
GammaL_at_bias_pt
GammaL_wSopt
Optimal Source Reflection Coefficients for Mininum NF, Simultaneous Conjugate Matching,
and Load Reflection Coefficient for Simultaneous Conjugate Matching, and with source
matched for NFmin
Note: if the device (or circuit) is unstable at the bias point, the simultaneous conjugate matching impedances
are undefined and GammaL_at_bias_pt and GammaS_at_bias_pt default to 0. Also, MAG is set equal to the
maximum stable gain, |S21|/|S12|.
Gamma_S (NFmin)
Gamma_L when NFmin
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
5.00m
10.0m
15.0m
20.0m
0.000
25.0m
IBB=0.000
IBB=10.0u
IBB=20.0u
IBB=30.0u
IBB=40.0u
IBB=50.0u
IBB=60.0u
IBB=70.0u
IBB=80.0u
IBB=90.0u
IBB=100.u
VCE
IC.i,A
m3
m3
VCE=
IC.i=13.18580m
IBB=0.000060
600.0000m
K
1.1081
Stability Factor
Matching for Gain Zsource Zload
DUT*
max_gain(S_bp)
16.1195
Max Avaliable Gain (dB) Zsource
9.0268 / -46.0973
Zload
44.0380 / 56.7293
Simultaneous Match
(0.000 to 0.000)Sopt_at_bias_pt
GammaS_at_bias_pt
GammaL_at_bias_pt
GammaL_wSopt
Gamma_S (NFmin)
Gamma_L when NFmin
Use these equations to find the simultaneously conjugate matching condition. Noted that if such a biased condition
is not unconditionally stable, the simultaneous matching is impossible and thus Zsource and Zload can’t be defined.
Example: Biased@VCE=3V, IBB=20uA, K < 1
Example: Biased@VCE=0.6V, IBB=60uA, K > 1
Zsource and Zload can’t be found
Zsource and Zload are not defined
Gamma_L@NFmin
Optimum Gamma_S@NFmin
Zsource and Zload can be found
For noise matching
For maximum gain matching
Max Available/Stable Gain (dB)
Max Available/Stable Gain (dB)
2.28 m3
Arrange all the equations, tables, and draws we’ve done, and rename this datadisplay page as “Noise Condition.”
Now, you can move maker m3 to any biased-point and observe all the information you need.
m2
VCE=
NFm in[0]=595.2716m
IBB=0.000010
3.000000
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
2
4
6
8
10
0
12
I BB=0. 000
I BB=10. 0uI BB=20. 0u
I BB=30. 0uI BB=40. 0uI BB=50. 0uI BB=60. 0uI BB=70. 0uI BB=80. 0u
I BB=90. 0uI BB=100. u
VCE
NFmin[0]
m2
m2
VCE=
NFm in[0]=595.2716m
IBB=0.000010
3.000000
m 1
VCE=
dB(S21[0])=16.007
IBB=0.000010
3.000
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
-20
-15
-10
-5
0
5
10
15
-25
20
I BB=0. 000
I BB=10. 0u
I BB=20. 0uI BB=30. 0uI BB=40. 0uI BB=50. 0uI BB=60. 0uI BB=70. 0uI BB=80. 0uI BB=90. 0uI BB=100. u
VCE
dB(S21[0])
m1
m 1
VCE=
dB(S21[0])=16.007
IBB=0.000010
3.000
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
-14
-12
-10
-8
-6
-4
-2
-16
0 I BB=0. 000
I BB=10. 0u
I BB=20. 0u
I BB=30. 0u
I BB=40. 0u
I BB=50. 0u
I BB=60. 0uI BB=70. 0uI BB=80. 0u
I BB=90. 0uI BB=100. u
VCE
dB(S11[0])
I BB=0. 000
I BB=10. 0u
I BB=20. 0u
I BB=30. 0u
I BB=40. 0u
I BB=50. 0u
I BB=60. 0u
I BB=70. 0uI BB=80. 0u
I BB=90. 0u
I BB=100. u
dB(S22[0])
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
-25
-20
-15
-10
-5
-30
0
I BB=0. 000
I BB=10. 0u
I BB=20. 0u
I BB=30. 0u
I BB=40. 0uI BB=50. 0uI BB=60. 0u
I BB=70. 0uI BB=80. 0uI BB=90. 0uI BB=100. u
VCE
dB(S12)
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
-10
-5
0
5
10
15
20
-15
25
I BB=0. 000
I BB=10. 0u
I BB=20. 0u
I BB=30. 0u
I BB=40. 0uI BB=50. 0uI BB=60. 0uI BB=70. 0uI BB=80. 0uI BB=90. 0uI BB=100. u
VCE
MAG,dB
M inim um Nois e Figure v ers us IBB and VCETrans is tor dB(S21) v ers us IBB and VCE
Max im um Av ailable Gain v ers us IBB and VCE
dB(S12) vers us IBB and VCE
dB(S11) and dB(S22) v ers us IBB and VCE
m 4
VCE=
Pgain_as soc =-2.051
IBB=0.000000
1.200
0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 3. 50. 0 4. 0
- 10
- 5
0
5
10
15
20
- 15
25
I B B = 0 . 0 0 0
I B B = 1 0 . 0 u
I B B = 2 0 . 0 u
I B B = 3 0 . 0 uI B B = 4 0 . 0 u
I B B = 5 0 . 0 uI B B = 6 0 . 0 uI B B = 7 0 . 0 uI B B = 8 0 . 0 uI B B = 9 0 . 0 uI B B = 1 0 0 . u
VCE
Pgain_assoc
m 4
m 4
VCE=
Pgain_as soc =-2.051
IBB=0.000000
1.200
As s oc iated Power Gain (input matc hed for NFm in,
output then c onjugately m atc hed) v ers us IBB and VCE
Eqn M AG =m ax_gain( S)
M ax im um av ailable/s table gain at all frequenc ies
Eqn f r equency=SP. f r eq[ 0, 0, 0]
Eqn I Cindex=f ind_index( I C[ VCEindex] , m 3)
Eqn VCEindex=f ind_index( DC. VCE[ 0, : : ] , indep( m3) )
Eqn I C=- SRC1. i
Eqn
DC_power =m3*indep( m 3)
Eqn G amm aS_at _bias_pt =sm _gam ma1( S_bp)
Eqn G amm aL_at _bias_pt =sm _gam ma2( S_bp)
Eqn Zopt=zopt ( Sopt _at _bias_pt , Z0[ 0,0, 0] )
Eqn S_11=S_bp( 1, 1)
Eqn S_12=S_bp( 1, 2)
Eqn
S_21=S_bp( 2, 1)
Eqn
S_22=S_bp( 2, 2)
Eqn
S_22p_at _bias=S_22p[ I Cindex, VCEindex]
Eqn
Pgain_assoc_at _bias=Pgain_assoc[ ICindex, VCEindex]
Eqn Zload_wSopt =zopt ( conj( S_22p_at _bias) , Z0[ 0, 0, 0] )
Eqn K=st ab_f act ( S_bp)
Eqn Pgain_assoc=pwr _gain( S[ 0] , zopt ( Sopt [ 0] , Z0[ 0, 0, 0] ) , zopt ( conj( S_22p) , Z0[ 0, 0, 0] ) , Z0[ 0, 0, 0] )
Eqn
S_22p=S22[ 0] +( S12[ 0] *S21[ 0] *Sopt [ 0] ) / ( 1- S11[ 0] *Sopt [ 0] )
Eqn G amm aL_wSopt =conj( S_22p_at _bias)
Eqn S_bp=S[ I Cindex, VCEindex, 0]
Eqn
NFm in_at _bias_pt =NFm in[ I Cindex, VCEindex, 0]
S-param eters at the bias point s pec ified by m arker m 3.
Sourc e impedanc e for m inim um nois e figure at the bias
point s pec ified by m ark er m 3.
Stability fac tors at the bias point m 3.
Zs ourc e and Zload are the s ourc e and load im pedanc es to pres ent to
the dev ic e for s im ultaneous c onjugate m atc hing, at the bias point m3.
These are not defined and return 0 if K<1.
S_22p : reflec tion look ing into the output of the dev ic e,
when the s ourc e is optim al for m inim um nois e figure.
Gam m aL_wSopt is the c om plex c onjugate of S22_p, and
is the optimal load reflec tion c oeffic ient when Sopt is the s ourc e
reflec tion c oeffic ient. Zload_wSopt is the c orres ponding impedanc e.
Sim ultaneous c onjugate m atc h s ource and load reflec tion c oeffic ients
at bias point m 3. Thes e are not defined and return 0 if K<1.
Trans duc er power gain with the s ourc e reflec tion c oeffic ient Sopt for m inim um noise figure, and the load
then c onjugately matc hed. z opt() is jus t us ed to c onv ert a reflec tion c oeffic ient to an im pedanc e.
Collec tor DC c urrent
Find index for the s wept v ariable VCE and ICE
ac c ording to m ark er "m3" x -ax is .
M inim um nois e figure at the m 3 bias point.
DC power c om s um ption when bias ed at m ark er "m 3" (bas e c urrent is ignored)
m 3
VCE=
IC.i=5.417352m
IBB=0.000020
3.000000
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
5.00m
10.0m
15.0m
20.0m
0.000
25.0m
I BB=0. 000
I BB=10. 0u
I BB=20. 0u
I BB=30. 0u
I BB=40. 0u
I BB=50. 0u
I BB=60. 0u
I BB=70. 0u
I BB=80. 0u
I BB=90. 0u
I BB=100. u
VCE
IC.i,A
m3
m 3
VCE=
IC.i=5.417352m
IBB=0.000020
3.000000
I/V Curv e (Selec t Bias ing Point v ia m ak er m 3)
Eqn Sopt_at _bias_pt =Sopt [ I Cindex, VCEindex, 0]
Eqn Zsour ce=sm _z1( S_bp, Z0[ 0, 0, 0] )
Eqn
Zload=sm _z2( S_bp, Z0[ 0, 0, 0] )
Source reflec tion c oeffic ient for m inimum nois e figure
at frequenc y s pec ified by m ark er m 3. Sopt is the s -param eter
for optim um nois e perform anc e.
(1) (2)
Bas ic inform ation at the bias point m 3.
Optimum reflec tion c oeffic ient(im pedanc e) for m inim um nois e at the bias point m 3.
Output Conjugately M atc hing Im pdeanc e Calc ulation (when input is nois e m atc hed)
Input/Output Sim ultaneous ly Conjugate M atc hed (input is NOT nois e matc hed)
Move marker m3 to selectbias point.
All listings and impedances on Smith Chartwill be updated.
Matching for Gain Zs ourc e Zload
DUT*
(0.000 to 0.000)
Sopt_at_bias_pt
GammaS_at_bias_pt
GammaL_at_bias_pt
GammaL_wSopt
Optim al Sourc e Reflec tion Coeffic ients for M ininum NF, Simultaneous Conjugate M atc hing,
and Load Reflec tion Coeffic ient for Sim ultaneous Conjugate M atc hing, and with s ourc e
m atc hed for NFm in
Note: if the dev ic e (or c irc uit) is uns table at the bias point, the s im ultaneous c onjugate m atc hing im pedances
are undefined and Gam m aL_at_bias _pt and Gam m aS_at_bias _pt default to 0. Als o, M AG is s et equal to the
m ax im um stable gain, |S21|/|S12|.
2.00m
4.00m
6.00m
8.00m
10.0m
12.0m
14.0m
16.0m
18.0m
0.000
20.0m
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0.4
2.0
IC
NFmin,dB
NFmin versus IC, at VCE (set by m3)
2.00m
4.00m
6.00m
8.00m
10.0m
12.0m
14.0m
16.0m
18.0m
0.000
20.0m
-15
-10
-5
0
5
10
15
-20
20
IC
dB(S21)
dB(S21) v ers us IC, at VCE (s et by m 3)
indep( m 3)
3. 0000
m3[ 0]
5. 4174 m
DC_power [0]
16. 252 m
f r equency
2. 400 G
VCE IC DC power (W)
dB( S_11)
- 6. 7279
dB( S_12)
- 23. 460
dB( S_21)
17. 996
dB( S_22)
- 7. 0302
Trans is tor S-param eter at bias point m 3
K
0. 6776
Stability Fac tor
Z0[ 0, 0, 0]
50. 0000
Charac teris tic s Im pedanc e
m ax_gain( S_bp)
20. 7283
M ax Av aliable/Stable Gain (dB)Zsour ce
50. 0000
Zload
50. 0000
Sim ultaneous M atc h
Matching for Noise Figure
NFm in_at _bias_pt
0. 6512
M inimum Nois e Figure (dB)
Sopt _at _bias_pt
0. 2799 / 57. 8169
Soure Reflec tion Coeff. for NFm in
Zopt
59. 0670 + j30. 3691
Zopt for NFm in
Zload_wSopt
31. 8982 + j31. 7136
Conjugate M atc hed Load
(for input m atc hed to NFm in)
Zopt Zload_wSopt
DUT*
Pgain_assoc_at _bias
18. 6761
Power Gain (dB)
at this nois e m atc hed c ondition
Gam ma_S (NFm in)
Gam ma_L when NFm in
Bias Point Selector
Updated Information according to the Bias Point m3
Eqn M uL=m u( S_bp)
Eqn M uS=m u_pr im e( S_bp)
M uL
0. 7081
M uL
0. 7081
M AG [ I Cindex, VCEindex, 0]
20. 7283
M ax Av aliable/Stable Gain (dB)
2.29 Datadisplay page

42. 41
4.
(1) Bias_MinNF.dsn Bias_MinNF.dds Bias_MinNF_choose.dsn
Bias_MinNF_choose.dds
2.30 IBB
IBBstep
VAR
VAR2
Z0=50
VCEstep=0.2 V
VCEmax=4 V
VCEmin=0 V
IBBstep=1 uA
IBBmax=30 uA
IBBmin=0 uA
Eqn
Var
Rload=50
IBB=0 A
DC
DC1
Step=VCEstep
Stop=VCEmax
Start=VCEmin
SweepVar="VCE"
DC
ParamSweep
Sweep2
SimInstanceName[4]=
SimInstanceName[3]=
SimInstanceName[2]=
SimInstanceName[1]="SP1"
SweepVar="VCE"
PARAMETER SWEEP
ParamSweep
Sweep1
SweepVar="IBB"
SimInstanceName[1]="Sweep2"
SimInstanceName[2]="DC1"
SimInstanceName[3]=
SimInstanceName[4]=
PARAMETER SWEEP
Simulating with finer
step and range.
2.30 I-V
(2) 2.31 NFmin Pgain_assc MAG VCE
3 IC 6.12 mA VCE IC NFmin
(a) 20 mW 18.89 mW
(
) 16 mW
(b) ( IC NFmin
) NF
NF NF
NF 1.5 dB NF
1.5 dB NF
NF
(c)
( ) 15 dB
Pgain_assoc 15 dB
Pgain_assoc MAG
NF
(d) Smith Chart

43. 42
S11 S22 (−5 dB ~ −3 dB)
0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0
1.00m
2.00m
3.00m
4.00m
5.00m
6.00m
7.00m
0.000
8.00m
IBB=0.000
IBB=1.00u
IBB=2.00u
IBB=3.00u
IBB=4.00u
IBB=5.00u
IBB=6.00u
IBB=7.00u
IBB=8.00u
IBB=9.00u
IBB=10.0u
IBB=11.0u
IBB=12.0u
IBB=13.0u
IBB=14.0u
IBB=15.0u
IBB=16.0u
IBB=17.0u
IBB=18.0u
IBB=19.0u
IBB=20.0u
IBB=21.0u
IBB=22.0u
IBB=23.0u
IBB=24.0u
IBB=25.0u
IBB=26.0u
IBB=27.0u
IBB=28.0u
IBB=29.0u
IBB=30.0u
VCE
IC.i,A
m3
m3
VCE=
IC.i=6.120396m
IBB=0.000023
3.000000
1.00m
2.00m
3.00m
4.00m
5.00m
6.00m
7.00m
0.000
8.00m
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0.4
2.0
IC
NFmin,dB
m5
m5
indep(m5)=
vs(NFmin[VCEindex,0],IC.i[VCEindex])=0.670226
0.006120
NFmin versus IC, at VCE (set by m3)
MuL
0.7391
MuL
0.7391
K
0.7203
Stability Factor
indep(m3)
3.0000
m3[0]
6.1204 m
DC_power[0]
18.361 m
DC power (W)ICVCE
NFmin_at_bias_pt
0.6702
Minimum Noise Figure (dB)
1.00m
2.00m
3.00m
4.00m
5.00m
6.00m
7.00m
0.000
8.00m
0
5
10
15
20
-5
25
IC
MAG[VCEindex,0]
m6
Pgain_assoc[VCEindex]
m7
m6
indep(m6)=
vs(MAG[VCEindex,0],IC.i[VCEindex])=21.044851
0.006120
m7
indep(m7)=
plot_vs(Pgain_assoc[VCEindex], IC.i[VCEindex])=18.892510
0.006120
MAG[ICindex,VCEindex,0]
21.0449
Max Avaliable/Stable Gain (dB)
Pgain_assoc_at_bias
18.8925
Power Gain (dB)
at this noise matched condition
Select a biasing point that has a reasonable gain, NF, and power consumption (constrained by spec.)
2.31 I-V Curve NFmin Pgain_assc MAG
5.
(1) IBB = 23 uA VCE = 3 V IC = 6.12 mA
18.36 mW 0.67 dB
18.89 dB 1 MSG
21.04 dB
(
0 ~ 10 GHz 0 ~ 16 GHz
20 GHz 40 GHz )

44. 43
(2) Bias_MinNF_choose.dsn Bias_MinNF_stability_BW.dsn
2.32
Options
Options1
Tnom=25
Temp=16.85
OPTIONS
S_Param
SP1
Freq=
CalcNoise=y es
Step=50 MHz
Stop=10 GHz
Start=0.05 GHz
S-PARAMETERS
DC
DC1
Step=
Stop=
Start=
SweepVar=
DC
VAR
VAR1
Z0=50
Rload=50
IBB=23 uA
VCE=3 V
Eqn
Var
Term
Term2
Z=50 Ohm
Num=2DC_Block
DC_Block2
DC_Feed
DC_Feed1
I_DC
SRC2
Idc=IBB
DC_Block
DC_Block1
DC_Feed
DC_Feed2Term
Term1
Z=50 Ohm
Num=1
bf p640esd_ADS
X1
BFP640ESD
I_Probe
IC
V_DC
SRC1
Vdc=VCE
Sweep frequency for a fixed biased-point
2.32
(3) Datadisplay
m1
freq=
NFmin=670.2263m
2.400000GHz
1 2 3 4 5 6 7 8 90 10
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0.4
2.0
freq, GHz
NFmin,dB
m1 m1
freq=
NFmin=670.2263m
2.400000GHz
1 2 3 4 5 6 7 8 90 10
5
10
15
20
25
0
30
freq, GHz
dB(S21)
1 2 3 4 5 6 7 8 90 10
-50
-45
-40
-35
-30
-25
-20
-55
-15
freq, GHz
dB(S12)
1 2 3 4 5 6 7 8 90 10
15
20
25
30
35
10
40
freq, GHz
MAG,dB Minimum Noise Figure versus frequencyTransistor dB(S21) versus frequency
Maximum Available(Stable) Gain versus frequency
dB(S12) versus frequency
m2
freq=
Pgain_assoc=18.893
2.400GHz
1 2 3 4 5 6 7 8 90 10
10
15
20
25
30
35
40
45
5
50
freq, GHz
Pgain_assoc
m2
m2
freq=
Pgain_assoc=18.893
2.400GHz
Associated Power Gain (input matched for NFmin,
output then conjugately matched) v ersus f requency
m3
freq=
MuS=0.746
2.400GHz
1 2 3 4 5 6 7 8 90 10
1
-1
2
freq, GHz
MuS
m3
MuL
m3
freq=
MuS=0.746
2.400GHz
1 2 3 4 5 6 7 8 90 10
-7
-6
-5
-4
-3
-2
-1
-8
0
freq, GHz
dB(S11)
dB(S11) versus frequency
1 2 3 4 5 6 7 8 90 10
-12
-10
-8
-6
-4
-2
-14
0
freq, GHz
dB(S22)
dB(S22) versus frequency Stability factor
Transistor S-parameter
Eqn MAG=max_gain(S) Maximum available(stable) gain at all frequencies
Eqn frequency=SP.freq
Eqn GammaS_all_freq=sm_gamma1(S)
Eqn GammaL_all_freq=sm_gamma2(S)
Eqn Zopt=zopt(Sopt,Z0)
Eqn Zload_wSopt=zopt(conj(S_22p),Z0)
Eqn K=stab_fact(S)
Eqn Pgain_assoc=pwr_gain(S,zopt(Sopt,Z0),zopt(conj(S_22p),Z0),Z0)
Eqn S_22p=S22+(S12*S21*Sopt)/(1-S11*Sopt)
Eqn GammaL_wSopt=conj(S_22p)
S-parameters, stabilityfactors, and MAG at all frequencies
Source impedance for minimum noise figure
Stabilityfactor at all frequencies
Zsource and Zload are the source and load impedances to present to
the device for simultaneous conjugate matching. These are not defined
and return 0 if K<1.
S_22p : reflection looking into the output of the device,
when the source is optimal for minimum noise figure.
GammaL_wSopt is the complexconjugate of S22_p, and
is the optimal load reflection coefficient when Sopt is the source
reflection coefficient. Zload_wSopt is the corresponding impedance.
Simultaneous conjugate match source and load reflection coefficients
at bias point m3. These are not defined and return 0 if K<1.
Transducer power gain with the source reflection coefficient Sopt for minimum noise figure, and the load
then conjugatelymatched. zopt() is just used to convert a reflection coefficient to an impedance.
Eqn Zsource=sm_z1(S,Z0)
Eqn Zload=sm_z2(S,Z0)
Optimum reflection coefficient(impedance) for minimum noise at all frequencies
Output ConjugatelyMatching Impdeance Calculation (when input is noise matched)
Input/Output SimultaneouslyConjugate Matched (input is NOT noise matched)
Eqn MuL=mu(S)
Eqn MuS=mu_prime(S)
2.32

45. 44
(4) 2.33
2.4 GHz
Eqn Source_stabcir1=s_stab_circle(S,51)
Eqn Load_stabcir1=l_stab_circle(S,51)
indep(Source_stabcir1) (0.000 to 51.000)
Source_stabcir1
indep(Load_stabcir1) (0.000 to 51.000)
Load_stabcir1
2.33
(5) Datadisplay Rectangular plot Trace Expression 2.34
maker fm1 fm1 2.4 GHz
fm1
datadisplay
Move marker fm1 to desiredfrequency point.
Frequency Point Selector
fm1
indep(fm1)=
plot_vs([0::sweep_size(frequency)-1],frequency)=47.00000
2.400000G
1.0E9 2.0E9 3.0E9 4.0E9 5.0E9 6.0E9 7.0E9 8.0E9 9.0E90.0 1.0E10
0.0
1.0E6
frequency
fm1
fm1
indep(fm1)=
plot_vs([0::sweep_size(frequency)-1],frequency)=47.00000
2.400000G
2.34
(6) Datadisplay Smith Chart 2.35 rhos
Smith Chart 2000 ( ) Smith Chart

46. 45
Eqn tindex=[0::2000]
Eqn rhos=sqrt(tindex/2000)*exp(j*2*sqrt(pi*tindex))
tindex is a vector of numbers 0,1,2,3,...,2000.
rhos are 2001 complex reflection coefficients.
Show 2000 points on Smith Chart
indep(rhos) (0.000 to 2000.000)
rhos
indep(rhos) (0.000 to 2000.000)
rhos
indep(rhos) (0.000 to 2000.000)
rhos
indep(rhos) (0.000 to 2000.000)
rhos
Scatter type
Use lighter symbol color
Copy
Smith Chart 1Smith Chart 2
Preparing 2 Smith Charts for input and output stability circles
Plot equation “rhos” on a Smith Chart
2.35 Smith Chart
(7) 2.36 Smith Chart
AutoScale Smith Chart 1
list
Smith Chart
2.4 GHz
(8) 2.37
(Shunt) (Series)
BJT CE FET CS (Degeneration)
CE CS

47. 46
indep(Source_stabcir) (0.000 to 51.000)
Source_stabcir
indep(rhos) (0.000 to 2000.000)
rhos
indep(Load_stabcir) (0.000 to 51.000)
Load_stabcir
indep(rhos) (0.000 to 2000.000)
rhos
indep(Source_stabcir) (0.000 to 51.000)
Source_stabcir
indep(Load_stabcir) (0.000 to 51.000)
Load_stabcir
Outside
Source Stable Region
Outside
Load Stable Region
Source Stability Circle Load Stability Circle
Source Stability Circle Load Stability Circle
Set Smith Chart Radius < 1
Show the Stable region
Stable
Stable
Unstable
Unstable
Eqn Source_stabcir=s_stab_circle(S[fm1],51)
Eqn Load_stabcir=l_stab_circle(S[fm1],51)
Source and Load Stability Circles
Draw the stability circles at frequency “fm1”
2.36 2.4 GHz
1R
2R
6R
5R
3R
4R
• Stabilization methods described below are used to stabilize the transistor
unconditionally.
Stabilization of input port through series or shunt resistance, eg., R1, R2.
Stabilization of output port through series or shunt resistance, eg., R3, R4.
Stabilization using series or shunt negative feedback, eg., R5, R6. Inductances and
capacitances are also commonly used as feedback elements.
Stabilization results in a loss of gain and an increase in noise figure.
shunt negative feedback
series negative feedback
(degeneration)
2.37

48. 47
(9) 2.37 2.38
( )
2.39 DC block
2.40
1R 3R
2R 4R
1R 3R 1R
4R 2R
3R
2R 4R
Case (a): Input series Case (b): Input parallel Case (c): Output series Case (d): Output parallel
Case (e)
Input series / Output series
Case (f)
Input series / Output parallel
Case (g)
Input parallel/ Output series
Case (h)
Input parallel/ Output parallel
2.38
2R 4R
Blocks are needed to prevent DC biasing
current flow through the stabilizing resistors.
2.39 DC block
1R 3R
VBias VBiasDon’t block your bias
1R 3R
VBias VBias
2.40

49. 48
(10) 2.38(a)
Smith Chart ( Gonzalez
3.3 Stability Considerations ) 2.41
Datadisplay maker Smith
Chart r (
maker g)
7.7
9
(11) 2.41 MAG
MSG
0.5 dB 18.9 dB
16.5 dB 2.5 dB MAG 19.9 dB Pgain_assoc
3.4 dB 3.4
dB 2.4 GHz
indep(Source_stabcir) (0.000 to 51.000)
Source_stabcir
indep(rhos) (0.000 to 2000.000)
rhos
m4
m4
indep(m4)=
rhos=0.733 / 179.349
impedance = Z0 * (0.154 + j0.006)
1075
Input series resistance = 0.154*50 Ohm = 7.7 Ohm
1R
Case (a): Input series
R
R1
R=9 Ohm
DC_Block
DC_Block2
I_DC
SRC2
Idc=IBB
DC_Feed
DC_Feed2 bf p640esd_ADS
X1
BFP640ESD
I_Probe
IC
indep(Source_stabcir) (0.000 to 51.000)
Source_stabcir
indep(rhos) (0.000 to 2000.000)
rhos
Inside
Source Stable Region
Stable
Unstable
1 2 3 4 5 6 7 8 90 10
1
-1
2
freq, GHz
MuS
m3
MuL
m3
freq=
MuS=1.036
2.400GHz
Unstable
Stable
Stabilization at 2.4 GHz /
Input Series R Mu=0.746, MAG/MSG= 21 dB, NFmin = 0.67 dB, Pgain_assoc=18.9 dB
Mu=1.036, MAG/MSG= 19.9 dB, NFmin = 1.16 dB, Pgain_assoc=16.5 dB
Before stabilizing
After stabilizing
Draw a circle to roughly
evaluate the input series
stabilizing resistance
Not whole band stable
It is stable at 2.4 GHz
2.41

50. 49
(12) 2.37
( )
2.42
g
indep(Source_stabcir) (0.000 to 51.000)
Source_stabcir
indep(rhos) (0.000 to 2000.000)
rhos
2R
Case (b): Input parallel
Input parallel stabilize is impossible
Mu= -, MAG/MSG= -, NFmin = -, Pgain_assoc= -
Stabilization at 2.4 GHz /
Input Parallel R
Stabilizing can’t be achieved
2.42
(13) 2.43 2.44 (10)
(11)
m4
indep(m4)=
rhos=0.614 / -179.141
impedance = Z0 * (0.239 - j0.007)
755
indep(Load_stabcir) (0.000 to 51.000)
Load_stabcir
indep(rhos) (0.000 to 2000.000)
rhos
m4
m4
indep(m4)=
rhos=0.614 / -179.141
impedance = Z0 * (0.239 - j0.007)
755
Output series R = 0.239*50 Ohm = 11.95 Ohm
3R
Case (c): Output series
R
R1
R=20 Ohm
DC_Block
DC_Block2
bf p640esd_ADS
X1
BFP640ESD
I_Probe
IC
Mu=0.746, MAG/MSG= 21 dB, NFmin = 0.67 dB, Pgain_assoc=18.9 dB
MuL=1.028, MAG/MSG= 19.96 dB, NFmin = 0.7 dB, Pgain_assoc=16.9 dB
indep(Load_stabcir) (0.000 to 51.000)
Load_stabcir
indep(rhos) (0.000 to 2000.000)
rhos
Outside
Load Stable Region
1 2 3 4 5 6 7 8 90 10
1
-1
2
freq, GHz
MuS
m3
MuL
m4
m3
freq=
MuS=1.024
2.400GHz
m4
freq=
MuL=1.028
2.400GHz
Unstable
Stable
Stable
Unstable
Stabilization at 2.4 GHz /
Output Series R
Draw a circle to roughly
evaluate the output series
stabilizing resistance
Before stabilizing
After stabilizing
Not whole band stable
It is stable at 2.4 GHz
2.43

51. 50
m4
indep(m4)=
rhos=0.555 / 1.014
impedance = Z0 * (3.491 + j0.099)
616
indep(Load_stabcir) (0.000 to 51.000)
Load_stabcir
indep(rhos) (0.000 to 2000.000)
rhos
m4
m4
indep(m4)=
rhos=0.555 / 1.014
impedance = Z0 * (3.491 + j0.099)
616
Output parallel R= 1/(0.286/50) Ohm = 174.8 Ohm
Mu=0.746, MAG/MSG= 21 dB, NFmin = 0.67 dB, Pgain_assoc=18.9 dB
4R
Case (d): Output parallel
Mu=1.015, MAG/MSG= 20.25 dB, NFmin = 0.69 dB, Pgain_assoc=17.32 dB
R
R1
R=140 Ohm
DC_Block
DC_Block3
DC_Block
DC_Block2
bf p640esd_ADS
X1
BFP640ESD
I_Probe
IC
indep(Load_stabcir) (0.000 to 51.000)
Load_stabcir
indep(rhos) (0.000 to 2000.000)
rhos
Outside
Load Stable Region
Stable
Unstable
1 2 3 4 5 6 7 8 90 10
1
-1
2
freq, GHz
MuS
m3
MuL
m4
m3
freq=
MuS=1.012
2.400GHz
m4
freq=
MuL=1.015
2.400GHz
Unstable
Stable
Before stabilizing
After stabilizing
Stabilization at 2.4 GHz /
Output Parallel R
Not whole band stable
It is stable at 2.4 GHz
2.44
(14) 2.45 2.38
case(e)~(h)
ADS tuning
1R
4R
Case (f)
Input series / Output parallel
MuS=1.62, MuL= 1.67, MAG/MSG= 14.8 dB, NFmin = 1.24 dB, Pgain_assoc=13.3 dB
1 2 3 4 5 6 7 8 90 10
2
3
4
5
1
6
freq, GHz
MuS
m3
MuL
m4
m3
freq=
MuS=1.620
2.400GHz
m4
freq=
MuL=1.667
2.400GHz
R
R1
R=47 OhmR
R2
R=9 Ohm
DC_Block
DC_Block3
DC_Block
DC_Block2
bf p640esd_ADS
X1
BFP640ESD
I_Probe
IC
Mu=0.746, MAG/MSG= 21 dB, NFmin = 0.67 dB, Pgain_assoc=18.9 dB
Before stabilizing
After stabilizing
Stabilization at 2.4 GHz / Input Series R and Output Parallel R
Whole band stable
2.45

52. 51
(15) (9) 2.38
10 GHz ( )
2.46
Smith Chart (
)
(2.4 GHz ) MAG NFmin
Pgain_assoc
(a)
(b) S11 S22
(c) S11 S22
indep(rhos) (0.000 to 2000.000)
rhos
Minimum series resistance
1 1 GHzf =
1 1.5 GHzf =1 2 GHzf =
1 3 GHzf =
1 5 GHzf =
Increasing frequency
2.46
(16) (15)
(15)
(17) (15)
L C
2.47

53. 52
2.48
2.49 RLC
(18) 2.48 2.49
(2.4 GHz ) MAG NFmin Pgain_assoc
1Z 3Z
High-band Stabilization
2Z 4Z
2.47
1Z 3Z
Low-band Stabilization
2Z 4Z
2.48
1Z 3Z
Band-pass Stabilization
2Z 4Z
2.49

54. 53
(19) 2.50
(
) 2.50
(2.4 GHz ) MAG NFmin
Pgain_assoc
R
R1
R=? Ohm
Term
Term2
Z=50 Ohm
Num=2
bfp640esd_ADS
X1
BFP640ESD
Term
Term1
Z=50 Ohm
Num=1
DC_Feed
DC_Feed2
DC_Block
DC_Block2
DC_Block
DC_Block1
DC_Feed
DC_Feed1
I_Probe
IC
V_DC
SRC1
Vdc=VCE
I_DC
SRC2
Idc=IBB
R
R1
R=? Ohm
DC_Block
DC_Block3 Term
Term2
Z=50 Ohm
Num=2
bfp640esd_ADS
X1
BFP640ESD
Term
Term1
Z=50 Ohm
Num=1
DC_Feed
DC_Feed2
DC_Block
DC_Block2
DC_Block
DC_Block1
DC_Feed
DC_Feed1
I_Probe
IC
V_DC
SRC1
Vdc=VCE
I_DC
SRC2
Idc=IBB
Shunt Feedback Stabilization
Feedback Resistance
Isolated from DC network
2.50
(20) (17) 2.51
L
L3
R=
R
R6
DC_Block
DC_Block6
C
C4
L
L2
R=
DC_Block
DC_Block5
R
R5
DC_Block
DC_Block4
C
C3
R
R4
C
C2
R
R3
R
R2
C
C1
DC_Block
DC_Block3
L
L1
R=
R
R1
Term
Term2
Z=50 Ohm
Num=2
bfp640esd_ADS
X1
BFP640ESD
Term
Term1
Z=50 Ohm
Num=1
DC_Feed
DC_Feed2
DC_Block
DC_Block2
DC_Block
DC_Block1
DC_Feed
DC_Feed1
I_Probe
IC
V_DC
SRC1
Vdc=VCE
I_DC
SRC2
Idc=IBB
Frequency-selective Shunt Feedback Stabilization
2.51

55. 54
(21) 2.52
BJT
50
( 50
IC )
R
R7
Term
Term2
Z=50 Ohm
Num=2
bfp640esd_ADS
X1
BFP640ESD
Term
Term1
Z=50 Ohm
Num=1
DC_Feed
DC_Feed2
DC_Block
DC_Block2
DC_Block
DC_Block1
DC_Feed
DC_Feed1
I_Probe
IC
V_DC
SRC1
Vdc=VCE
I_DC
SRC2
Idc=IBB
C
C5
R
R7
Term
Term2
Z=50 Ohm
Num=2
bfp640esd_ADS
X1
BFP640ESD
Term
Term1
Z=50 Ohm
Num=1
DC_Feed
DC_Feed2
DC_Block
DC_Block2
DC_Block
DC_Block1
DC_Feed
DC_Feed1
I_Probe
IC
V_DC
SRC1
Vdc=VCE
I_DC
SRC2
Idc=IBB
L
L4
R=
Term
Term2
Z=50 Ohm
Num=2
bfp640esd_ADS
X1
BFP640ESD
Term
Term1
Z=50 Ohm
Num=1
DC_Feed
DC_Feed2
DC_Block
DC_Block2
DC_Block
DC_Block1
DC_Feed
DC_Feed1
I_Probe
IC
V_DC
SRC1
Vdc=VCE
I_DC
SRC2
Idc=IBB
Series Feedback Stabilization (Degeneration)
C
C1
L
L4
R=
R
R2
Term
Term2
Z=50 Ohm
Num=2
bfp640esd_ADS
X1
BFP640ESD
Term
Term1
Z=50 Ohm
Num=1
DC_Feed
DC_Feed2
DC_Block
DC_Block2
DC_Block
DC_Block1
DC_Feed
DC_Feed1
I_Probe
IC
V_DC
SRC1
Vdc=VCE
I_DC
SRC2
Idc=IBB
Considered with bias
Considered with bias
Bypass to increase AC gain
No DC disturb
High frequency degeneration
No DC disturb
Bandpass degeneration
DC path
2.52

56. 55
(22)
( )
(23) 2.53
( Smith Chart
) (1k Ohm)
2.4 GHz 1.2 dB MAG 19.56 dB
18.2 dB S11 S22 −10 dB −15 dB
1 GHz 6 GHz
Smith Chart
MuS=1.012, MuL= 1.014, MAG/MSG= 19.56 dB, NFmin = 1.2 dB, Pgain_assoc=18.2dB
1 2 3 4 5 6 7 8 90 10
1.05
1.10
1.15
1.20
1.25
1.00
1.30
freq, GHz
MuS
m3
MuL
m4
m3
freq=
MuS=1.012
2.400GHz
m4
freq=
MuL=1.014
2.400GHz
Stabilization at 2.4 GHz / Input Parallel R and Shunt Feedback
Mu=0.746, MAG/MSG= 21 dB, NFmin = 0.67 dB, Pgain_assoc=18.9 dB
Before stabilizing
After stabilizing
R
R2
R=1 kOhm
R
R1
R=800 Ohm
DC_Block
DC_Block5
DC_Block
DC_Block4
DC_Block
DC_Block2
Term
Term2
Z=50 Ohm
Num=2
DC_Feed
DC_Feed1
I_DC
SRC2
Idc=IBB
DC_Block
DC_Block1
DC_Feed
DC_Feed2Term
Term1
Z=50 Ohm
Num=1
bf p640esd_ADS
X1
BFP640ESD
I_Probe
IC
V_DC
SRC1
Vdc=VCE
2.53

57. 56
(24) DC Block 2.54
(50 ) 1/10 1/20 1/20 26
pF 27 pF
SRF
2.4 GHz SRF block
2.4 GHz
1/10
SRF
C
C2
C=27 pF
C
C1
C=27 pF
R
R2
R=1 kOhm
R
R1
R=800 Ohm
DC_Block
DC_Block2
Term
Term2
Z=50 Ohm
Num=2
DC_Feed
DC_Feed1
I_DC
SRC2
Idc=IBB
DC_Block
DC_Block1
DC_Feed
DC_Feed2Term
Term1
Z=50 Ohm
Num=1
bf p640esd_ADS
X1
BFP640ESD
I_Probe
IC
V_DC
SRC1
Vdc=VCE
Put a practical value of
capacitance
Put a practical value of
capacitance
ω
< 01
20
Z
j C
> 26 pFC
@2.4 GHz
2.54 DC Block
(25)
100 GHz
10 20 30 40 50 60 70 80 900 100
1.05
1.10
1.15
1.20
1.25
1.30
1.00
1.35
freq, GHz
MuS
m3
MuL
m4
m3
freq=
MuS=1.013
2.550GHz
m4
freq=
MuL=1.016
2.550GHz
Check the stability at higher frequencies
2.55

58. 57
6.
(1) 2.56
( choke)
(2)
RF choke RF choke 2.57
choke RF
(VCC) ( 3 GHz ) SRF
choke λ/4 RF short(
bypass ) RF open choke SMD
RF λ/4
RF open RF short λ/4 RF short RF
open choke RF λ/4
SMD
choke
R
R7
bf p640esd_ADS
X4
BFP640ESD
R
R9
R
R8
R
R15
bfp640esd_ADS
X6
BFP640ESD
R
R16
R
R17
R
R14R
R10
R
R11
bfp640esd_ADS
X5
BFP640ESD
R
R12
R
R13R
R3
R
R4
bf p640esd_ADS
X2
BFP640ESD
R
R6
bf p640esd_ADS
X3
BFP640ESD
R
R5
Common Passive Biasing Circuits
VCE
IC
VCC
2.56

59. 58
MLIN
TL5
R
R24
R
R25
bfp640esd_ADS
X10
BFP640ESD
MRSTUB
Stub1
bfp640esd_ADS
X8
BFP640ESD
R
R21
R
R20
MLIN
TL1
C
C3
bfp640esd_ADS
X9
BFP640ESD
R
R23
R
R22
MLIN
TL3
MLOC
TL2
L
L1
R=
R
R18
R
R19
bfp640esd_ADS
X7
BFP640ESD
RF Chokes
Inductor as RF choke
λ/4 transmission line
as RF choke
RF short
RF bypass
RF open
RF open
λ/4 transmission line
as RF choke
λ/4 open stub
RF short
RF open
Radial open stub
RF short
RF open
RF open
2.57 choke
7. LNA
(1) Datadisplay
Bias_MinNF_Matching.dsn Bias_MinNF_Matching.dds 2.58
S_Param
SP1
Freq=
CalcNoise=yes
Step=50 MHz
Stop=3 GHz
Start=2 GHz
S-PARAMETERS
VAR
VAR1
Z0=50
Rload=50
VCC=3.3 V
Eqn
Var
Options
Options1
Tnom=25
Temp=16.85
OPTIONS
DC
DC1
Step=
Stop=
Start=
SweepVar=
DC
DC_Block
DC_Block2
DC_Block
DC_Block1
Term
Term1
Z=50 Ohm
Num=1
R
R4
R=96 kOhm
R
R2
R=1 kOhm
C
C2
C=27 pF
R
R1
R=800 Ohm
C
C1
C=27 pF
I_Probe
IB
R
R3
R=50 Ohm
L
L1
R=
L=18 nH
V_DC
SRC1
Vdc=VCC
I_Probe
IC
bfp640esd_ADS
X1
BFP640ESD
Term
Term2
Z=50 Ohm
Num=2
Stabilizing Ckt
Voltage feedback biasing
Use VCC
Here, we use a 3.3
V supply voltage Sweep from 2 GHz ~ 3 GHz
2.58 LNA

60. 59
(2) 2.58
ADS ADS
(3) 2.58 2.59
2.4 GHz~2.5 GHz
1.2 dB 18 dB ~ 17.8 dB Smith Chart
(Sopt )
(Gamma_L_wSopt ) 2 GHz 3 GHz 1 GHz
Smith Chart
m1
freq=
NFmin=1.203725
2.400000GHz
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.92.0 3.0
1.190
1.195
1.200
1.205
1.210
1.215
1.185
1.220
freq, GHz
NFmin,dB
m1
m1
freq=
NFmin=1.203725
2.400000GHz
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.92.0 3.0
16.4
16.6
16.8
17.0
17.2
17.4
17.6
17.8
18.0
16.2
18.2
freq, GHz
dB(S21)
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.92.0 3.0
-23.0
-22.8
-22.6
-22.4
-23.2
-22.2
freq, GHz
dB(S12)
m5
freq=
MAG=18.937
2.400GHz
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.92.0 3.0
18.2
18.4
18.6
18.8
19.0
19.2
18.0
19.4
freq, GHz
MAG,dB
m5
m5
freq=
MAG=18.937
2.400GHz
MinimumNoise Figure versus frequencyTransistordB(S21) versus frequency
Maximum Available(Stable) Gain versus frequency
dB(S12) versus frequency
m2
freq=
Pgain_assoc=17.981
2.400GHz
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.92.0 3.0
17.2
17.4
17.6
17.8
18.0
18.2
18.4
17.0
18.6
freq, GHz
Pgain_assoc
m2
m2
freq=
Pgain_assoc=17.981
2.400GHz
Associated PowerGain (input matched for NFmin,
output then conjugately matched) versus frequency
Eqn M AG=m ax _gain(S) Maximumavailable(stable) gain at all frequencies
Eqn frequency =SP.freq
Eqn Gam m aS_all_freq=s m _gamm a1(S)
Eqn
Gam m aL_all_freq=s m _gamm a2(S)
Eqn Zopt=zopt(Sopt,Z0)
Eqn Zload_wSopt=z opt(c onj(S_22p),Z0)
Eqn K=stab_fac t(S)
Eqn Pgain_as s oc=pwr_gain(S,z opt(Sopt,Z0),z opt(c onj(S_22p),Z0),Z0)
Eqn S_22p=S22+(S12*S21*Sopt)/(1-S11*Sopt)
Eqn Gam m aL_wSopt=conj(S_22p)
S-parameters at the bias point specified by marker fm.
Source impedance for minimum noise figure
Stability factor at all frequencies
Zsource and Zload are the source and load impedances to present to
the device for simultaneous conjugate matching. These are not defined
and return 0 if K<1.
S_22p : reflection looking into the output of the device,
when the source is optimal for minimumnoise figure.
GammaL_wSopt is the complex conjugate of S22_p, and
is the optimal load reflection coefficient when Sopt is the source
reflection coefficient. Zload_wSopt is the corresponding impedance.
Simultaneous conjugate match source and load reflection coefficients
at bias point m3. These are not defined and return 0 if K<1.
Transducer powergain with the source reflection coefficient Sopt forminimumnoise figure, and the load
then conjugately matched. zopt()is just used to convert a reflection coefficient to an impedance.
Eqn
Zsource=s m_z 1(S,Z0)
Eqn Zload=s m _z2(S,Z0)
Optimumreflection coefficient(impedance)for minimum noise at all frequencies
Output Conjugately Matching Impdeance Calculation (when input is noise matched)
Input/Output Simultaneously Conjugate Matched (input is NOTnoise matched)
m11
freq=
Sopt=0.171 / 138.227
impedance =Z0 * (0.755 + j0.178)
2.400GHz
m12
freq=
GammaL_wSopt=0.171 / 52.058
impedance =Z0 * (1.185 + j0.329)
2.450GHz
freq (2.000GHz to 3.000GHz)
Sopt
m11
GammaS_all_freq
GammaL_all_freq
GammaL_wSopt
m12
m11
freq=
Sopt=0.171 / 138.227
impedance =Z0 * (0.755 + j0.178)
2.400GHz
m12
freq=
GammaL_wSopt=0.171 / 52.058
impedance =Z0 * (1.185 + j0.329)
2.450GHz
Optimal Source Reflection Coefficients for MininumNF,Simultaneous Conjugate Matching,
and Load Reflection Coefficientfor Simultaneous Conjugate Matching,and with source
matched for NFmin
Note: if the device (orcircuit) is unstable at the bias point, the simultaneous conjugate matching impedances
are undefined and GammaL_at_bias_pt and GammaS_at_bias_pt default to 0. Also, MAG is set equal to the
maximum stable gain, |S21|/|S12|.
Gamma_S (NFmin)
Gamma_L when NFmin
fm1
indep(fm1)=
plot_vs([0::sweep_size(frequency)-1],frequency)=8.000000
2.400000G
2.1E9 2.2E9 2.3E9 2.4E9 2.5E9 2.6E9 2.7E9 2.8E9 2.9E92.0E9 3.0E9
0.0
1.0E6
frequenc y
fm1
fm1
indep(fm1)=
plot_vs([0::sweep_size(frequency)-1],frequency)=8.000000
2.400000G
Eqn MuL=mu(S)
m3
freq=
MuS=1.050
2.400GHz
m4
freq=
MuL=1.073
2.400GHz
2. 1 2. 2 2. 3 2. 4 2. 5 2. 6 2. 7 2. 8 2. 92. 0 3. 0
1. 04
1. 05
1. 06
1. 07
1. 08
1. 09
1. 03
1. 10
freq, GHz
MuS
m3
MuL
m4
m3
freq=
MuS=1.050
2.400GHz
m4
freq=
MuL=1.073
2.400GHz
Eqn MuS=mu_prime(S)
m9
freq=
dB(S(1,1))=-8.693
2.400GHz
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.92.0 3.0
-9.0
-8.8
-8.6
-8.4
-8.2
-8.0
-9.2
-7.8
freq, GHz
dB(S11)
m9
m9
freq=
dB(S(1,1))=-8.693
2.400GHz
dB(S11)versus frequency
m10
freq=
dB(S(2,2))=-18.825
2.500GHz
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.92.0 3.0
-19.6
-19.4
-19.2
-19.0
-18.8
-18.6
-18.4
-18.2
-18.0
-19.8
-17.8
freq, GHz
dB(S22)
m10
m10
freq=
dB(S(2,2))=-18.825
2.500GHz
dB(S22)versus frequency
m11
freq=
Sopt=0.171 / 138.227
impedance = Z0 * (0.755 + j0.178)
2.400GHz
m12
freq=
GammaL_wSopt=0.171 / 52.058
impedance = Z0 * (1.185 + j0.329)
2.450GHz
freq (2.000GHz to 3.000GHz)
Sopt
m11
GammaS_all_freq
GammaL_all_freq
GammaL_wSopt
m12
m11
freq=
Sopt=0.171 / 138.227
impedance = Z0 * (0.755 + j0.178)
2.400GHz
m12
freq=
GammaL_wSopt=0.171 / 52.058
impedance = Z0 * (1.185 + j0.329)
2.450GHz
Gamma_S (NFmin)
Gamma_L when NFmin
NFmin
Sweep from 2 GHz ~ 3 GHz :
The optimum noise point and the corresponding
Gamma_L are close to 50 Ohm.
2.59 LNA
(4)
[A]
[B]
[C]
[D]

61. 60
(5) [A] [D]
2.60 ”rhos” Smith Chart
GammaS GammaL maker Case [A]
Case [B] maker fm1
Case [C] GammaS ( Smith Chart
1 maker) GammaS
GammaLopt NF_at_GammaS Case [D]
GammaL ( Smith Chart 2 maker)
GammaL GammaSopt
NF_at_GammaSopt
Eqn GammaLopt=conj(S22[fm1] +S12[fm1]*S21[fm1]*GammaS/(1-S11[fm1]*GammaS))
Eqn GammaLopt_NFmin=GammaL_w Sopt[fm1]
(C) Optimal Gamma_L w hen the Gamma_S is at "maker GammaS"
(A) Optimal Gamma_L w hen the Gamma_S is at Sopt (optimal for minimum noise figure.)
Eqn GammaSopt=conj(S11[fm1]+S12[fm1]*S21[fm1]*GammaL/(1-S22[fm1]*GammaL))
(D) Optimal Gamma_S w hen the Gamma_L at "maker GammaL"
Source reflection coefficientEqn GammaS_ConjMatch=GammaS_all_freq[fm1]
Zsource is the impedance at marker GammaS.Eqn Zsource2=Z0*(1+GammaS)/(1-GammaS)
(B) Gamma_S for simultaneous conjugate matching at fm1
Reflection Coefficients Calculation
indep(rhos) (0.000 to 2000.000)
rhos
indep(rhos) (0.000 to 2000.000)
rhos
GammaS
GammaL
Smith Chart 1
Smith Chart 2
Eqn NF_lin_at_GammaS=NFmin_lin+4*(Rn[fm1]/Z0[fm1])*mag(GammaS-Sopt[fm1])**2/((1-mag(GammaS)**2)*mag(1+Sopt[fm1])**2)
Eqn NFmin_lin=10**(NFmin[fm1]/10)
Eqn NF_at_GammaS=10*log(NF_lin_at_GammaS)
Eqn NF_at_GammaS_ConjMatch=if (stab_fact(S[fm1]) >1) then 10*log(NF_lin_at_GammaS_ConjMatch) else 1000
Eqn NF_lin_at_GammaS_ConjMatch=NFmin_lin+4*(Rn[fm1]/Z0[fm1])*mag(GammaS_ConjMatch-Sopt[fm1])**2/((1-mag(GammaS_ConjMatch)**2)*mag(1+Sopt[fm1])**2 +1e-20)
(C) Noise figure for an arbitray Gamma_S (marker GammaS)
(B) Noise figure for simultaneously conjugate matching. (Only defined if K is >1. Otherwise the noise figure is set to 1000.)
(D) Noise figure for an arbitray Gamma_L (the source reflection coefficient is at GammaSopt)
Eqn NF_lin_at_GammaSopt=NFmin_lin+4*(Rn[fm1]/Z0[fm1])*mag(GammaSopt-Sopt[fm1])**2/((1-mag(GammaSopt)**2)*mag(1+Sopt[fm1])**2)
Eqn NF_at_GammaSopt=10*log(NF_lin_at_GammaSopt)
Noise Figure Calculation
(A) NFmin_lin (Miminum noise factor)
Create two Smith Charts with “rhos” on them, and separately put
makers named “GammaS” and “GammaL” on them.
Find reflection coefficients
for case [A] to [D]
Calculate NF for case [B] to [D]
2.60 Case[A] [D]
(6) 2.61 Case[A] [D]
(7) 2.62 ADS GA Gp
ADS ns_circle()

62. 61
Eqn Gt_num=mag(S21[fm1])**2 *(1-mag(GammaS)**2) *(1-mag(GammaLopt)**2)
Eqn Gt_den=mag((1-S11[fm1]*GammaS)*(1-S22[fm1]*GammaLopt) -S21[fm1]*S12[fm1]*GammaS*GammaLopt)**2
Eqn Gt_num_NFmin=mag(S21[fm1])**2 *(1-mag(Sopt[fm1])**2) *(1-mag(GammaLopt_NFmin)**2)
Eqn Gt_den_NFmin=mag((1-S11[fm1]*Sopt[fm1])*(1-S22[fm1]*GammaLopt_NFmin) -S21[fm1]*S12[fm1]*Sopt[fm1]*GammaLopt_NFmin)**2
Eqn Gtrans_power_NFmin=10*log(Gt_num_NFmin/Gt_den_NFmin)
(C) Gtrans_power: transducer power gain with the source reflection coefficient at marker GammaS, and the load then conjugately matched.
(A) Gtrans_power_NFmin: transducer power gain with the source reflection coefficient Sopt for minimum noise figure, and the load then conjugately matched.
Eqn Gtload_num=mag(S21[fm1])**2 *(1-mag(GammaSopt)**2) *(1-mag(GammaL)**2)
Eqn Gtload_den=mag((1-S11[fm1]*GammaSopt)*(1-S22[fm1]*GammaL) -S21[fm1]*S12[fm1]*GammaSopt*GammaL)**2
Eqn Gtrans_power_load=if (Gtload_num>0) then 10*log(Gtload_num/Gtload_den) else 1e6
(D) Gtrans_load : transducer power gain with the load reflection coefficient at marker GammaL, and the source then optimumly noise matched.
Eqn Gtrans_power=if (Gt_num>0) then 10*log(Gt_num/Gt_den) else 1e6
Transducer Power Gain Calculation
(B) Max. transducer power gain is equal to MAG(or MSG) when simulyaneously matched.
Transducer gain for case [A] to [D]
2.61 Case[A] [D]
Eqn Noise_circleMin=ns_circle(NFmin[fm1],NFmin[fm1],Sopt[fm1],Rn[fm1]/Z0[fm1],51)
Eqn Noise_circles=ns_circle(NFmin[fm1]+NFstep_size*[1::num_NFcircles],NFmin[fm1],Sopt[fm1],Rn[fm1]/Z0[fm1],51)
Eqn GAcircleMax=ga_circle(S[fm1],max_gain(S[fm1]))
Eqn GAcircles=ga_circle(S[fm1],max_gain(S[fm1])-GAstep_size*[0::num_GAcircles])
Eqn GPcircles=gp_circle(S[fm1],max_gain(S[fm1])-GPstep_size*[0::num_GPcircles])
Equations to Plot Noise and Gain Circles
Noise Circle
Available Power Gain Circle
Operating Power Gain Circle
Eqn num_NFcircles=3
Eqn NFstep_size=0.2 Eqn GAstep_size=1
Eqn num_GAcircles=3 Eqn num_GPcircles=3
Eqn GPstep_size=1
Set step size and number of circles to plot
Plot the transistor GA, Gp, and
Noise Circles on the Smith Chart.
2.62 GA Gp
(8) list Case[A]
Case[B] list Case[A]
1.2 dB 17.98 dB 50
(37.76 + j8.89) (59.8 + j15.87)
Case[B]
NF_at_GammaS_ConjMatch
2.1526
sm_z1(S[fm1],Z0[fm1])
9.1969 + j7.2047
sm_z2(S[fm1],Z0[fm1])
48.1343 + j70.9704
max_gain(S[fm1])
18.9366
NF with Zsource (valid for K>1)
Simultaneous Conjugate Matched (valid for K>1)
Zsource Zload MAG (or MSG for K<1)
(B) Matching Condition for Simultaneously Conjugate Matched
NFmin[fm1]
1.2037
NFmin (dB)
zopt(Sopt[fm1],Z0[fm1])
37.7643 + j8.8868
Source Impedance Zopt at NFmin
zin(GammaLopt_NFmin,Z0[fm1])
59.8045 + j15.8659
Optiomal Load Impedance
for source Zopt at NFmin Transducer Power Gain (dB)
Gtrans_power_NFmin
17.9810
(A) Matching Condition for Minimum Noise Figure
2.63 Case[A] [B]

63. 62
(9) 2.64 Smith Chart 1 GA GAcircles Noise_circles
( ) ( ) maker GammaS
2.64 list
GammaS GammaS
( ) list 2.63
Case[A] ( GammaS
Case[A] ) GammaS
GammaS
indep(GammaS)=
rhos=-0.11872 + j0.12612
impedance = 38.26607 + j9.95049
60
indep(rhos) (0.000 to 2000.000)
rhos
GammaSgain=18.937
gain=17.937
gain=16.937
gain=15.937
cir_pts (0.000 to 51.000)
GAcircles
indep(GammaLopt) (60.000 to 60.000)
GammaLopt
ns figure=1.404ns figure=1.604ns figure=1.804
Noise_circles
(0.000 to 0.000)
Sopt[fm1]
GammaLopt_NFmin
GammaS
indep(GammaS)=
rhos=-0.11872 + j0.12612
impedance = 38.26607 + j9.95049
60
NF at GammaS (dB)
NF_at_GammaS
1.2042
Zsource2
38.2661 + j9.9505
Source Impedance at GammaS
zin(GammaLopt,Z0[fm1])
58.7305 + j15.5482
Optiomal Load Impedance at GammaS Transducer Power Gain (dB)
Gtrans_power
17.9575
(C) Matching Condition for Arbitray GammaS
Gamma_S (NFmin)
Gamma_L when NFmin
GA = 17.937 dB
GA = 16.937 dB
GA = 15.937 dB
GA = 18.937 dB
NF= 1.404 dB
NF= 1.604 dB
NF= 1.804 dB
NFmin= 1.204 dB
2.64 GammaS ( )
(10) maker GammaS GA
( )
list 0.2 dB 0.8 dB

64. 63
− source
stability circle Smith Chart
GammaS
indep(GammaS)=
rhos=-0.45577 + j0.18782
impedance = 17.56757 + j8.71721
486
indep(rhos) (0.000 to 2000.000)
rhos
GammaS
gain=18.937
gain=17.937
gain=16.937
gain=15.937
cir_pts (0.000 to 51.000)
GAcircles
indep(GammaLopt) (486.000 to 486.000)
GammaLopt
ns figure=1.404ns figure=1.604ns figure=1.804
Noise_circles
(0.000 to 0.000)
Sopt[fm1]
GammaLopt_NFmin
GammaS
indep(GammaS)=
rhos=-0.45577 + j0.18782
impedance = 17.56757 + j8.71721
486
NF at GammaS (dB)
NF_at_GammaS
1.4718
Zsource2
17.5676 + j8.7172
Source Impedance at GammaS
zin(GammaLopt,Z0[fm1])
57.1651 + j46.3908
Optiomal Load Impedance at GammaS Transducer Power Gain (dB)
Gtrans_power
18.7382
(C) Matching Condition for Arbitray GammaS
Gamma_S (NFmin)
Gamma_L when NFmin
2.65 GammaS ( )
(11) 2.66 Smith Chart 2 GP GPcircles
( ) List GammaL
Loal-pull

65. 64
GammaL
indep(GammaL)=
rhos=0.36056 / 35.02213
impedance = Z0 * (1.61272 + j0.76714)
260
indep(rhos) (0.000 to 2000.000)
rhos
GammaL
gain=18.937
gain=17.937
gain=16.937
gain=15.937
cir_pts (0.000 to 51.000)
GPcircles
indep(GammaSopt) (260.000 to 260.000)
GammaSopt
GammaL
indep(GammaL)=
rhos=0.36056 / 35.02213
impedance = Z0 * (1.61272 + j0.76714)
260
NF_at_GammaSopt
1.6094
...ammaSopt,Z0[fm1])
15.0293 + j4.4503
zin(GammaL,Z0[fm1])
80.6361 + j38.3568
Gtrans_power_load
18.6958
NF with optimal Zsource
Optimal Zsource
when Zload is at GammaL Zload at GammaL Transducer Power gain (dB)
(D) Matching Condition for Arbitray GammaL
2.66 GammaL
(12) LNA 2.67
50 2.4
GHz ~ 2.5 GHz 1.2 dB 17.8 dB
C
C5
C=27 pF
Term
Term2
Z=50 Ohm
Num=2
L
L3
R=
L=1.68 nH
C
C4
C=0.27 pF
L
L2
R=
L=6 nH
C
C3
C=6 pF
Term
Term1
Z=50 Ohm
Num=1
R
R4
R=96 kOhm
R
R2
R=1 kOhm
C
C2
C=27 pF
R
R1
R=800 Ohm
C
C1
C=27 pF
I_Probe
IB
R
R3
R=50 Ohm
L
L1
R=
L=18 nH
V_DC
SRC1
Vdc=VCC
I_Probe
IC
bfp640esd_ADS
X1
BFP640ESD
2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.492.40 2.50
17.8
18.0
17.6
18.2
freq, GHz
Pgain_assoc
m2
m2
freq=
Pgain_assoc=17.903
2.450GHz
2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.492.40 2.50
1.192
1.194
1.196
1.198
1.200
1.202
1.204
1.206
1.208
1.190
1.210
freq, GHz
NFmin,dB
m1
m1
freq=
NFmin=1.202077
2.450000GHz
Gamma_S (NFmin)
Gamma_L when NFmin
freq (2.400GHz to 2.500GHz)
Sopt
GammaS_all_freq
GammaL_all_freq
GammaL_wSopt
Matched to 50 Ohm
2.67 LNA

66. 65
8.
(1) LNA Pout Pin
P1dB IP3
2.5
Datasheet
ADS
2.4 GHz ~ 2.5 GHz 17.8 dB
1.2 dB
13 dB 1.5 dB