射頻電子 - [第六章] 低雜訊放大器設計

高頻電子電路第六章低雜訊放大器設計

李健榮助理教授

Department of Electronic EngineeringNational Taipei University of Technology

大綱

• 無線收發機的基本架構• 回顧：功率-增益關係式

• 可資用功率增益圓• 非雙埠同時共軛匹配的放大器設計法：可可可可資用功率增益設計資用功率增益設計資用功率增益設計資用功率增益設計法法法法

• 雙埠網路雜訊理論• 固定雜訊指數圓

Department of Electronic Engineering, NTUT2/15

無線收發機的基本架構

• 發射機(Transmitter, TX)

• 接收機(Receiver, RX)

高功率

低雜訊


回顧：功率-增益關係式

2 22

212 2

22

1 1

1 1s LL

TAVS in s L

PG S

P S

− Γ − Γ= =

− Γ Γ − Γ

2 22

212 2

11

1 1

1 1s LL

TAVS s out L

PG S

P S

− Γ − Γ= =

− Γ − Γ Γ

22

212 2

22

11

1 1LL

pin in L

PG S

P S

− Γ= =

− Γ − Γ

22

212 2

11

1 1

1 1sAVN

AAVS s out

PG S

P S

− Γ= =

− Γ − Γ

• 功率轉換增益GT (Transducer Power Gain)

• 操作功率增益Gp (Operating Power Gain)

• 可資用功率增益GA (Available Power Gain)

Transistor[S]+

−sE

sZ

LZ

PAVNPAVS PLPin

Ms

interface interfaceML

輸入總是匹配，考慮不同輸出匹配

輸出總是匹配，考慮不同輸入匹配

同時考慮不同輸入、輸出匹配


功率轉換增益GT (Transducer Power Gain)

• 雙埠同時共軛匹配：最大轉換增益匹配

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

Transistor[S]+

−sE

sZ

LZ

見第五章投影片slide 32

Department of Electronic Engineering, NTUT

inΓ

1E

oZ

oZTransistor

oG

Outputmatching

LG

Inputmatching

sG

s in∗Γ = Γ L out

∗Γ = ΓoutΓ

• 功率轉換增益 GTinΓsΓ LΓoutΓ

輸出端的匹配目標輸入端的匹配目標

5/15

可資用功率增益圓(I)

( )2 2

21 2

212222

1111

1

1 11

s

A a

ss

s

SG S g

SS

S

− Γ= = ⋅ − ∆Γ − − Γ − Γ

• 無條件穩定雙向(bilateral)情況:

( ) ( )

2

2 2 2 2 221 22 11 1

1

1 2Re

sAa

s s

Gg

S S S C

− Γ= =

− + Γ − ∆ − Γ

1 11 22C S S ∗= − ∆

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 a

a

a

K S S g S S gr

g S

− +=

+ − ∆� 圓心 � 半徑

• 可資用功率增益圓(Available Power-Gain Circle):

其中

把GA改寫成只跟電晶體S參數與Γs有關：

Ga與ga為電晶體S參數與Γs的函數。可造成固定ga的Γs值，其軌跡為一個圓形，也稱為可資用功率增益圓(available power-gain circle)。

22

212 2

11

1 1

1 1sAVN

AAVS s out

PG S

P S

− Γ= =

− Γ − Γ

12 21 22 11 22 12 21 2222

11 11 111 1 1s s s s

outs s s

S S S S S S S SS

S S S

Γ − Γ + Γ − ∆ΓΓ = + = =− Γ − Γ − Γ

11 22 12 21S S S S∆ = −


可資用功率增益圓(II)


,max ,max_@A s GAG Γ

1 1@A sG Γ2 2@A sG Γ

3 3@A sG Γ

Γs平面 Γs平面

18 dB17 dB

16 dB

15 dB

14 dB

GaCircleGaCircle1GaCircle1=ga_circle(S,{18, 17, 16, 15 ,14} ,51)

GaCircle

MeasEqnMeas1GAmax=max_gain(S)

EqnMeas

GaCircleGaCircle1GaCircle1=ga_circle(S,GAmax ,51, 5, 1)

GaCircle ga_circle()函數之用法請參考ADS的Help說明

7/15

設計程序

1E

oZ

oZTransistor

oG

Outputmatching

LG

Inputmatching

sG

sΓ LΓoutΓ

• 可資用功率增益設計法� � �

18 dB17 dB

16 dB

15 dB

14 dB

�

Γs平面�先選要配到的Γs (不一定在GA,max，待會就會講到為什麼了)

�選完 Γs後可以得到 Γout

�知道 Γout後，再讓Γout與其共軛匹配即可：

L out∗Γ = Γ


雙埠網路雜訊理論

• 雜訊因子(noise factor)可由等效雜訊電阻與雜訊電導表示：

NoisyTwo-portsY

si

2

4n

n

eR

kTB≡

2

4u

u

iG

kTB≡

2

4s

s

iG

kTB≡

( ) ( )2 22

1 1u c s c s nu c s n

s s

G G G B B RG Y Y RF

G G

+ + + ++ + = + = +

, ,and


s c optB B B= − = 2us c opt

n

GG G G

R= + =and

2min 1 2 1 2 u

n opt c n c cn

GF R G G R G G

R

= + + = + + +

( ) ( )2 2

minn

s opt s opts

RF F G G B B

G = + − + −

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

• 固定雜訊指數圓

9/15

固定雜訊指數圓


min ,@ s optNF Γ Γs平面 Γs平面

0.8 dB min 0.3 dBNF =

1.3 dB

1.8 dB

2.3 dB

1 1@ sNF Γ

2 2@ sNF Γ

3 3@ sNF Γ

ns_circle()函數之用法請參考ADS的Help說明

NsCircleNsCircle1NsCircle1=ns_circle(nf2,NFmin,Sopt,Rn/50,51)

NsCircle

VARVAR4

Num_NF_Circles=5NF_Stepsize=0.5

EqnVar

NsCircleNsCircle1NsCircle1=ns_circle(NFmin+NF_Stepsize*[1::Num_NF_Circles],NFmin,Sopt,Rn/50,51)

NsCircle

min ,@ s optNF Γ

10/15

低雜訊放大器設計(增益與雜訊的取捨)

GA circles

NF circles

Inputmatching

OutputmatchingAmplifier

sΓ LΓ0Z

0Z

inΓ outΓoutZ

inZ


Min. noise figure, min ,, s optNF Γ

Max. available power gain, s in∗Γ = Γ

11/15

利用ADS在史密斯圖上進行取捨設計


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)

Gam

maL

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

Noi

se_c

ircl

es

(0.000 to 0.000)

Sop

t[fm

1]G

amm

aLop

t_N

Fmin


60

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


486

indep(rhos) (0.000 to 2000.000)

rho

s

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

ma

Lop

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

Noi

se_c

ircle

s

(0.000 to 0.000)

Sop

t[fm

1]G

amm

aLo

pt_

NFm

in


486

Gamma_S (NFmin)

Gamma_L when NFmin

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

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

12/15

在ADS建置完整的LNA設計環境(I)


Move marker mBiasPt to desired bias point. Smith Chart and data below will be updated.

2.400 GHz 50.000

System Impedance, Z0RF Frequency Move markers GammaS and GammaL to select arbitrary source and load reflection coeffic ients The impedances, power gains,and noise figures below will be updated. The transducer power gains are invalid if the markers are moved into the unstable regions.

Eqn num _NFc i rc les =3Eqn NFs tep_s iz e=0.2Eqn GAs tep_s iz e=1

Eqn num _GAc i rc les =3

Zs ourc e, Gam m a_S

Zload, Gam m a_L

DUT*

Eqn num _GPc i rc les =3Eqn GPs tep_s iz e=1

indep( r hos) ( 0. 000 t o 2000. 000)

rhos

GammaS

indep( Sour ce_st abcir ) ( 0. 000 t o 51. 000)

Sour

ce_s

tabc

ir

gain=20. 728

gain=19. 728

gain=18. 728

gain=17. 728

cir _pt s ( 0. 000 t o 51. 000)

GAc

ircles

indep( G am m aLopt ) ( 161. 000 t o 161. 000)G

amm

aLop

t

ns f igur e=0. 851ns f igur e=1. 051ns f igur e=1. 251

Noise

_circ

lesNo

ise_c

ircleM

in

G am m aSindep( G am m aS) =r hos=0. 15388 + j0. 23837im pedance = 59. 49677 + j30. 84754

161

indep( r hos) ( 0. 000 t o 2000. 000)

rhos

GammaL

indep( Load_st abcir ) ( 0. 000 t o 51. 000)

Load

_sta

bcir

gain=20. 728

gain=19. 728

gain=18. 728

gain=17. 728

cir _pt s ( 0. 000 t o 51. 000)

GPc

ircles

indep( G am m aSopt ) ( 246. 000 t o 246. 000)

Gam

maS

opt

G am m aLindep( G am m aL) =

r hos=0. 35071 / - 54. 37157im pedance = Z0 * ( 1. 22760 - j0. 79805)

246

Available Gain Circle: Noise Circles:Source Stability Circle:Source Gamma Corresponding Load Gamma (Black Dot)

Power Gain Circles:Load Stability Circle:Load Gamma Corresponding Source Gamma (Black Dot)

Load Stab le Region

Outside

Eqn t index=[ 0: : 2000]

Eqn r hos=sqr t ( t index/ 2000) *exp( j*2*sqr t ( pi* t index) )

Eqn I Cindex2=f ind_index( I C[ VCEindex2] , m BiasPt )

Eqn VCEindex2=f ind_index( DC. VCE[ 0, : : ] , indep( m BiasPt ) )

Eqn Sour ce_st abcir =s_st ab_cir cle( S_bpm , 51)

Eqn Load_st abcir =l_st ab_cir cle( S_bpm , 51)

Eqn G am m aLopt =conj( S_22m +S_12m *S_21m *G am m aS/ ( 1- S_11m *G am m aS) )

Eqn G t _num =m ag( S_21m ) **2 * ( 1- m ag( G am m aS) **2) * ( 1- m ag( G am m aLopt ) **2)

Eqn G t _den=m ag( ( 1- S_11m *G am m aS) *( 1- S_22m *G am m aLopt ) - S_21m *S_12m *G am m aS*G am m aLopt ) **2

Eqn G am m aLopt _NFm in=conj( S_22m +S_12m *S_21m *Sopt _at _m BiasPt / ( 1- S_11m *Sopt _at _m BiasPt ) )

Eqn G t _num _NFm in=m ag( S_21m ) **2 * ( 1- m ag( Sopt _at _m BiasPt ) **2) * ( 1- m ag( G am m aLopt _NFm in) **2)

Eqn G t _den_NFm in=m ag( ( 1- S_11m *Sopt _at _m BiasPt ) * ( 1- S_22m *G am m aLopt _NFm in) - S_21m *S_12m *Sopt _at _m BiasPt *G am m aLopt _NFm in) **2

Eqn G t r ans_power _NFm in=10* log( G t _num _NFm in/ G t _den_NFm in)

Eqn NF_lin_at _G am m aS=NFm in_lin+4*( Rn_at _m BiasPt / Z0_r ef ) *m ag( G am m aS- Sopt _at _m BiasPt ) **2/ ( ( 1- m ag( G am m aS) **2) *m ag( 1+Sopt _at _m BiasPt ) **2)

Eqn NFm in_lin=10**( NFm in_at _m BiasPt / 10)

Eqn NF_at _G am m aS=10* log( NF_lin_at _G am m aS)

Eqn NF_at _G am m aS_ConjM at ch=if ( st ab_f act ( S_bpm ) >1) t hen 10* log( NF_lin_at _G am m aS_ConjM at ch) else 1000

Eqn NF_lin_at _G am m aS_ConjM at ch=NFm in_lin+4*( Rn_at _m BiasPt / Z0_r ef ) *m ag( G am m aS_ConjM at ch- Sopt _at _m BiasPt ) **2/ ( ( 1- m ag( G am m aS_ConjM at ch) **2) *m ag( 1+Sopt _at _m BiasPt ) **2 +1e- 20)

( C) O pt im al G am m a_L when t he G am m a_S is at " m aker G am m aS"

( A) O pt im al G am m a_L when t he G am m a_S is at Sopt ( opt im al f or m inim um noise f igur e. )

( C) Noise f igur e f or an ar bit r ay G am m a_S ( m ar ker G am m aS)

( B) Noise f igur e f or sim ult aneously conjugat e m at ching. ( O nly def ined if K is >1. O t her wise t he noise f igur e is set t o 1000. )

( C) G t r ans_power : t r ansducer power gain wit h t he sour ce r ef lect ion coef f icient at m ar ker G am m aS, and t he load t hen conjugat ely m at ched.

( A) G t r ans_power _NFm in: t r ansducer power gain wit h t he sour ce r ef lect ion coef f icient Sopt f or m inim um noise f igur e, and t he load t hen conjugat ely m at ched.

Eqn G am m aSopt =conj( S_11m +S_12m *S_21m *G am m aL/ ( 1- S_22m *G am m aL) )

( D) O pt im al G am m a_S when t he G am m a_L at " m aker G am m aL"

Eqn G t load_num =m ag( S_21m ) **2 * ( 1- m ag( G am m aSopt ) **2) * ( 1- m ag( G am m aL) **2)

Eqn G t load_den=m ag( ( 1- S_11m *G am m aSopt ) * ( 1- S_22m *G am m aL) - S_21m *S_12m *G am m aSopt *G am m aL) **2

Eqn G t r ans_power _load=if ( G t load_num >0) t hen 10* log( G t load_num / G t load_den) else 1e6

( D) G t r ans_load : t r ansducer power gain wit h t he load r ef lect ion coef f icient at m ar ker G am m aL, and t he sour ce t hen opt im um ly noise m at ched.( D) Noise f igur e f or an ar bit r ay G am m a_L ( t he sour ce r ef lect ion coef f icient is at G am m aSopt )

Eqn NF_lin_at _G am m aSopt =NFm in_lin+4*( Rn_at _m BiasPt / Z0_r ef ) *m ag( G am m aSopt - Sopt _at _m BiasPt ) **2/ ( ( 1- m ag( G am m aSopt ) **2) *m ag( 1+Sopt _at _m BiasPt ) **2)

Eqn NF_at _G am m aSopt =10* log( NF_lin_at _G am m aSopt )

Sour ce r ef lect ion coef f icientEqn G am m aS_ConjM at ch=sm _gam m a1( S_bpm )

Zsour ce is t he im pedance at m ar ker G am m aS.Eqn Zsour ce2=Z0[ 0, 0, 0] * ( 1+G am m aS) / ( 1- G am m aS)

Eqn G t r ans_power =if ( G t _num >0) t hen 10* log( G t _num / G t _den) else 1e6

Eqn Noise_cir cleM in=ns_cir cle( NFm in_at _m BiasPt , NFm in_at _m BiasPt , Sopt _at _m BiasPt , Rn_at _m BiasPt / Z0_r ef , 51)

Eqn Noise_cir cles=ns_cir cle( NFm in_at _m BiasPt +NFst ep_size* [ 1: : num _NFcir cles] , NFm in_at _m BiasPt , Sopt _at _m BiasPt , Rn_at _m BiasPt / Z0_r ef , 51)

Eqn G Acir cleM ax=ga_cir cle( S_bpm , m ax_gain( S_bpm ) )

Eqn G Acir cles=ga_cir cle( S_bpm , m ax_gain( S_bpm ) - G Ast ep_size* [ 0: : num _G Acir cles] )

Eqn G Pcir cles=gp_cir cle( S_bpm , m ax_gain( S_bpm ) - G Pst ep_size* [ 0: : num _G Pcir cles] )

Set st ep size and num ber of cir cles t o plot

st ab_f act ( S[ I Cindex2, VCEindex2, 0] )

0. 6776

St abilit y K

t index is a vect or of num ber s 0, 1, 2, 3, . . . , 2000.

r hos ar e 2001 com plex r ef lect ion coef f icient s.

( B) G am m a_S f or sim ult aneous conjugat e m at ching at bias point m BiasPt .

NF at G am m aS ( dB)

NF_at _G am m aS

0. 6512

Zsour ce2

59. 4968 + j30. 8475

Sour ce I m pedance at G am m aS

. . . am m aLopt , Z0[ 0, 0, 0] )

31. 9360 + j31. 5019

O pt iom al Load I m pedance at G am m aS Tr ansducer Power G ain ( dB)

G t r ans_power

18. 6454

NFm in[ I Cindex2, VCEindex2, 0]

0. 6512

NFm in ( dB)

. . . ex2, VCEindex2, 0] , Z0[ 0, 0, 0] )

59. 0670 + j30. 3691

Sour ce I m pedance Zopt at NFm in

. . . m m aLopt _NFm in, Z0[ 0, 0, 0] )

31. 8982 + j31. 7136

O pt iom al Load I m pedance f or sour ce Zopt at NFm in Tr ansducer Power G ain ( dB)

G t r ans_power _NFm in

18. 6761

NF_at _G am m aS_ConjM at ch

1000

. . . ex2, VCEindex2, 0] , Z0[ 0, 0, 0] )

50. 0000

. . . ex2, VCEindex2, 0] , Z0[ 0, 0, 0] )

50. 0000

. . . gain( S[ I Cindex2, VCEindex2, 0] )

20. 7283

NF wit h Zsour ce ( valid f or K>1)

Sim ult aneous Conjugat e M at ched ( valid f or K>1)

Zsour ce Zload M AG ( or M SG f or K<1) NF_at _G am m aSopt

0. 8436

. . . aSopt , Z0[ 0, 0, 0] )

29. 2563 + j12. 1537

zin( G am m aL, Z0[ 0, 0, 0] )

61. 3802 - j39. 9026

G t r ans_power _load

16. 9127

NF wit h opt im al Zsour ce O pt im al Zsour ce when Zload is at G am m aL Zload at G am m aL Tr ansducer Power gain ( dB)

GAcirclesNoise_circles

Source_stabcirGPcirclesLoad_stabcir

Outside

Sourc e Stab le Region

0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0

0.5

1.0

1.52.0

2.5

3.03.5

4.0

4.55.0

5.5

6.06.5

7.0

7.5

0.0

8.0

I BB=0. 000

I BB=2. 000E- 6

I BB=4. 000E- 6

I BB=6. 000E- 6

I BB=8. 000E- 6

I BB=1. 000E- 5

I BB=1. 200E- 5

I BB=1. 400E- 5

I BB=1. 600E- 5

I BB=1. 800E- 5

I BB=2. 000E- 5

I BB=2. 200E- 5

I BB=2. 400E- 5

I BB=2. 600E- 5

I BB=2. 800E- 5

I BB=3. 000E- 5

VCE

IC.i

, m

A

mBiasPt

m Bias PtVCE=IC.i=5.417352mIBB=0.000020

3.000000

(A) Matching Condition for Minimum Noise Figure

(B) Matching Condition for Simultaneously Conjugate Matched (C) Matching Condition for Arbitray GammaS (D) Matching Condition for Arbitray GammaL

Find t he index of VCE and I C of t he biased point m BiasPt

Show 2000 point s on Sm it h Char t

Equations to Plot Noise, Gain, and Stability Circ les

Noise Circle

Available Power Gain Circle

Operating Power Gain Circle

Source and Load Stability Circles

Transducer Power Gain CalculationNoise Figure Calculation

Reflection Coeffic ients Calculation

4 Different Matching Condition:

(A) M atc h for m in im um NF

(D) M atc h for optim um NF wi th arb i tray Gam m a_L (Output Power)

(B) Sim ula taneous ly Conjugate M atc hI nput : m at ched m in. noise, out put : conjugat e m at ched

I nput : m at ched opt im um noise, O ut put : G am m aL

( A) NFm in_lin ( M im inum noise f act or )

( B) M ax. t r ansducer power gain is equal t o M AG ( or M SG ) when sim ulyaneously m at ched.

I nput : conjugat e m at ched, out put : conjugat e m at ched

(C) M atc h wi th arb i tray Gam m a_S (Gain c ons ideration)I nput : G am m aS, O ut put : conjugat e m at ched

Bias Point Selector

Eqn S_11m =S_bpm ( 1, 1)

Eqn S_12m =S_bpm ( 1, 2)

Eqn S_21m =S_bpm ( 2, 1)

Eqn S_22m =S_bpm ( 2, 2)

Eqn S_bpm =S[ I Cindex2, VCEindex2, 0]

Eqn NFm in_at _m BiasPt =NFm in[ I Cindex2, VCEindex2, 0]

Eqn Sopt _at _m BiasPt =Sopt [ I Cindex2, VCEindex2, 0]

Eqn Z0_r ef =Z0[ 0, 0, 0]

Eqn Rn_at _m BiasPt =Rn[ I Cindex2, VCEindex2, 0]

Transistor S-parameter at mBiasPt

O pt im um r ef lect ion coef f . ( NFm in)

Ref er ence im pedance

Rn at bias point

NFm in @ m BiasPt

13/15

在ADS建置完整的LNA設計環境(II)


0.5 1.0 1 .5 2.0 2 .5 3.0 3 .50 .0 4.0

1 .0

1 .5

2 .0

2 .5

0 .5

3 .0

I BB=0. 000

I BB=2. 00uI BB=4. 00uI BB=6. 00uI BB=8. 00uI BB=10. 0uI BB=12. 0uI BB=14. 0uI BB=16. 0uI BB=18. 0uI BB=20. 0uI BB=22. 0uI BB=24. 0uI BB=26. 0uI BB=28. 0uI BB=30. 0u

VCEN

Fm

in[0

]

m2

m 2VCE=NFm in [0 ]=727.6303mIBB=0.000002

3.000000

0.5 1 .0 1.5 2 .0 2.5 3 .0 3.50 .0 4 .0

-15

-10

-5

0

5

10

15

-20

20

I BB=0. 000

I BB=2. 00u

I BB=4. 00uI BB=6. 00uI BB=8. 00uI BB=10. 0uI BB=12. 0uI BB=14. 0uI BB=16. 0uI BB=18. 0uI BB=20. 0uI BB=22. 0uI BB=24. 0uI BB=26. 0uI BB=28. 0uI BB=30. 0u

VCE

dB

(S2

1[0

])

m1

m 1VCE=dB(S21[0 ])=6 .954IBB=0.000002

3.000

0.5 1 .0 1.5 2 .0 2.5 3 .0 3 .50 .0 4.0

-16

-14

-12-10

-8-6

-4

-2

-18

0 I BB=0. 000

I BB=2. 00uI BB=4. 00uI BB=6. 00uI BB=8. 00uI BB=10. 0uI BB=12. 0uI BB=14. 0uI BB=16. 0uI BB=18. 0uI BB=20. 0uI BB=22. 0uI BB=24. 0uI BB=26. 0uI BB=28. 0uI BB=30. 0u

VCE

dB

(S1

1[0

])

I BB=0. 000I BB=2. 00uI BB=4. 00uI BB=6. 00uI BB=8. 00uI BB=10. 0uI BB=12. 0uI BB=14. 0uI BB=16. 0uI BB=18. 0uI BB=20. 0uI BB=22. 0uI BB=24. 0uI BB=26. 0uI BB=28. 0uI BB=30. 0u

dB

(S2

2[0

])

0 .5 1 .0 1.5 2 .0 2.5 3 .0 3 .50 .0 4 .0

-20

-15

-10

-5

-25

0

I BB=0. 000I BB=2. 00uI BB=4. 00uI BB=6. 00uI BB=8. 00uI BB=10. 0uI BB=12. 0uI BB=14. 0uI BB=16. 0uI BB=18. 0uI BB=20. 0uI BB=22. 0uI BB=24. 0uI BB=26. 0uI BB=28. 0uI BB=30. 0u

VCE

dB

(S1

2)

0 .5 1 .0 1.5 2 .0 2.5 3 .0 3.50 .0 4 .0

0

5

10

15

20

-5

25

I BB=0. 000

I BB=2. 00u

I BB=4. 00u

I BB=6. 00uI BB=8. 00uI BB=10. 0uI BB=12. 0uI BB=14. 0uI BB=16. 0uI BB=18. 0uI BB=20. 0uI BB=22. 0uI BB=24. 0uI BB=26. 0uI BB=28. 0uI BB=30. 0u

VCE

MA

G,

dB

M inim um No is e Figure v ers us IBB and VCETrans is to r dB(S21) v ers us IBB and VCE

M ax im um Av a ilab le Gain v ers us IBB and VCE

dB(S12) v ers us IBB and VCE

dB(S11) and dB(S22) v ers us IBB and VCE

0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 3. 50. 0 4. 0

0

5

10

15

- 5

20

I B B = 0 . 0 0 0

I B B = 2 . 0 0 u

I B B = 4 . 0 0 uI B B = 6 . 0 0 uI B B = 8 . 0 0 uI B B = 1 0 . 0 uI B B = 1 2 . 0 uI B B = 1 4 . 0 uI B B = 1 6 . 0 uI B B = 1 8 . 0 uI B B = 2 0 . 0 uI B B = 2 2 . 0 uI B B = 2 4 . 0 uI B B = 2 6 . 0 uI B B = 2 8 . 0 uI B B = 3 0 . 0 u

VCE

Pgain

_ass

oc

m 4

m 4VCE=Pga in_as s oc =19.273IBB=0.000030

3.000

As s oc ia ted Power Gain (input m atc hed fo r NFm in , ou tpu t then c on juga te ly m atc hed) v e rs us IBB and VCE

Eqn M AG =m ax_gain( S) M ax im um av ai lable ga in a t a l l frequenc ies

Eqn f r equency=SP. f req[ 0, 0, 0]

Eqn I Cindex=f ind_index( I C[ VCEindex] , m 3)

Eqn VCEindex=f ind_index( DC. VCE[ 0, : : ] , indep( m 3) )

Eqn I C=-SRC1. i

Eqn DC_power =m3* indep( m 3)

Eqn G am maS_at _bias_pt =sm_gam ma1( S_bp)

Eqn G am maL_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[ I Cindex, 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 am maL_wSopt =conj( S_22p_at _bias)

Eqn S_bp=S[ I Cindex, VCEindex, 0]

Eqn NFmin_at _bias_pt =NFm in[ I Cindex, VCEindex, 0]

S-param eters a t the b ias poin t s pec i fied by m ark er m 3.

Sourc e im pedanc e fo r m in im um no is e figure a t the biaspoin t s pec i fied by m ark er m 3.

Stabi l i ty fac to r a t the b ias poin t m 3.

Zs ourc e and Zload a re the s ourc e and load im pedanc es to p res ent to the dev ic e for s im ul taneous c on juga te m atc h ing, at the b ias po int m 3.Thes e a re not defined and re turn 0 i f K<1.

S_22p : re flec tion look ing into the ou tpu t of the dev ic e , when the s ourc e is optim a l fo r m in im um no is e figure.

Gam m aL_wSopt is the c om plex c onjuga te o f S22_p, and is the op tim a l load reflec tion c oe ffic ient when Sopt is the s ourc e re flec tion c oeffi c ien t. Zload_wSopt is the c orres ponding im pedanc e.

Sim u ltaneous c on juga te m atc h s ourc e and load re flec tion c oeffi c ien tsa t b ias po in t m 3. Thes e a re no t de fined and re turn 0 i f K<1.

Trans duc er power gain wi th the s ourc e re flec tion c oeffi c ien t Sopt for m in im um nois e figure , and the load then c on juga te ly m atc hed. z opt() i s jus t us ed to c onv ert a re flec tion c oe ffi c ien t to an im pedanc e.

Co llec to r DC c urren t

Find index for the s wept v ariable VCE and ICE ac c ord ing to m ark er "m 3" x -ax is .

M in im um nois e figure at the m 3 bias po in t.

DC power c om s um ption when bias ed at m ark er "m 3" (bas e c urren t i s ignored)

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

I BB=0. 000

I BB=2. 00u

I BB=4. 00u

I BB=6. 00u

I BB=8. 00u

I BB=10. 0u

I BB=12. 0uI BB=14. 0u

I BB=16. 0u

I BB=18. 0uI BB=20. 0u

I BB=22. 0u

I BB=24. 0uI BB=26. 0uI BB=28. 0u

I BB=30. 0u

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] )

Sourc e reflec tion c oe ffic ient for m in im um nois e figure a t frequenc y s pec i fied by m ark er m 3. Sop t is the s -param eterfor optim um no is e perform anc e.

(1) (2)

Bas ic in fo rm ation at the b ias po int m 3.

Optim um reflec tion c oe ffi c ien t(im pedanc e) fo r m inim um no is e at the b ias po int m 3.

Outpu t Conjuga te ly M atc h ing Im pdeanc e Ca lc u la tion (when input i s no is e m atc hed)

Inpu t/Output Sim ul taneous ly Conjuga te M atc hed (input i s NOT no is e m atc 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 a l Sourc e Reflec tion Coeffic ients fo r M in inum NF, Sim ul taneous Con juga te M atc h ing, and Load Reflec tion Coeffic ien t fo r 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 (o r c i rc ui t) is uns tab le a t the b ias poin t, the s im u l taneous c on juga te m atc hing im pedanc es are undefined and Gam m aL_at_bias _p t and Gam m aS_at_bias _p t de fau l t to 0 . Als o, M AG is s e t equal to the m ax im um s tab le gain , |S21 |/|S12|.

1.0

0m

2.0

0m

3.0

0m

4.0

0m

5.0

0m

6.0

0m

7.0

0m

0.0

00

8.0

0m

0 .6

0.8

1.0

1.2

1.4

1.6

1.8

0.4

2.0

IC

NF

min

, d

B

m 5

m 5indep(m 5)=v s (NFm in [VCEindex ,0],IC.i [VCEindex ])=0.651189

0.005417NFmin versus IC, at VCE (set by m3)

1.0

0m

2.0

0m

3.0

0m

4.0

0m

5.0

0m

6.0

0m

7.0

0m

0.0

00

8.0

0m

-15

-10

-5

0

5

10

15

-20

20

IC

dB

(S2

1)

dB(S21) v ers us IC, a t VCE (s e t by m 3)

indep( m3)

3. 0000

m 3[ 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 to r S-param eter at b ias po int 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 a liable Ga in (dB) Zsource

50. 0000

Zload

50. 0000

Sim ultaneous M atc h

Matching for Noise Figure

NFm in_at _bias_pt

0. 6512

M in im um 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

Con juga te M atc hed Load (fo r inpu t m atc hed to NFm in)

Zopt Zload_wSopt

DUT*

Pgain_assoc_at _bias

18. 6761

Power Ga in (dB) a t th is no is e m atc hed c ondi tion

Gam m a_S (NFm in)

Gam m a_L when NFm in

Bias Point Selector

Updated Information according to the Bias Point m3

14/15

在ADS建置完整的LNA設計環境(III)


Move marker mBiasPt to desiredfrequency point. Smith Chart and data below will be updated.

Move markers GammaS and GammaL to select arbitrary source and load reflection coeffic ients The impedances, power gains,and noise figures below will be updated. The transducer power gains are invalid if the markers are moved into the unstable regions.

Eqn num _NFc irc les =3Eqn NFs tep_s iz e=0.2Eqn GAs tep_s iz e=1

Eqn num _GAc irc les =3

Zs ourc e, Gam m a_S

Zload, Gam m a_L

DUT*

Eqn num _GPc i rc les =3Eqn GPs tep_s i z e=1

G am m aSindep( G am m aS) =r hos=- 0. 25766 - j0. 01061

im pedance = 29. 50724 - j0. 67091

133

indep( r hos) ( 0. 000 t o 2000. 000)

rhos

GammaS

indep( Sour ce_st abcir ) ( 0. 000 t o 51. 000)

Sour

ce_s

tabc

ir

g a in = 2 1 . 0 0 4

g a in = 2 0 . 0 0 4

g a in = 1 9 . 0 0 4

g a in = 1 8 . 0 0 4

cir _pt s ( 0. 000 t o 51. 000)

GAc

ircles

indep( G am m aLopt ) ( 133. 000 t o 133. 000)

Gam

maL

opt

n s f ig u r e = 0 . 8 6 7n s f ig u r e = 1 . 0 6 7

n s f ig u r e = 1 . 2 6 7

Noise

_circ

lesNo

ise_c

ircleM

in

G am m aSindep( G am m aS) =r hos=- 0. 25766 - j0. 01061

im pedance = 29. 50724 - j0. 67091

133 G am m aLindep( G am m aL) =r hos=0. 35071 / - 54. 37157im pedance = Z0 * ( 1. 22760 - j0. 79805)

246

indep( r hos) ( 0. 000 t o 2000. 000)

rhos

GammaL

indep( Load_st abcir ) ( 0. 000 t o 51. 000)

Load

_sta

bcir

g a in = 2 1 . 0 0 4

g a in = 2 0 . 0 0 4

g a in = 1 9 . 0 0 4

g a in = 1 8 . 0 0 4

cir _pt s ( 0. 000 t o 51. 000)

GPc

ircles

indep( G amm aSopt ) ( 246. 000 t o 246. 000)

Gam

maS

opt

G am m aLindep( G am m aL) =r hos=0. 35071 / - 54. 37157im pedance = Z0 * ( 1. 22760 - j0. 79805)

246

Available Gain Circle: Noise Circles:Source Stability Circle:Source Gamma Corresponding Load Gamma (Black Dot)

Power Gain Circles:Load Stability Circle:Load Gamma Corresponding Source Gamma (Black Dot)

Load Stable Reg ion

Eqn t index=[ 0: : 2000]

Eqn r hos=sqr t ( t index/ 2000) * exp( j*2*sqr t ( pi* t index) )

Eqn Sour ce_st abcir =s_st ab_cir cle( S[ f m 1] , 51)

Eqn Load_st abcir =l_st ab_cir cle( S[ f m 1] , 51)

Eqn G amm aLopt =conj( S22[ f m1] +S12[ f m 1] * S21[ f m 1] *G am m aS/ ( 1- S11[ f m 1] * G am maS) )

Eqn G t _num=m ag( S21[ f m 1] ) * *2 *( 1- m ag( G am m aS) ** 2) *( 1- m ag( G am m aLopt ) **2)

Eqn G t _den=m ag( ( 1- S11[ f m 1] *G am m aS) *( 1- S22[ f m 1] *G am maLopt ) - S21[ f m 1] *S12[ f m 1] * G am maS*G amm aLopt ) * *2

Eqn G amm aLopt _NFm in=conj( S22[ f m 1] +S12[ f m 1] * S21[ f m1] * Sopt [ f m1] / ( 1- S11[ f m1] *Sopt [ f m1] ) )

Eqn G t _num_NFmin=m ag( S21[ f m1] ) **2 *( 1- m ag( Sopt [ f m1] ) * *2) * ( 1- mag( G amm aLopt _NFm in) * *2)

Eqn G t _den_NFm in=mag( ( 1- S11[ f m 1] *Sopt [ f m 1] ) * ( 1- S22[ f m1] *G amm aLopt _NFm in) - S21[ f m 1] * S12[ f m1] * Sopt [ f m1] * G amm aLopt _NFm in) **2

Eqn G t r ans_power _NFm in=10*log( G t _num _NFm in/ G t _den_NFm in)

Eqn NF_lin_at _G am m aS=NFmin_lin+4* ( Rn[ f m 1] / Z0[ f m1] ) *m ag( G am maS- Sopt [ f m1] ) * *2/ ( ( 1- m ag( G am m aS) ** 2) * m ag( 1+Sopt [ f m1] ) * *2)

Eqn NFm in_lin=10** ( NFmin[ f m1] / 10)

Eqn NF_at _G amm aS=10*log( NF_lin_at _G am m aS)

Eqn NF_at _G amm aS_ConjM at ch=if ( st ab_f act ( S[ f m1] ) >1) t hen 10*log( NF_lin_at _G am m aS_ConjM at ch) else 1000

Eqn NF_lin_at _G am m aS_ConjM at ch=NFm in_lin+4*( Rn[ f m 1] / Z0[ f m 1] ) * mag( G amm aS_ConjM at ch- Sopt [ f m 1] ) ** 2/ ( ( 1- m ag( G amm aS_ConjM at ch) ** 2) * m ag( 1+Sopt [ f m1] ) * *2 +1e- 20)

( C) O pt im al G am ma_L when t he G am m a_S is at " maker G am m aS"

( A) O pt im al G am ma_L when t he G am m a_S is at Sopt ( opt im al f or m inimum noise f igur e. )

( C) Noise f igur e f or an ar bit r ay G am m a_S ( m ar ker G am maS)

( B) Noise f igur e f or sim ult aneously conjugat e m at ching. ( O nly def ined if K is >1. O t her wise t he noise f igur e is set t o 1000. )

( C) G t r ans_power : t r ansducer power gain wit h t he sour ce r ef lect ion coef f icient at mar ker G amm aS, and t he load t hen conjugat ely mat ched.

( A) G t r ans_power _NFmin: t r ansducer power gain wit h t he sour ce r ef lect ion coef f icient Sopt f or m inim um noise f igur e, and t he load t hen conjugat ely mat ched.

Eqn G amm aSopt =conj( S11[ f m1] +S12[ f m 1] *S21[ f m 1] *G am m aL/ ( 1- S22[ f m1] *G amm aL) )

( D) O pt im al G am ma_S when t he G am m a_L at " m aker G am m aL"

Eqn G t load_num =m ag( S21[ f m1] ) * *2 *( 1- m ag( G am m aSopt ) ** 2) *( 1- m ag( G am m aL) ** 2)

Eqn G t load_den=mag( ( 1- S11[ f m 1] *G am m aSopt ) *( 1- S22[ f m 1] *G am m aL) - S21[ f m 1] *S12[ f m 1] * G am maSopt * G amm aL) * *2

Eqn G t r ans_power _load=if ( G t load_num>0) t hen 10* log( G t load_num / G t load_den) else 1e6

( D) G t r ans_load : t r ansducer power gain wit h t he load r ef lect ion coef f icient at m ar ker G am m aL, and t he sour ce t hen opt imumly noise m at ched.( D) Noise f igur e f or an ar bit r ay G am m a_L ( t he sour ce r ef lect ion coef f icient is at G am m aSopt )

Eqn NF_lin_at _G am m aSopt =NFmin_lin+4* ( Rn[ f m 1] / Z0[ f m 1] ) *m ag( G am maSopt - Sopt [ f m 1] ) **2/ ( ( 1- mag( G amm aSopt ) * *2) *m ag( 1+Sopt [ f m 1] ) **2)

Eqn NF_at _G amm aSopt =10*log( NF_lin_at _G am m aSopt )

Sour ce r ef lect ion coef f icientEqn G amm aS_ConjM at ch=sm _gam m a1( S[ f m 1] )

Zsour ce is t he im pedance at m ar ker G am m aS.Eqn Zsour ce2=Z0*( 1+G am m aS) / ( 1- G am m aS)

Eqn G t r ans_power =if ( G t _num >0) t hen 10*log( G t _num / G t _den) else 1e6

Eqn Noise_cir cleM in=ns_cir cle( NFm in[ f m 1] , NFm in[ f m 1] , Sopt [ f m 1] , Rn[ f m1] / Z0[ f m 1] , 51)

Eqn Noise_cir cles=ns_cir cle( NFm in[ f m 1] +NFst ep_size*[ 1: : num _NFcir cles] , NFm in[ f m 1] , Sopt [ f m 1] , Rn[ f m 1] / Z0[ f m 1] , 51)

Eqn G Acir cleM ax=ga_cir cle( S[ f m 1] , m ax_gain( S[ f m 1] ) )

Eqn G Acir cles=ga_cir cle( S[ f m 1] , max_gain( S[ f m 1] ) - G Ast ep_size* [ 0: : num _G Acir cles] )

Eqn G Pcir cles=gp_cir cle( S[ f m 1] , max_gain( S[ f m 1] ) - G Pst ep_size* [ 0: : num _G Pcir cles] )

Set st ep size and num ber of cir cles t o plot

st ab_f act ( S[ f m 1] )

0. 7083

St abilit y K

t index is a vect or of number s 0, 1, 2, 3, . . . , 2000.

r hos ar e 2001 com plex r ef lect ion coef f icient s.

( B) G am m a_S f or sim ult aneous conjugat e m at ching at bias point m BiasPt .

NF at G amm aS ( dB)

NF_at _G amm aS

0. 9252

Zsour ce2

29. 5072 - j0. 6709

Sour ce I m pedance at G am maS

. . . am m aLopt , Z0[ f m 1] )

34. 8292 + j54. 1030

O pt iom al Load I m pedance at G amm aS Tr ansducer Power G ain ( dB)

G t r ans_power

20. 3030

NFmin[ f m 1]

0. 6669

NFmin ( dB)

zopt ( Sopt [ f m 1] , Z0[ f m1] )

58. 8848 + j26. 9719

Sour ce I mpedance Zopt at NFm in

. . . maLopt _NFm in, Z0[ f m 1] )

32. 4007 + j30. 7066

O pt iom al Load I m pedance f or sour ce Zopt at NFm in Tr ansducer Power G ain ( dB)

G t r ans_power _NFm in

18. 8942

NF_at _G amm aS_ConjM at ch

1000

sm _z1( S[ f m 1] , Z0[ f m1] )

50. 0000

sm _z2( S[ f m 1] , Z0[ f m 1] )

50. 0000

m ax_gain( S[ f m 1] )

21. 0038

NF wit h Zsour ce ( valid f or K>1)

Sim ult aneous Conjugat e M at ched ( valid f or K>1)

Zsour ce Zload M AG ( or MSG f or K<1) NF_at _G am maSopt

0. 8562

. . . aSopt , Z0[ f m1] )

29. 1731 + j10. 0394

zin( G am m aL, Z0[ f m 1] )

61. 3802 - j39. 9026

G t r ans_power _load

17. 1906

NF wit h opt imal Zsour ce O pt imal Zsour ce when Zload is at G am m aL Zload at G am maL Tr ansducer Power gain ( dB)

GAcirclesNoise_circles

Source_stabcirGPcirclesLoad_stabcir

Sourc e Stab le Reg ion

(A) Matching Condition for Minimum Noise Figure

(B) Matching Condition for Simultaneously Conjugate Matched (C) Matching Condition for Arbitray GammaS (D) Matching Condition for Arbitray GammaL

Find t he index of VCE and I C of t he biased point mBiasPt

Show 2000 point s on Smit h Char t

Equations to Plot Noise, Gain, and Stability Circ les

Noise Circle

Available Power Gain Circle

Operating Power Gain Circle

Source and Load Stability Circles

Transducer Power Gain CalculationNoise Figure Calculation

Reflection Coeffic ients Calculation

4 Different Matching Condition:

(A) M atc h fo r m in im um NF

(D) M atc h fo r op tim um NF with arb i tray Gam m a_L (Output Power)

(B) Sim u la taneous ly Conjugate M atc hI nput : m at ched m in. noise, out put : conjugat e m at ched

I nput : m at ched opt im um noise, O ut put : G amm aL

( A) NFm in_lin ( M im inum noise f act or )

( B) Max. t r ansducer power gain is equal t o M AG ( or MSG ) when sim ulyaneously m at ched.

I nput : conjugat e mat ched, out put : conjugat e mat ched

(C) M atc h with a rbi tray Gam m a_S (Gain c ons idera tion)I nput : G amm aS, O ut put : conjugat e m at ched

Frequency Point Selectorfm1indep(fm1)=plot_vs([0::sweep_size(frequency)-1],frequency)=6.000000

2.360000G

2.32E9

2.34E9

2.36E9

2.38E9

2.40E9

2.42E9

2.44E9

2.46E9

2.48E9

2.30E9

2.50E9

0. 0

1. 0E6

f r equency

fm1

fm1indep(fm1)=plot_vs([0::sweep_size(frequency)-1],frequency)=6.000000

2.360000G

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