Agilent ADS 模擬手冊 [實習2] 放大器設計

IV

([email protected])

April 2014

1

(Advanced Design System, ADS)

I ADS II DCS

1900 III

IV

ADS

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

3

s os

s o

Z Z

Z Z

−Γ =+

L oL

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 2111

221L

inL

S SS

S

ΓΓ = +− Γ

Transistor

[S]+

−sE

sZ

outΓinΓ

sΓ

Find input reflection coefficient:

12 2122

111s

outs

S SS

S

ΓΓ = +− Γ

Find output reflection coefficient:

1.3 inΓ outΓ

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

sZLZ

PAVNPAVS PLPin

Ms

interface interface

ML

inΓ

sΓ

outΓ

LΓ

1.4

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 Lp

in

PG

P=

• The transducer power gain LT p s

AVS

PG G M

P= =

• The available power gain AVN TA

AVS L

P GG

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

oZTransistor

oG

Output

matching

LG

Input

matching

sG

sΓ LΓ��

1.6 ( PA )

6

AG LNA 1.7

( sΓ ) sΓ outΓ outΓ

( L out∗Γ = Γ )

1E

oZ

oZTransistor

oG

Output

matching

LG

Input

matching

sG

sΓ LΓoutΓ� � �

1.7 ( LNA )

sΓ LΓ [ ]S 1.8

22

212 2

22

11

1 1L

p

in L

G SS

− Γ=

− Γ − Γ

• The Power Gain Gp

• The Transducer Power Gain GT

2 2 2 22 2

21 212 2 2 2

22 11

1 1 1 1

1 1 1 1s L s L

T

s in L s out L

G S SS S

− Γ − Γ − Γ − Γ= =

− Γ Γ − Γ − Γ − Γ Γ

• The Available Power Gain GA

22

212 2

11

1 1

1 1s

A

s out

G SS

− Γ=

− Γ − Γ 1.8

5.

1

1.2

<1sΓ <1LΓ inΓ outΓ 1inΓ <

inP 1outΓ <

( 1 )

1inΓ >

( 1outΓ >

7

Transistor

[S]+

−sE

sZ

outΓ

LZ

inΓ

sΓ LΓ

12 2111

221L

inL

S SS

S

ΓΓ = +− Γ

12 2122

111s

outs

S SS

S

ΓΓ = +− Γ

1sΓ <

12 2122

11

11

sout

s

S SS

S

ΓΓ = + <− Γ

1LΓ <

12 2111

22

11

Lin

L

S SS

S

ΓΓ = + <− Γ

and

( )22 11 12 212 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

8

LC

LCLr

1inΓ =

11 1S <

12 2111

221L

inL

S SS

S

ΓΓ = +− 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 2122

111s

outs

S SS

S

ΓΓ = +− Γ

22 1S < 22 1S >Case (1): Case (2):

• Criteria: virtually make , then and0sΓ = 22out SΓ =s oZ Z=

stable regionstable region

-planesΓ -planesΓ

0sΓ =0sΓ =

sCsC

sCsrsr

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

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

oZTransistor

oG

Output

matching

LG

Input

matching

sG

sΓLΓ22S

=12 0S

2 22

212 2

11 22

1 1

1 1s L

TU s o L

s L

G S G G GS S

− Γ − Γ= =

− Γ − Γ2

2

11

1

1s

s

s

GS

− Γ=

− Γ

2

21oG S=2

2

22

1

1L

L

L

GS

− 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 22 2

21 212 2 2 2

22 11

1 1 1 1

1 1 1 1s L s L

T

s in L s out L

G S SS S

− Γ − Γ − Γ − Γ= =

− Γ Γ − Γ − Γ − Γ Γ

12 2111

221L

inL

S SS

S

ΓΓ = +− Γ

• Transducer Power Gain GT

Unilateral condition12 0S =

11in SΓ =

1.12 (Unilateral case)

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 1.132

21p pG S g= ⋅ pg

(Normalized gain factor) 0 1 1pg =

pG 21S pg pG

pg pg

LΓ

( LΓ ) pG 1.6

11

( )2 2

21 2

212211

2222

1

1 11

L

p p

LL

L

SG S g

SS

S

− Γ= = ⋅ − ∆Γ − − Γ − Γ

• Unconditionally stable bilateral case:

( ) ( )

2 2

2 2 2 2 2 222 11 11 22 2

1 1

1 1 2Re

L Lp

L L L L

gS 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

pp

p

g CC

g S

∗

=+ − ∆ ( )

2 212 21 12 21

2 2

22

1 2

1

p p

p

p

K S S g S S gr

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

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

13

( )2 2

21 2

212222

1111

1

1 11

s

A a

ss

s

SG S g

SS

S

− Γ= = ⋅ − ∆Γ − − Γ − Γ

• Unconditionally stable bilateral case:

( ) ( )

2

2 2 2 2 221 22 11 1

1

1 2 Re

sAa

s s

Gg

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 − =

( )12 2

111a

a

a

g CC

g S

∗

=+ − ∆ ( )

2 212 21 12 21

2 2

11

1 2

1

a aa

a

K S S g S S gr

g S

− +=

+ − ∆� Center � Radius

• Available Power-Gain Circle:

where

1.16

9. (Available Power-Gain Circle)

AG 1.8 outΓ AG

outΓ AG 1.162

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.

(

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

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}}

SaSa(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_c irc le(Sa,51)

indep(In_stable_circle) (0.000 to 51.000)

In_s

tabl

e_ci

rcle

indep(Out_stable_circle) (0.000 to 51.000)

Out

_sta

ble_

circ

le

(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_c irc le(Sa,51)

Eqn Cs_cal=s_stab_c irc le_center_radius(Sa,"center")

Eqn rs_cal=s_stab_c irc le_center_radius(Sa,"radius")

CL_cal

1.310 / 47.706

rL_cal

0.457

Eqn CL_cal=l_stab_c irc le_center_radius(Sa,"center")

Eqn rL_cal=l_stab_c irc le_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

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_

circ

le_2

0dB

Gp_

circ

le_1

8dB

Gp_

circ

le_1

6dB


Out

_sta

ble_

circ

le

Eqn Gmax2=max_gain(Sa)



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

( )

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)


Out

_sta

ble_

circ

le

c ir_pts (0.000 to 51.000)

Gp_

circ

les

Eqn Gp_circles_step=gp_circle(Sa, ,51,3,2)


Out

_sta

ble_

circ

le

c ir_pts (0.000 to 51.000)

Gp_

circ

les_

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)



cir_pts (0.000 to 51.000)

Ga_

circ

le_2

0dB

Ga_

circ

le_1

8dB

Ga_

circ

le_1

6dB

indep(In_stable_circle) (0.000 to 51.000)

In_s

tabl

e_ci

rcle

Constant Available Power-Gain Circles:

Use ga_circle() function to get constant

gain circles.

1.22

18

4.

ADS

ga_circle() 1.22

5.

S_Param

1.23 1.24

Data Display

Ideal amplifier behavioral model

MuPrimeMuPrime2MuPrime2=mu_prime(S)

MuPrime

MuPrimeMuPrime1MuPrime1=mu_prime(S)

MuPrime

MuMu1Mu1=mu(S)

Mu

GaCircleGaCircle1GaCircle1=ga_circle(S,[20,18,16],51)

GaCircle

GpCircleGpCircle1GpCircle1=gp_circle(S,[20,18,16],51)

GpCircle

L_StabCircleL_StabCircle1L_StabCircle1=l_stab_circle(S,51)

LStabCircle

S_StabCircleS_StabCircle1S_StabCircle1=s_stab_circle(S,51)

SStabCircle

S_ParamSP1

Step=1.0 MHzStop=800 MHzStart=800 MHz

S-PARAMETERS

Amplif ier2AMP1

S12=polar(0.035,40)S22=polar(0.8,-35)S11=polar(0.65,-95)S21=polar(5,115)

TermTerm2

Z=50 OhmNum=2

TermTerm1

Z=50 OhmNum=1

You can just use the measuring components in S_Param palette within schematic.

1.23

cir_pts (0.000 to 51.000)

GaC

ircle

1

indep(S_StabCircle1) (0.000 to 51.000)

S_S

tabC

ircle

1

c ir_pts (0.000 to 51.000)

GpC

ircle

1

indep(L_StabCircle1) (0.000 to 51.000)

L_S

tabC

ircle

1

Constant Operating Power-Gain Circles

Output Stability Circle

Constant Available Power-Gain Circles

Output Stability Circle

1.24

19

1.4

ADS

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) ( )231.38 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 )

21

PSD (dBm/Hz)

Frequency (Hz)

Bandwidth B (Hz)

kT

2.1

2. ( )

NAP kTB= ( )o17 C 290 K= 1 Hz

( )214 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

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



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

23

P (dBm)

Frequency (Hz)

Noise Floor of Spectrum Analyzer

−144

−136



Only white noise

White noise + other noise

2.4

P (dBm)

Frequency (Hz)

Spectrum Analyzer

−136


above floor: measurable

below floor: unmeasurable

2.5

P (dBm)

Frequency (Hz)

Spectrum Analyzer A

−136


P (dBm)

Frequency (Hz)

Spectrum Analyzer B

−127


2.6

3. ( )

2.7

80 MHz

95 dBm− 80 dBm−

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

25

5.

NAP kTB=

2.8

R NAP kTB=2, 4n rmsv kTBR= , 4n rmsv kTBR=

( )2, 4n rmsv B kTR= 2V 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

,

12 n rms

NA

vP 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 rmsiNoise-free resistor

2, 4n rmsv kTBR=

2

,2,

44n rms

n rms

v kTBi kTGB

R R

= = =

Thevenin’s Equivalent Circuit Norton’s Equivalent Circuit

2.9

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:

oeq

NT

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

27

aG aG

o a eqN G kT B=

i oeq

a

N NT

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 = 210 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

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

eqONeq

Off eq

T TN N T YTY 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

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 SG N G N NSNR N N T

FS 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= − = − =

30

P (dBm)

Frequency (Hz)

−100

−60

SNRi = 40 dB

P (dBm)

Frequency (Hz)

−80

−40

SNRo= 32 dB

−72

Gain = 20 dBNF = ?

NF = 8 dB

Amplifier

2.13 SNR

9.

( )

2.14 ADS

( ) ( )2 2 2

min minn n

s opt s opt s opts s

R RF 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

1s

ss

YZ

− Γ=+ Γ

0

11

1opt

optopt

YZ

− Γ=

+ Γ

( ) ( )2

min 220

4

1 1

s optns

s opt

RF F

Z

Γ − ΓΓ = +

− Γ + Γ

2.14

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

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

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

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_ADSX1

Use “Design Parameters…” to assign a symbol for this transistor

2.19 bfp640esd_ADS.dsn (symbol)

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_ParamSP1

Freq=2.4 GHzCalcNoise=yes

S-PARAMETERS

OptionsOptions1

Tnom=25Temp=16.85

OPTIONS

VARVAR2

Z0=50VCEstep=0.2 VVCEmax=4 VVCEmin=0 VIBBstep=10 uAIBBmax=100 uAIBBmin=0 uA

EqnVar

VARVAR1

Rload=50IBB=0 AVCE=0 V

EqnVar

DCDC1

Step=VCEstepStop=VCEmaxStart=VCEminSweepVar="VCE"

DCParamSweepSweep2

Step=VCEstepStop=VCEmaxStart=VCEminSimInstanceName[6]=SimInstanceName[5]=SimInstanceName[4]=SimInstanceName[3]=SimInstanceName[2]=SimInstanceName[1]="SP1"SweepVar="VCE"

PARAMETER SWEEP

TermTerm2

Z=50 OhmNum=2

TermTerm1

Z=50 OhmNum=1

DC_FeedDC_Feed2

DC_BlockDC_Block2

DC_BlockDC_Block1

DC_FeedDC_Feed1

bfp640esd_ADSX1

BFP640ESD

I_ProbeIC

V_DCSRC1Vdc=VCE

ParamSweepSweep1SweepVar="IBB"SimInstanceName[1]="Sweep2"SimInstanceName[2]="DC1"SimInstanceName[3]=SimInstanceName[4]=SimInstanceName[5]=SimInstanceName[6]=Start=IBBminStop=IBBmaxStep=IBBstep

PARAMETER SWEEP

I_DCSRC2Idc=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 noiseUse “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)

36

S_ParamSP1

Freq=2.4 GHzCalcNoise=yes

S-PARAMETERS

VARVAR2


EqnVar

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=10.0uIBB=20.0uIBB=30.0uIBB=40.0uIBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u

VCE

dB(S

21[0

])

m1

m1VCE=dB(S21[0])=19.172IBB=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


VCE

NF

min

[0]

m2

m2VCE=NFmin[0]=600.9052mIBB=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

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

m3VCE=IC.i=5.406418mIBB=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

m3VCE=IC.i=2.902361mIBB=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

NF

min

, 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

m3VCE=IC.i=5.406418mIBB=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

NF

min

, 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

1.21.4

1.6

1.8

2.0

0.4

2.2

IC

NF

min

, 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

1.21.4

1.6

1.8

2.0

0.4

2.2

IC

NF

min

, 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

1.21.4

1.6

1.8

2.0

0.4

2.2

IC

NF

min

, 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 )

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


VCE

MA

G, d

B

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=20.0uIBB=30.0uIBB=40.0uIBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u

VCE

dB(S

12)

dB(S12) versus IBB and VCE

m1VCE=dB(S21[0])=15.888IBB=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


VCE

dB(S

21)

m1

m1VCE=dB(S21[0])=15.888IBB=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=30.0uIBB=40.0uIBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u

VCE

dB(S

11[0

])

IBB=0.000

IBB=10.0u

IBB=20.0u

IBB=30.0u

IBB=40.0uIBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u

dB(S

22[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(S

21)

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)

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 biaspoint 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-parameterfor 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

IB B =0.000

IB B =10.0u

IB B =20.0uIB B =30.0uIB B =40.0uIB B =50.0uIB B =60.0uIB B =70.0uIB B =80.0uIB B =90.0uIB B =100.u

VCE

Pga

in_a

ssoc

m4

m4VCE=Pgain_assoc=18.676IBB=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

m3VCE=IC.i=5.417352mIBB=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

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 coefficientsat 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

m3VCE=IC.i=5.417352mIBB=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)

So

pt_

at_

bia

s_p

tG

am

ma

S_

at_

bia

s_p

tG

am

ma

L_

at_

bia

s_p

tG

am

ma

L_

wS

op

t

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: i f 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

m3VCE=IC.i=13.18580mIBB=0.000060

600.0000mK

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)S

opt

_at

_b

ias_

ptG

am

ma

S_a

t_b

ias_

pt

Ga

mm

aL

_at_

bia

s_p

tG

am

ma

L_w

Sop

t

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.

m2VCE=NFm in[0 ]=595.2716mIBB=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. 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

NF

min

[0]

m2

m2VCE=NFm in[0 ]=595.2716mIBB=0.000010

3.000000 m 1VCE=dB(S21[0])=16.007IBB=0.000010

3.000

0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0

-20-15

-10

-50

5

1015

-25

20

I BB=0. 000


VCE

dB

(S2

1[0

])

m1

m 1VCE=dB(S21[0])=16.007IBB=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. 0uI BB=40. 0uI BB=50. 0uI BB=60. 0uI BB=70. 0uI BB=80. 0uI BB=90. 0uI BB=100. u

VCE

dB

(S1

1[0

])

I BB=0. 000

I BB=10. 0u

I BB=20. 0u

I BB=30. 0uI BB=40. 0uI BB=50. 0uI BB=60. 0uI BB=70. 0uI BB=80. 0uI BB=90. 0uI BB=100. u

dB

(S2

2[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


VCE

dB

(S1

2)

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


VCE

MA

G,

dB

M in im um Nois e Figure v ers us IBB and VCETrans is tor dB(S21) v ers us IBB and VCE

Max im um Av ai lab le 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 4VCE=Pgain_as soc =-2.051IBB=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 uI B B = 2 0 . 0 uI B B = 3 0 . 0 uI B B = 4 0 . 0 uI 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

_ass

oc

m 4

m 4VCE=Pgain_as soc =-2.051IBB=0.000000

1.200

As s oc ia ted Power Gain (input matc hed for NFm in, output then c on jugate ly m atc hed) v ers us IBB and VCE

Eqn M AG =m ax_gain( S) M ax im um av a i lab le /s tab le ga in a t a l l 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 a t the b ias po in t s pec i fied by m arker m 3.

Sourc e impedanc e for m in im um no is e figure a t the b iaspo in t s pec i fied by m ark er m 3.

Stab i l i ty fac tors a t the b ias poin t 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 ul taneous c on jugate m atc h ing, a t the b ias po in t m3.These are not defined and re turn 0 i f K<1.

S_22p : re flec tion look ing into the output o f the dev ic e, when the s ourc e is optim al for m in im um no is e figure.

Gam m aL_wSopt is the c om plex c on jugate of S22_p, and is the optimal load re flec tion c oeffic ient when Sopt is the s ourc e re flec tion c oeffic ient. Zload_wSopt is the c orres ponding impedanc e.

Sim ul taneous c on jugate m atc h s ource and load re flec tion c oeffic ientsat b ias po in t m 3. Thes e are not defined and re turn 0 i f K<1.

Trans duc er power ga in wi th the s ourc e re flec tion c oeffic ient Sopt for m in im um no ise figure , and the load then c on jugate ly matc hed. z opt() is jus t us ed to c onv ert a re flec tion c oeffic ient to an im pedanc e.

Col lec tor DC c urrent

Find index for the s wept v ariab le VCE and ICE ac c ording to m ark er "m3" x -ax is .

M in im um no is e figure a t the m 3 b ias po in t.

DC power c om s um ption when b ias ed a t m ark er "m 3" (bas e c urrent is ignored)

m 3VCE=IC.i=5.417352mIBB=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 3VCE=IC.i=5.417352mIBB=0.000020

3.000000

I/V Curv e (Se lec t Bias ing Poin t 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 re flec tion c oeffic ient for m in imum no is e figure a t frequenc y s pec i fied by m ark er m 3. Sopt is the s -param eterfor optim um no is e perform anc e.

(1) (2)

Bas ic in form ation a t the b ias po in t m 3.

Optimum re flec tion c oeffic ient(im pedanc e) for m in im um no is e a t the bias po in t m 3.

Output Conjugate ly M atc h ing Im pdeanc e Calc u la tion (when input is nois e m atc hed)

Input/Output Sim ul taneous ly Conjugate M atc hed (input is NOT no is e matc hed)

Move marker m3 to select bias point. All listings and impedances on Smith Chart will be updated.

Matching for Gain Zs ourc e Zload

DUT*

(0 .000 to 0 .000)

So

pt_

at_

bia

s_

pt

Ga

mm

aS

_a

t_b

ias

_p

tG

am

ma

L_

at_

bia

s_

pt

Ga

mm

aL

_w

So

pt

Op tim al Sourc e Reflec tion Coeffic ients for M in inum NF, Simul taneous Conjugate M atc h ing, and Load Reflec tion Coeffic ient for Sim ul taneous Conjugate M atc h ing, and wi th s ourc e m atc hed for NFm in

Note: i f the dev ic e (or c i rc u it) is uns tab le a t the b ias po in t, the s im ul taneous c on jugate m atc h ing im pedances are undefined and Gam m aL_at_b ias _pt and Gam m aS_at_bias _pt defau l t to 0 . Als o, M AG is s et equal to the m ax im um stab le ga in , |S21|/|S12|.

2.0

0m

4.0

0m

6.0

0m

8.0

0m

10

.0m

12

.0m

14

.0m

16

.0m

18

.0m

0.0

00

20

.0m

0 .6

0.8

1.0

1.2

1.4

1.6

1.8

0.4

2.0

IC

NF

min

, d

B

NFmin versus IC, at VCE (set by m3)

2.0

0m

4.0

0m

6.0

0m

8.0

0m

10

.0m

12

.0m

14

.0m

16

.0m

18

.0m

0.0

00

20

.0m

-15

-10

-5

0

5

10

15

-20

20

IC

dB

(S2

1)

dB(S21) v ers us IC, a t 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 a t b ias po in t m 3

K

0. 6776

Stab i l i ty Fac torZ0[ 0, 0, 0]

50. 0000

Charac teris tic s Im pedanc e

m ax_gain( S_bp)

20. 7283

M ax Av al iab le /Stable Gain (dB)Zsour ce

50. 0000

Zload

50. 0000

Sim ul taneous 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. fo r NFm in

Zopt

59. 0670 + j30. 3691

Zopt for NFm inZload_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) a t th is no is e m atc hed c ondi tion

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 a l iable /Stab le Gain (dB)

2.29 Datadisplay page

41

4.

(1) Bias_MinNF.dsn Bias_MinNF.dds Bias_MinNF_choose.dsn

Bias_MinNF_choose.dds

2.30 IBB

IBBstep

VARVAR2


EqnVar

Rload=50IBB=0 A

DCDC1

Step=VCEstepStop=VCEmaxStart=VCEminSweepVar="VCE"

DCParamSweepSweep2

SimInstanceName[4]=SimInstanceName[3]=SimInstanceName[2]=SimInstanceName[1]="SP1"SweepVar="VCE"

PARAMETER SWEEPParamSweepSweep1SweepVar="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

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=0.000IBB=1.00uIBB=2.00uIBB=3.00uIBB=4.00uIBB=5.00uIBB=6.00uIBB=7.00uIBB=8.00uIBB=9.00uIBB=10.0uIBB=11.0uIBB=12.0uIBB=13.0uIBB=14.0uIBB=15.0uIBB=16.0uIBB=17.0uIBB=18.0uIBB=19.0uIBB=20.0uIBB=21.0uIBB=22.0uIBB=23.0uIBB=24.0uIBB=25.0uIBB=26.0uIBB=27.0uIBB=28.0uIBB=29.0uIBB=30.0u

VCE

IC.i,

A

m3

m3VCE=IC.i=6.120396mIBB=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

NF

min

, dB

m5

m5indep(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

MA

G[V

CE

inde

x,0]

m6

Pga

in_a

ssoc

[VC

Ein

dex] m7

m6indep(m6)=vs(MAG[VCEindex,0],IC.i[VCEindex])=21.044851

0.006120

m7indep(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 )

43

(2) Bias_MinNF_choose.dsn Bias_MinNF_stability_BW.dsn

2.32

OptionsOptions1

Tnom=25Temp=16.85

OPTIONSS_ParamSP1

Freq= CalcNoise=y esStep=50 MHzStop=10 GHzStart=0.05 GHz

S-PARAMETERS

DCDC1

Step=Stop=Start=SweepVar=

DCVARVAR1

Z0=50Rload=50IBB=23 uAVCE=3 V

EqnVar

TermTerm2

Z=50 OhmNum=2DC_Block

DC_Block2

DC_FeedDC_Feed1

I_DCSRC2Idc=IBB

DC_BlockDC_Block1

DC_FeedDC_Feed2Term

Term1

Z=50 OhmNum=1

bf p640esd_ADSX1

BFP640ESD

I_ProbeIC

V_DCSRC1Vdc=VCE

Sweep frequency for a fixed biased-point

2.32

(3) Datadisplay

m1freq=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

NF

min

, dB

m1 m1freq=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(S

21)

1 2 3 4 5 6 7 8 90 10

-50

-45

-40

-35

-30

-25

-20

-55

-15

freq, GHz

dB(S

12)

1 2 3 4 5 6 7 8 90 10

15

20

25

30

35

10

40

freq, GHz

MA

G, d

BMinimum Noise Figure versus frequencyTransistor dB(S21) versus frequency

Maximum Available(Stable) Gain versus frequency

dB(S12) versus frequency

m2freq=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

Pga

in_a

ssoc

m2


2.400GHz

Associated Power Gain (input matched f or NFmin, output then conjugately matched) v ersus f requency

m3freq=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(S

11)


1 2 3 4 5 6 7 8 90 10

-12

-10

-8

-6

-4

-2

-14

0

freq, GHz

dB(S

22)

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, stability factors, and MAG at all frequencies

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 minimum noise 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.



Eqn Zsource=sm_z1(S,Z0)

Eqn Zload=sm_z2(S,Z0)

Optimum reflection coefficient(impedance) for minimum noise at all frequencies



Eqn MuL=mu(S)

Eqn MuS=mu_prime(S)

2.32

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)

Sou

rce_

stab

cir1

indep(Load_stabcir1) (0.000 to 51.000)Lo

ad_s

tabc

ir1

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

fm1indep(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 1.0E100.0

1.0E6

frequency

fm1


2.400000G

2.34

(6) Datadisplay Smith Chart 2.35 rhos

Smith Chart 2000 ( ) Smith Chart

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

46

indep(Source_stabcir) (0.000 to 51.000)

Sou

rce_

stab

cir

indep(rhos) (0.000 to 2000.000)

rhos

indep(Load_stabcir) (0.000 to 51.000)

Load

_sta

bcir

indep(rhos) (0.000 to 2000.000)

rhos


Sou

rce_

stab

cir


Load

_sta

bcir

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 regionStable

Stable

UnstableUnstable

Eqn Source_stabcir=s_stab_circle(S[fm1],51)

Eqn Load_stabcir=l_stab_circle(S[fm1],51)

Source and Load Stability CirclesDraw 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

47

(9) 2.37 2.38

( )

2.39 DC block

2.40

1R 3R

2R 4R

1R 3R 1R

4R2R

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

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


Sou

rce_

stab

cir

indep(rhos) (0.000 to 2000.000)

rhos

m4

m4indep(m4)=rhos=0.733 / 179.349impedance = Z0 * (0.154 + j0.006)

1075

Input series resistance = 0.154*50 Ohm = 7.7 Ohm

1R

Case (a): Input series

RR1R=9 Ohm

DC_BlockDC_Block2

I_DCSRC2Idc=IBB

DC_FeedDC_Feed2 bf p640esd_ADS

X1

BFP640ESD

I_ProbeIC


Sou

rce

_sta

bci

r

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

Mu

L

m3freq=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

49

(12) 2.37

( )

2.42

g


Sou

rce_

stab

cir

indep(rhos) (0.000 to 2000.000)

rhos 2R

Case (b): Input parallel

Input parallel stabilize is impossible

Mu= -, MAG/MSG= -, NFmin = -, Pgain_assoc= -


Input Parallel R

Stabilizing can’t be achieved

2.42

(13) 2.43 2.44 (10)

(11)

m4indep(m4)=rhos=0.614 / -179.141impedance = Z0 * (0.239 - j0.007)

755


Load

_sta

bcir

indep(rhos) (0.000 to 2000.000)

rhos

m4

m4indep(m4)=rhos=0.614 / -179.141impedance = Z0 * (0.239 - j0.007)

755

Output series R = 0.239*50 Ohm = 11.95 Ohm

3R

Case (c): Output series

RR1R=20 Ohm

DC_BlockDC_Block2

bf p640esd_ADSX1

BFP640ESD

I_ProbeIC

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


Load

_sta

bcir

indep(rhos) (0.000 to 2000.000)

rhos

OutsideLoad Stable Region

1 2 3 4 5 6 7 8 90 10

1

-1

2

freq, GHz

Mu

S

m3

Mu

L

m4

m3freq=MuS=1.024

2.400GHz

m4freq=MuL=1.028

2.400GHz

Unstable

Stable

Stable

Unstable


Output Series R

Draw a circle to roughly

evaluate the output series

stabilizing resistance

Before stabilizing

After stabilizing



2.43

50


616


Loa

d_st

abc

ir

indep(rhos) (0.000 to 2000.000)

rho

s m4


616

Output parallel R= 1/(0.286/50) Ohm = 174.8 Ohm


4R

Case (d): Output parallel

Mu=1.015, MAG/MSG= 20.25 dB, NFmin = 0.69 dB, Pgain_assoc=17.32 dB

RR1R=140 Ohm

DC_BlockDC_Block3

DC_BlockDC_Block2

bf p640esd_ADSX1

BFP640ESD

I_ProbeIC


Loa

d_s

tab

cir

indep(rhos) (0.000 to 2000.000)

rho

s

OutsideLoad Stable Region

Stable

Unstable

1 2 3 4 5 6 7 8 90 10

1

-1

2

freq, GHz

Mu

S

m3

MuL

m4

m3freq=MuS=1.012

2.400GHz

m4freq=MuL=1.015

2.400GHz

Unstable

Stable

Before stabilizing

After stabilizing


Output Parallel R



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

Mu

L

m4

m3freq=MuS=1.620

2.400GHz

m4freq=MuL=1.667

2.400GHz

RR1R=47 OhmR

R2R=9 Ohm

DC_BlockDC_Block3

DC_BlockDC_Block2

bf p640esd_ADSX1

BFP640ESD

I_ProbeIC


Before stabilizing

After stabilizing

Stabilization at 2.4 GHz / Input Series R and Output Parallel R

Whole band stable

2.45

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

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

53

(19) 2.50

(

) 2.50

(2.4 GHz ) MAG NFmin

Pgain_assoc

RR1R=? Ohm

TermTerm2

Z=50 OhmNum=2

bfp640esd_ADSX1

BFP640ESD

TermTerm1

Z=50 OhmNum=1

DC_FeedDC_Feed2

DC_BlockDC_Block2

DC_BlockDC_Block1

DC_FeedDC_Feed1

I_ProbeIC

V_DCSRC1Vdc=VCE

I_DCSRC2Idc=IBB

RR1R=? Ohm

DC_BlockDC_Block3 Term

Term2

Z=50 OhmNum=2

bfp640esd_ADSX1

BFP640ESD

TermTerm1

Z=50 OhmNum=1

DC_FeedDC_Feed2

DC_BlockDC_Block2

DC_BlockDC_Block1

DC_FeedDC_Feed1

I_ProbeIC

V_DCSRC1Vdc=VCE

I_DCSRC2Idc=IBB

Shunt Feedback Stabilization

Feedback ResistanceIsolated from DC network

2.50

(20) (17) 2.51

LL3R=

RR6

DC_BlockDC_Block6

CC4

LL2R=

DC_BlockDC_Block5

RR5

DC_BlockDC_Block4 C

C3

RR4

CC2

RR3

RR2

CC1

DC_BlockDC_Block3

LL1R=

RR1

TermTerm2

Z=50 OhmNum=2

bfp640esd_ADSX1

BFP640ESD

TermTerm1

Z=50 OhmNum=1

DC_FeedDC_Feed2

DC_BlockDC_Block2

DC_BlockDC_Block1

DC_FeedDC_Feed1

I_ProbeIC

V_DCSRC1Vdc=VCE

I_DCSRC2Idc=IBB

Frequency-selective Shunt Feedback Stabilization

2.51

54

(21) 2.52

BJT

50

( 50

IC )

RR7

TermTerm2

Z=50 OhmNum=2

bfp640esd_ADSX1

BFP640ESD

TermTerm1

Z=50 OhmNum=1

DC_FeedDC_Feed2

DC_BlockDC_Block2

DC_BlockDC_Block1

DC_FeedDC_Feed1

I_ProbeIC

V_DCSRC1Vdc=VCE

I_DCSRC2Idc=IBB

CC5

RR7

TermTerm2

Z=50 OhmNum=2

bfp640esd_ADSX1

BFP640ESD

TermTerm1

Z=50 OhmNum=1

DC_FeedDC_Feed2

DC_BlockDC_Block2

DC_BlockDC_Block1

DC_FeedDC_Feed1

I_ProbeIC

V_DCSRC1Vdc=VCE

I_DCSRC2Idc=IBB

LL4R=

TermTerm2

Z=50 OhmNum=2

bfp640esd_ADSX1

BFP640ESD

TermTerm1

Z=50 OhmNum=1

DC_FeedDC_Feed2

DC_BlockDC_Block2

DC_BlockDC_Block1

DC_FeedDC_Feed1

I_ProbeIC

V_DCSRC1Vdc=VCE

I_DCSRC2Idc=IBB

Series Feedback Stabilization (Degeneration)

CC1

LL4R=

RR2

TermTerm2

Z=50 OhmNum=2

bfp640esd_ADSX1

BFP640ESD

TermTerm1

Z=50 OhmNum=1

DC_FeedDC_Feed2

DC_BlockDC_Block2

DC_BlockDC_Block1

DC_FeedDC_Feed1

I_ProbeIC

V_DCSRC1Vdc=VCE

I_DCSRC2Idc=IBB

Considered with biasConsidered with bias

Bypass to increase AC gain

No DC disturb

High frequency degeneration

No DC disturb

Bandpass degeneration

DC path

2.52

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

m3freq=MuS=1.012

2.400GHz

m4freq=MuL=1.014

2.400GHz

Stabilization at 2.4 GHz / Input Parallel R and Shunt Feedback


Before stabilizing

After stabilizing

RR2R=1 kOhm

RR1R=800 Ohm

DC_BlockDC_Block5

DC_BlockDC_Block4

DC_BlockDC_Block2

TermTerm2

Z=50 OhmNum=2

DC_FeedDC_Feed1

I_DCSRC2Idc=IBB

DC_BlockDC_Block1

DC_FeedDC_Feed2Term

Term1

Z=50 OhmNum=1

bf p640esd_ADSX1

BFP640ESD

I_ProbeIC

V_DCSRC1Vdc=VCE

2.53

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

CC2C=27 pF

CC1C=27 pF

RR2R=1 kOhm

RR1R=800 Ohm

DC_BlockDC_Block2

TermTerm2

Z=50 OhmNum=2

DC_FeedDC_Feed1

I_DCSRC2Idc=IBB

DC_BlockDC_Block1

DC_FeedDC_Feed2Term

Term1

Z=50 OhmNum=1

bf p640esd_ADSX1

BFP640ESD

I_ProbeIC

V_DCSRC1Vdc=VCE

Put a practical value of

capacitance

Put a practical value of

capacitance

ω< 01

20Z

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

Mu

S

m3

MuL

m4

m3freq=MuS=1.013

2.550GHz

m4freq=MuL=1.016

2.550GHz

Check the stability at higher frequencies

2.55

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

RR7

bf p640esd_ADSX4

BFP640ESD

RR9

RR8

RR15

bf p640esd_ADSX6

BFP640ESD

RR16

RR17

RR14R

R10

RR11

bf p640esd_ADSX5

BFP640ESD

RR12

RR13R

R3

RR4

bf p640esd_ADSX2

BFP640ESD

RR6

bf p640esd_ADSX3

BFP640ESD

RR5

Common Passive Biasing Circuits

VCE

IC

VCC

2.56

58

MLINTL5

RR24

RR25

bfp640esd_ADSX10

BFP640ESD

MRSTUBStub1

bfp640esd_ADSX8

BFP640ESD

RR21

RR20

MLINTL1

CC3

bfp640esd_ADSX9

BFP640ESD

RR23

RR22

MLINTL3

MLOCTL2

LL1R=

RR18

RR19

bfp640esd_ADSX7

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

Radialopen stubRF short

RF open

RF open

2.57 choke

7. LNA

(1) Datadisplay

Bias_MinNF_Matching.dsn Bias_MinNF_Matching.dds 2.58

S_ParamSP1

Freq= CalcNoise=yesStep=50 MHzStop=3 GHzStart=2 GHz

S-PARAMETERSVARVAR1

Z0=50Rload=50VCC=3.3 V

EqnVar

OptionsOptions1

Tnom=25Temp=16.85

OPTIONS

DCDC1

Step=Stop=Start=SweepVar=

DC

DC_BlockDC_Block2

DC_BlockDC_Block1

TermTerm1

Z=50 OhmNum=1

RR4R=96 kOhm

RR2R=1 kOhm

CC2C=27 pF

RR1R=800 Ohm

CC1C=27 pF

I_ProbeIB

RR3R=50 Ohm

LL1

R=L=18 nH

V_DCSRC1Vdc=VCC

I_ProbeIC

bfp640esd_ADSX1

BFP640ESD

TermTerm2

Z=50 OhmNum=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

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

m1freq=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

NFm

in, d

B

m1


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

17.417.6

17.8

18.0

16.2

18.2

freq, GHz

dB(S

21)

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(S

12)

m5freq=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

MA

G, d

B

m5

m5freq=MAG=18.937

2.400GHz

Minimum Noise Figure versus frequencyTransistor dB(S21) versus frequency

Maximum Available(Stable) Gain versus frequency



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

Pg

ain

_a

ss

oc m2


2.400GHz

Associated Power Gain (input matched for NFmin, output then conjugately matched) versus frequency

Eqn M AG=m ax _gain (S) Maximum available(stable) gain at all frequencies

Eqn frequency =SP.freq

Eqn Gam m aS_a l l_ freq=s m _gamm a1(S)

EqnGam m aL_a l l_ freq=s m _gamm a2(S)

Eqn Zop t=zop t(Sop t,Z0)

Eqn Zload_wSop t=z opt(c onj (S_22p),Z0 )

Eqn K=stab_fac t(S)

Eqn Pga in_as s oc=pwr_ga in(S,z op t(Sop t,Z0),z opt(c onj (S_22p),Z0 ),Z0)

Eqn S_22p=S22+(S12*S21*Sop t)/(1 -S11*Sopt)

Eqn Gam m aL_wSop t=con j (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 minimum noise 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.



EqnZsource=s m_z 1(S,Z0 )

Eqn Zload=s m _z2(S,Z0 )

Optimum reflection coefficient(impedance) for minimum noise at all frequencies



m11freq=Sopt=0.171 / 138.227impedance = Z0 * (0.755 + j0.178)

2.400GHz

m12freq=GammaL_wSopt=0.171 / 52.058impedance = Z0 * (1.185 + j0.329)

2.450GHz

freq (2.000GHz to 3.000GHz)

Sop

t

m11

Gam

maS

_all_

freq

Gam

maL

_all_

freq

Gam

maL

_wS

opt

m12


2.400GHz


2.450GHz

Optimal Source Reflection Coeffic ients for Mininum NF, Simultaneous Conjugate Matching, and Load Reflec tion Coeffic ient 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


2.400000G

2 .1E9 2 .2E9 2 .3E9 2 .4E9 2 .5E9 2.6E9 2 .7E9 2 .8E9 2 .9E92 .0E9 3 .0E90 .0

1 .0E6

frequenc y

fm1


2.400000G

Eqn MuL=mu(S)

m3freq=MuS=1.050

2.400GHz

m4freq=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

Mu

S

m3

Mu

L

m4

m3freq=MuS=1.050

2.400GHz

m4freq=MuL=1.073

2.400GHz

Eqn MuS=mu_prime(S)

m9freq=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(S

11)

m9

m9freq=dB(S(1,1))=-8.693

2.400GHz


m10freq=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(S

22)

m10

m10freq=dB(S(2,2))=-18.825

2.500GHz



2.400GHz


2.450GHz


Sop

t

m11

Gam

maS

_all_

freq

Gam

maL

_all_

freq

Gam

maL

_wS

opt

m12


2.400GHz


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]

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()

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 CirclesNoise Circle

Available Power Gain Circle

Operating Power Gain Circle

Eqn num_NFcircles=3Eqn NFstep_size=0.2 Eqn GAstep_size=1

Eqn num_GAcircles=3 Eqn num_GPcircles=3Eqn 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 NFminzin(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]

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

GammaSindep(GammaS)=rhos=-0.11872 + j0.12612impedance = 38.26607 + j9.95049

60

indep(rhos) (0.000 to 2000.000)

rhos

GammaSgain=18.937

gain=17.937gain=16.937

gain=15.937

cir_pts (0.000 to 51.000)

GA

circ

les

indep(GammaLopt) (60.000 to 60.000)

Ga

mm

aLop

t ns figure=1.404ns figure=1.604ns figure=1.804

Noi

se_

circ

les

(0.000 to 0.000)

Sop

t[fm

1]G

amm

aLo

pt_

NFm

in


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

63

− source

stability circle Smith Chart


486

indep(rhos) (0.000 to 2000.000)

rhos

GammaSgain=18.937

gain=17.937gain=16.937

gain=15.937

cir_pts (0.000 to 51.000)

GA

circ

les

indep(GammaLopt) (486.000 to 486.000)

Gam

maL

opt ns figure=1.404ns figure=1.604ns figure=1.804

Noi

se_c

ircle

s

(0.000 to 0.000)

Sop

t[fm

1]

Gam

maL

opt_

NFm

in


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

64

GammaLindep(GammaL)=rhos=0.36056 / 35.02213impedance = Z0 * (1.61272 + j0.76714)

260

indep(rhos) (0.000 to 2000.000)

rho

s

GammaL

gain=18.937

gain=17.937

gain=16.937

gain=15.937

cir_pts (0.000 to 51.000)

GP

cir

cles

indep(GammaSopt) (260.000 to 260.000)

Ga

mm

aS

opt

GammaLindep(GammaL)=rhos=0.36056 / 35.02213impedance = 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

CC5C=27 pF

TermTerm2

Z=50 OhmNum=2

LL3

R=L=1.68 nH

CC4C=0.27 pF

LL2

R=L=6 nH

CC3C=6 pF

TermTerm1

Z=50 OhmNum=1

RR4R=96 kOhm

RR2R=1 kOhm

CC2C=27 pF

RR1R=800 Ohm

CC1C=27 pF

I_ProbeIB

RR3R=50 Ohm

LL1

R=L=18 nH

V_DCSRC1Vdc=VCC

I_ProbeIC

bfp640esd_ADSX1

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

Pga

in_a

ssoc

m2


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

NF

min

, dB

m1


2.450000GHz

Gamma_S (NFmin)

Gamma_L when NFmin


So

pt

Ga

mm

aS

_all_

freq

Ga

mm

aL

_all_

freq

Ga

mm

aL

_wS

opt

Matched to 50 Ohm

2.67 LNA

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

Engineering

Agilent ADS 模擬手冊 [實習2] 放大器設計