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射頻電子 - [第六章] 低雜訊放大器設計

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低雜訊放大器設計

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射頻電子 - [第六章] 低雜訊放大器設計

  1. 1. 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 Engineering National Taipei University of Technology
  2. 2. 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
  3. 3. 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 Department of Electronic Engineering, NTUT3/15
  4. 4. 回顧:功率-增益關係式 2 2 2 212 2 22 1 1 1 1 s LL T AVS in s L P G S P S − Γ − Γ = = − Γ Γ − Γ 2 2 2 212 2 11 1 1 1 1 s LL T AVS s out L P G S P S − Γ − Γ = = − Γ − Γ Γ 2 2 212 2 22 11 1 1 LL p in in L P G S P S − Γ = = − Γ − Γ 2 2 212 2 11 1 1 1 1 sAVN A AVS s out P G 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 interface ML 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 Department of Electronic Engineering, NTUT4/15
  5. 5. 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 2 2 2 21 212 2 2 2 22 11 1 1 1 1 1 1 1 1 s L s L T s in L s out L G S S S S − Γ − Γ − Γ − Γ = = − Γ Γ − Γ − Γ − Γ Γ Transistor [S]+ − sE sZ LZ 見第五章投影片slide 32 Department of Electronic Engineering, NTUT inΓ 1E oZ oZ Transistor oG Output matching LG Input matching sG s in ∗ Γ = Γ L out ∗ Γ = ΓoutΓ • 功率轉換增益 GT inΓsΓ LΓoutΓ 輸出端的匹配目標輸入端的匹配目標 5/15
  6. 6. 可資用功率增益圓(I) ( )2 2 21 2 212 222 11 11 1 1 1 1 s A a s s s S G S g S S S − Γ = = ⋅  − ∆Γ  − − Γ  − Γ   • 無條件穩定雙向(bilateral)情況: ( ) ( ) 2 2 2 2 2 2 21 22 11 1 1 1 2Re sA a s s G g S S S C − Γ = = − + Γ − ∆ − Γ 1 11 22C S S∗ = − ∆ s a aC rΓ − = ( ) 1 2 2 111 a a a g C C g S ∗ = + − ∆ ( ) 2 2 12 21 12 21 2 2 11 1 2 1 a a a a K S S g S S g r g S − + = + − ∆ 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)。 2 2 212 2 11 1 1 1 1 sAVN A AVS s out P G S P S − Γ = = − Γ − Γ 12 21 22 11 22 12 21 22 22 11 11 111 1 1 s s s s out s s s S S S S S S S S S S S S Γ − Γ + Γ − ∆Γ Γ = + = = − Γ − Γ − Γ 11 22 12 21S S S S∆ = − Department of Electronic Engineering, NTUT6/15
  7. 7. 可資用功率增益圓(II) Department of Electronic Engineering, NTUT ,max ,max_@A s GAG Γ 1 1@A sG Γ 2 2@A sG Γ 3 3@A sG Γ Γs平面 Γs平面 18 dB 17 dB 16 dB 15 dB 14 dB GaCircle GaCircle1 GaCircle1=ga_circle(S,{18, 17, 16, 15 ,14} ,51) GaCircle MeasEqn Meas1 GAmax=max_gain(S) Eqn Meas GaCircle GaCircle1 GaCircle1=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
  8. 8. 設計程序 1E oZ oZ Transistor oG Output matching LG Input matching sG sΓ LΓoutΓ • 可資用功率增益設計法 18 dB 17 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 Department of Electronic Engineering, NTUT8/15
  9. 9. 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: Noisy Two-portsYsi 2 4 n n e R kTB ≡ 2 4 u u i G kTB ≡ 2 4 s s i G kTB ≡ ( ) ( ) 2 2 2 1 1 u c s c s nu c s n s s G G G B B RG Y Y R F G G  + + + ++ +  = + = + , ,and Department of Electronic Engineering, NTUT s c optB B B= − = 2u s c opt n G G G G R = + =and 2 min 1 2 1 2 u n opt c n c c n G F R G G R G G R    = + + = + + +     ( ) ( ) 2 2 min n s opt s opt s R F F G G B B G  = + − + −   0 11 1 s s s Y Z − Γ = + Γ 0 11 1 opt opt opt Y Z − Γ = + Γ ( ) ( ) 2 min 22 0 4 1 1 s optn s s opt R F F Z Γ − Γ Γ = + − Γ + Γ • 固定雜訊指數圓 9/15
  10. 10. 固定雜訊指數圓 Department of Electronic Engineering, NTUT 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 NsCircle NsCircle1 NsCircle1=ns_circle(nf2,NFmin,Sopt,Rn/50,51) NsCircle VAR VAR4 Num_NF_Circles=5 NF_Stepsize=0.5 Eqn Var NsCircle NsCircle1 NsCircle1=ns_circle(NFmin+NF_Stepsize*[1::Num_NF_Circles],NFmin,Sopt,Rn/50,51) NsCircle min ,@ s optNF Γ 10/15
  11. 11. 低雜訊放大器設計(增益與雜訊的取捨) GA circles NF circles Input matching Output matching Amplifier sΓ LΓ 0Z 0Z inΓ outΓ outZinZ Department of Electronic Engineering, NTUT Min. noise figure, min ,, s optNF Γ Max. available power gain, s in ∗ Γ = Γ 11/15
  12. 12. 利用ADS在史密斯圖上進行取捨設計 Department of Electronic Engineering, NTUT GammaS indep(GammaS)= rhos=-0.11872 + j0.12612 impedance = 38.26607 + j9.95049 60 indep(rhos) (0.000 to 2000.000) rhos GammaSgain=18.937 gain=17.937 gain=16.937 gain=15.937 cir_pts (0.000 to 51.000) GAcircles indep(GammaLopt) (60.000 to 60.000) GammaLopt ns figure=1.404ns figure=1.604ns figure=1.804 Noise_circles (0.000 to 0.000) Sopt[fm1] GammaLopt_NFmin GammaS indep(GammaS)= rhos=-0.11872 + j0.12612 impedance = 38.26607 + j9.95049 60 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 GammaS indep(GammaS)= rhos=-0.45577 + j0.18782 impedance = 17.56757 + j8.71721 486 indep(rhos) (0.000 to 2000.000) rhos GammaS gain=18.937 gain=17.937 gain=16.937 gain=15.937 cir_pts (0.000 to 51.000) GAcircles indep(GammaLopt) (486.000 to 486.000) GammaLopt ns figure=1.404ns figure=1.604ns figure=1.804 Noise_circles (0.000 to 0.000) Sopt[fm1] GammaLopt_NFmin GammaS indep(GammaS)= rhos=-0.45577 + j0.18782 impedance = 17.56757 + j8.71721 486 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
  13. 13. 在ADS建置完整的LNA設計環境(I) Department of Electronic Engineering, NTUT Move marker mBiasPtto desired bias point. Smith Chartand data below will be updated. 2.400 GHz 50.000 System Impedance, Z0RFFrequency Move markers GammaSand GammaL to selectarbitrary source and load reflection coefficients The impedances,power gains,and noise figures below will be updated.The transducer power gains are invalid ifthe markers are moved into the unstable regions. Eqn num _NFc irc les =3 Eqn 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 irc les =3 Eqn 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) Source_stabcir gain=20. 728 gain=19. 728 gain=18. 728 gain=17. 728 cir _pt s ( 0. 000 t o 51. 000) GAcircles indep( G am m aLopt ) ( 161. 000 t o 161. 000) GammaLopt ns f igur e=0. 851ns f igur e=1. 051ns f igur e=1. 251 Noise_circles Noise_circleMin G am m aS indep( G am m aS) =r hos=0. 15388 + j0. 23837 im 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_stabcir gain=20. 728 gain=19. 728 gain=18. 728 gain=17. 728 cir _pt s ( 0. 000 t o 51. 000) GPcircles indep( G am m aSopt ) ( 246. 000 t o 246. 000) GammaSopt G am m aL indep( G am m aL) = r hos=0. 35071 / - 54. 37157 im 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 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) GAcircles Noise_circles Source_stabcir GPcircles Load_stabcir Outside Sourc e Stable Region 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 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,mA mBiasPt m Bias Pt VCE= IC.i=5.417352m IBB=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 PlotNoise,Gain,and Stability Circles Noise Circle Available Power Gain Circle Operating Power Gain Circle Source and Load Stability Circles Transducer Power Gain CalculationNoise Figure Calculation Reflection Coefficients Calculation 4 DifferentMatching Condition: (A) M atc h for m inim um NF (D) M atc h for optim um NF with arbitray Gam m a_L (Output Power) (B) Sim ulataneous ly Conjugate M atc h I 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 with arbitray 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 atmBiasPt 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
  14. 14. 在ADS建置完整的LNA設計環境(II) Department of Electronic Engineering, NTUT 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. 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. 0u I BB=20. 0uI BB=22. 0uI BB=24. 0uI BB=26. 0uI BB=28. 0u I BB=30. 0u VCE NFmin[0] m2 m 2 VCE= NFm in[0]=727.6303m IBB=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. 00u I BB=6. 00u I BB=8. 00uI BB=10. 0u I BB=12. 0u I BB=14. 0uI BB=16. 0uI BB=18. 0u I BB=20. 0uI BB=22. 0uI BB=24. 0uI BB=26. 0uI BB=28. 0uI BB=30. 0u VCE dB(S21[0]) m1 m 1 VCE= dB(S21[0])=6.954 IBB=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. 00u I BB=4. 00u I BB=6. 00u I BB=8. 00u I BB=10. 0u I BB=12. 0u I BB=14. 0uI BB=16. 0u I BB=18. 0uI BB=20. 0u I BB=22. 0uI BB=24. 0u I BB=26. 0uI BB=28. 0uI BB=30. 0u VCE dB(S11[0]) 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. 0u I BB=14. 0u I BB=16. 0uI BB=18. 0u I BB=20. 0uI BB=22. 0u I BB=24. 0u I BB=26. 0uI BB=28. 0u I BB=30. 0u dB(S22[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. 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. 0uI BB=16. 0u I BB=18. 0uI BB=20. 0u I BB=22. 0uI BB=24. 0uI BB=26. 0u I BB=28. 0uI BB=30. 0u VCE dB(S12) 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. 00u I BB=10. 0u I BB=12. 0u I BB=14. 0uI BB=16. 0u I BB=18. 0uI BB=20. 0uI BB=22. 0u I BB=24. 0uI BB=26. 0uI BB=28. 0uI BB=30. 0u VCE MAG,dB M inim um Noise Figure versus IBB and VCETrans istor dB(S21) v ers us IBB and VCE M axim um Av ailable Gain v ersus 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 u I B B = 6 . 0 0 u I B B = 8 . 0 0 u I B B = 1 0 . 0 u I B B = 1 2 . 0 uI B B = 1 4 . 0 uI B B = 1 6 . 0 u I B B = 1 8 . 0 uI B B = 2 0 . 0 uI B B = 2 2 . 0 uI B B = 2 4 . 0 u I B B = 2 6 . 0 uI B B = 2 8 . 0 uI B B = 3 0 . 0 u VCE Pgain_assoc m 4 m 4 VCE= Pgain_as soc=19.273 IBB=0.000030 3.000 As soc iated Power Gain (input m atc hed for NFm in, output then c onjugately m atc hed) v ers us IBB and VCE Eqn M AG =m ax_gain( S) M axim um av ailable gain at all 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 at the bias point s pec ified by m arker m 3. Source im pedanc e for m inim um nois e figure at the bias point s pec ified by m arker m 3. Stability fac tor at the bias point m 3. Zsourc e and Zload are the s ourc e and load im pedanc es to pres ent to the dev ice for s im ultaneous conjugate m atching, at the bias point m 3. Thes e are not defined and return 0 if K<1. S_22p : reflection look ing into the output of the dev ice, when the sourc e is optim al for m inim um nois e figure. Gam m aL_wSopt is the c om plex c onjugate of S22_p, and is the optim al load reflection c oeffic ient when Sopt is the s ource reflec tion coeffic ient. Zload_wSopt is the c orres ponding im pedance. Sim ultaneous c onjugate m atch s ource and load reflec tion c oefficients at bias point m 3. These are not defined and return 0 if K<1. Trans duc er power gain with the s ourc e reflec tion c oeffic ient Sopt for m inim um nois e figure, and the load then c onjugately m atc hed. zopt() is jus t us ed to c onv ert a reflec tion coeffic ient to an im pedance. Collec tor DC current Find index for the swept v ariable VCE and ICE acc ording to m ark er "m 3" x-axis . M inim um nois e figure at the m 3 bias point. DC power c om s um ption when biased at m arker "m 3" (bas e current is 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. 0u I BB=14. 0u I BB=16. 0u I BB=18. 0u I BB=20. 0u I BB=22. 0u I BB=24. 0u I BB=26. 0u I BB=28. 0u I BB=30. 0u VCE IC.i,A m3 m 3 VCE= IC.i=5.417352m IBB=0.000020 3.000000 I/V Curv e (Selec t Biasing Point via m aker 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 reflection c oeffic ient for m inim um nois e figure at frequenc y s pec ified by m ark er m 3. Sopt is the s-param eter for optim um noise perform ance. (1) (2) Bas ic inform ation at the bias point m 3. Optim um reflec tion c oeffic ient(im pedanc e) for m inim um noise at the bias point m 3. Output Conjugately M atching Im pdeance Calculation (when input is nois e m atc hed) Input/Output Sim ultaneous ly Conjugate M atc hed (input is NOT nois e m atc hed) Move marker m3 to selectbias point. All listings and impedances on Smith Chartwill be updated. Matching for Gain Zsourc e Zload DUT* (0.000 to 0.000) Sopt_at_bias_pt GammaS_at_bias_pt GammaL_at_bias_pt GammaL_wSopt Optim al Sourc e Reflection Coeffic ients for M ininum NF, Sim ultaneous Conjugate M atching, and Load Reflec tion Coeffic ient for Sim ultaneous Conjugate M atc hing, and with s ource m atc hed for NFm in Note: if the dev ic e (or circ uit) is uns table at the bias point, the s im ultaneous c onjugate m atc hing im pedances are undefined and Gam m aL_at_bias _pt and Gam m aS_at_bias_pt default to 0. Als o, M AG is set equal to the m ax im um stable gain, |S21|/|S12|. 1.00m 2.00m 3.00m 4.00m 5.00m 6.00m 7.00m 0.000 8.00m 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.4 2.0 IC NFmin,dB m 5 m 5 indep(m 5)= v s (NFm in[VCEindex ,0],IC.i[VCEindex])=0.651189 0.005417 NFmin versus IC, at VCE (set by m3) 1.00m 2.00m 3.00m 4.00m 5.00m 6.00m 7.00m 0.000 8.00m -15 -10 -5 0 5 10 15 -20 20 IC dB(S21) dB(S21) v ersus IC, at VCE (s et 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 tor S-param eter at bias point m 3 K 0. 6776 Stability Fac tor Z0[ 0, 0, 0] 50. 0000 Charac teris tic s Im pedanc e m ax_gain(S_bp) 20. 7283 M ax Av aliable Gain (dB) Zsource 50. 0000 Zload 50. 0000 Sim ultaneous M atc h Matching for Noise Figure NFm in_at _bias_pt 0. 6512 M inim um Nois e Figure (dB) Sopt _at _bias_pt 0. 2799 / 57. 8169 Soure Reflec tion Coeff. for NFm in Zopt 59. 0670 + j30. 3691 Zopt for NFm in Zload_wSopt 31. 8982 + j31. 7136 Conjugate M atc hed Load (for input m atched to NFm in) Zopt Zload_wSopt DUT* Pgain_assoc_at _bias 18. 6761 Power Gain (dB) at this nois e m atc hed condition 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
  15. 15. 在ADS建置完整的LNA設計環境(III) Department of Electronic Engineering, NTUT Move marker mBiasPt to desiredfrequency point. Smith Chart and data below will be updated. Move markers GammaSand GammaL to selectarbitrary source and load reflection coefficients The impedances,power gains,and noise figures below will be updated.The transducer power gains are invalid ifthe markers are moved into the unstable regions. Eqn num _NFc ircles=3 Eqn NFs tep_s iz e=0.2Eqn GAs tep_s iz e=1 Eqn num _GAc ircles=3 Zs ourc e, Gam m a_S Zload, Gam m a_L DUT* Eqn num _GPcirc les =3 Eqn GPs tep_siz e=1 G am m aS indep(G am m aS) = r hos=-0. 25766 - j0. 01061 im pedance = 29. 50724 - j0. 67091 133 indep(rhos) (0. 000 t o 2000. 000) rhos GammaS indep(Sour ce_st abcir) (0. 000 t o 51. 000) Source_stabcir 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) GAcircles indep(G am m aLopt ) (133. 000 t o 133. 000) GammaLopt n s f ig u r e = 0 . 8 6 7 n s f ig u r e = 1 . 0 6 7 n s f ig u r e = 1 . 2 6 7 Noise_circles Noise_circleMin G am m aS indep(G am m aS) = r hos=-0. 25766 - j0. 01061 im pedance = 29. 50724 - j0. 67091 133 G am m aL indep(G am m aL) = r hos=0. 35071 / -54. 37157 im pedance = Z0 * (1. 22760 - j0. 79805) 246 indep(rhos) ( 0. 000 t o 2000. 000) rhos GammaL indep( Load_st abcir ) (0. 000 t o 51. 000) Load_stabcir 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) GPcircles indep(G amm aSopt ) (246. 000 t o 246. 000) GammaSopt G am m aL indep(G am m aL) = r hos=0. 35071 / -54. 37157 im 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 Region Eqn t index=[ 0: : 2000] Eqn r hos=sqrt (t index/ 2000)*exp(j*2*sqrt (pi*t index)) Eqn Source_st abcir=s_st ab_circle(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 rans_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 igure. ) (C) Noise f igur e f or an ar bit ray G am m a_S ( m arker 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 igure is set t o 1000. ) ( C) G t rans_power : t ransducer power gain wit h t he source ref lect ion coef f icient at marker G amm aS, and t he load t hen conjugat ely mat ched. ( A) G t rans_power _NFmin: t ransducer power gain wit h t he sour ce ref 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 rans_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 rans_load : t r ansducer power gain wit h t he load ref 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 ray G am m a_L (t he source ref 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 ref lect ion coef f icient Eqn G amm aS_ConjM at ch=sm _gam m a1( S[ f m 1] ) Zsource is t he im pedance at m ar ker G am m aS. Eqn Zsource2=Z0*(1+G am m aS) / ( 1-G am m aS) Eqn G t rans_power=if ( G t _num >0) t hen 10*log(G t _num / G t _den) else 1e6 Eqn Noise_circleM in=ns_circle(NFm in[ f m 1] , NFm in[ f m 1] , Sopt [ f m 1] , Rn[ f m1] / Z0[ f m 1] , 51) Eqn Noise_circles=ns_circle(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 AcircleM ax=ga_cir cle( S[ f m 1] , m ax_gain(S[ f m 1] )) Eqn G Acircles=ga_cir cle( S[ f m 1] , max_gain(S[ f m 1] )-G Ast ep_size*[ 0: : num _G Acircles] ) Eqn G Pcircles=gp_cir cle( S[ f m 1] , max_gain(S[ f m 1] )-G Pst ep_size*[ 0: : num _G Pcircles] ) Set st ep size and num ber of circles t o plot st ab_f act (S[ f m 1] ) 0. 7083 St abilit y K t index is a vect or of numbers 0, 1, 2, 3, . . . , 2000. r hos are 2001 com plex ref 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 Zsource2 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 Source 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 source Zopt at NFm in Tr ansducer Power G ain (dB) G t rans_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 rans_power_load 17. 1906 NF wit h opt imal Zsource O pt imal Zsource when Zload is at G am m aL Zload at G am maL Transducer Power gain ( dB) GAcircles Noise_circles Source_stabcir GPcircles Load_stabcir Source Stable Region (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 PlotNoise,Gain,and Stability Circles Noise Circle Available PowerGain Circle Operating PowerGain Circle Source and Load Stability Circles Transducer Power Gain CalculationNoise Figure Calculation Reflection Coefficients Calculation 4 DifferentMatching Condition: (A) M atc h for m inim um NF (D) M atc h for optim um NF with arbitray Gam m a_L (Output Power) (B) Sim ulataneous ly Conjugate M atch I nput : m at ched min. 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 iminum 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 arbitray Gam m a_S (Gain c ons ideration) I nput : G amm aS, O ut put : conjugat e m at ched Frequency Point Selector fm1 indep(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 requency fm1 fm1 indep(fm1)= plot_vs([0::sweep_size(frequency)-1],frequency)=6.000000 2.360000G 15/15

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