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Agilent ADS 模擬手冊 [實習2] 放大器設計

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放大器設計

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Agilent ADS 模擬手冊 [實習2] 放大器設計

  1. 1. IV (rfsys.ntut@gmail.com) April 2014
  2. 2. 1 (Advanced Design System, ADS) I ADS II DCS 1900 III IV ADS
  3. 3. 2 1.1 ADS 1.2 1. 1.1 ( ) sE sZ ( ) LZ ( 50 ) sΓ LΓ [ ]S 1.2 1.1 inΓ inΓ outΓ outΓ in s ∗ Γ = Γ out L ∗ Γ = Γ 2. inΓ outΓ inΓ outΓ 1.3 Transistor [S] 2a 2b 1a 1b Port 1 Port 2 + −sE sZ outΓ LZ inΓ sΓ LΓ 1.1
  4. 4. 3 s o s s o Z Z Z Z − Γ = + L o L L o Z Z Z Z − Γ = + Source reflection coefficient: Load reflection coefficient: 1 11 1 12 2b S a S a= + 2 21 1 22 2b S a S a= + Transistor: + −sE sZ sΓ LZ LΓ Transistor [S] 1.2 1.3 inΓ outΓ inΓ outΓ sΓ LΓ [ ]S ( ) sΓ LΓ [ ]S inΓ [ ]S LΓ outΓ [ ]S sΓ in s ∗ Γ = Γ out L ∗ Γ = Γ Transistor [S] outΓ LZ inΓ LΓ 12 21 11 221 L in L S S S S Γ Γ = + − Γ Transistor [S]+ −sE sZ outΓinΓ sΓ Find input reflection coefficient: 12 21 22 111 s out s S S S S Γ Γ = + − Γ Find output reflection coefficient: 1.3 inΓ outΓ
  5. 5. 4 3. 1.4 AVSP (Available power) in s ∗ Γ = Γ AVSP inP in s ∗ Γ = Γ inP AVSP in s ∗ Γ ≠ Γ AVSP in AVSP P≠ in s AVSP M P= sM (Source mismatch factor) sM 1 ( dB ) AVNP (Available power from network) AVNP in s ∗ Γ = Γ AVNP ( LP ) out L ∗ Γ = Γ AVNP LP out L ∗ Γ ≠ Γ AVNP L AVNP P≠ L L AVNP M P= LM (Load mismatch factor) LM 1 ( dB ) 1sM = 1LM = Transistor [S]+ −sE sZ LZ PAVNPAVS PLPin Ms interface interface ML inΓ sΓ outΓ LΓ 1.4
  6. 6. 5 4. 1.5 pG (Operating power gain) pG (Power amplifier, PA) pG PA TG TG TG AG AG (Low noise amplifier, LNA) AG • The power gain L p in P G P = • The transducer power gain L T p s AVS P G G M P = = • The available power gain AVN T A AVS L P G G P M = = p TG G> A TG G> • When the Input and output are matched: p T AG G G= = From the amplifier input to load From the source to load 1.5 pG PA 1.6 ( LΓ ) LΓ inΓ inΓ ( s in ∗ Γ = Γ ) inΓ 1E oZ oZ Transistor oG Output matching LG Input matching sG sΓ LΓ 1.6 ( PA )
  7. 7. 6 AG LNA 1.7 ( sΓ ) sΓ outΓ outΓ ( L out ∗ Γ = Γ ) 1E oZ oZ Transistor oG Output matching LG Input matching sG sΓ LΓoutΓ 1.7 ( LNA ) sΓ LΓ [ ]S 1.8 2 2 212 2 22 11 1 1 L p in L G S S − Γ = − Γ − Γ • The Power Gain Gp • The Transducer Power Gain GT 2 2 2 2 2 2 21 212 2 2 2 22 11 1 1 1 1 1 1 1 1 s L s L T s in L s out L G S S S S − Γ − Γ − Γ − Γ = = − Γ Γ − Γ − Γ − Γ Γ • The Available Power Gain GA 2 2 212 2 11 1 1 1 1 s A s out G S S − Γ = − Γ − Γ 1.8 5. 1 1.2 <1sΓ <1LΓ inΓ outΓ 1inΓ < inP 1outΓ < ( 1 ) 1inΓ > ( 1outΓ >
  8. 8. 7 Transistor [S]+ − sE sZ outΓ LZ inΓ sΓ LΓ 12 21 11 221 L in L S S S S Γ Γ = + − Γ 12 21 22 111 s out s S S S S Γ Γ = + − Γ 1sΓ < 12 21 22 11 1 1 s out s S S S S Γ Γ = + < − Γ 1LΓ < 12 21 11 22 1 1 L in L S S S S Γ Γ = + < − Γ and ( )22 11 12 21 2 2 2 2 22 22 L S S S S S S ∗∗ − ∆ Γ − = − ∆ − ∆ ( )11 22 12 21 2 2 2 2 11 11 s S S S S S S ∗∗ − ∆ Γ − = − ∆ − ∆ 11 22 12 21S S S S∆ = − • Stability Circles include and where • Stable Condition: Output Stability Circle Input Stability Circle 1.9 ) inΓ outΓ 1 ( ) ( ) ( ) inΓ outΓ 1 1.9 1inΓ = 1outΓ = 1.10 LΓ inΓ 1 11S 0LΓ = 11in SΓ = 0LΓ = LΓ Case (1) 11 1S < Case (2) 11 1S > 1.11 Rollet’s condition( K- Test) -test
  9. 9. 8 LC LC Lr 1inΓ = 11 1S < 12 21 11 221 L in L S S S S Γ Γ = + − Γ 0LΓ = LC LC 0LΓ = Lr 1inΓ = • Criteria: virtually make , then and0LΓ = 11in SΓ =L oZ Z= -planeLΓ -planeLΓ Case (1): 11 1S >Case (2): stable region stable region Output stability circle Output stability circle 1.10 12 21 22 111 s out s S S S S Γ Γ = + − Γ 22 1S < 22 1S >Case (1): Case (2): • Criteria: virtually make , then and0sΓ = 22out SΓ =s oZ Z= stable region stable region -planesΓ -planesΓ 0sΓ =0sΓ = sC sC sC srsr sC 1outΓ = 1outΓ =Input stability circle Input stability circle 1.11 6. (Unilateral Transducer Power Gain) 1.8 TG sΓ LΓ [ ]S inΓ outΓ inΓ outΓ LΓ sΓ
  10. 10. 9 inΓ outΓ 12S 0 (Bilateral case) 12S 0 ( ) 12 0S = (Unilateral case) 1.12 inΓ 11S outΓ 22S U(Unilateral figure of merit) 12S ( ) 11S 1E oZ oZ Transistor oG Output matching LG Input matching sG sΓ LΓ22S =12 0S 2 2 2 212 2 11 22 1 1 1 1 s L TU s o L s L G S G G G S S − Γ − Γ = = − Γ − Γ 2 2 11 1 1 s s s G S − Γ = − Γ 2 21oG S= 2 2 22 1 1 L L L G S − Γ = − Γ (dB) (dB) (dB) (dB)TU s o LG G G G= + + • Unilateral Transducer Power Gain GTU • The term Gs and GL represent the gain or loss produced by the matching or mismatching of the input or output circuits. 2 2 2 2 2 2 21 212 2 2 2 22 11 1 1 1 1 1 1 1 1 s L s L T s in L s out L G S S S S − Γ − Γ − Γ − Γ = = − Γ Γ − Γ − Γ − Γ Γ 12 21 11 221 L in L S S S S Γ Γ = + − Γ • Transducer Power Gain GT Unilateral condition 12 0S = 11in SΓ = 1.12 (Unilateral case)
  11. 11. 10 1.12 12 0S = sG oG LG 21S 20 dB 20 dB sG dB LG dB sG dB LG dB sG oG LG 7. (Bilateral Transducer Power Gain) 6 Unilateral 12S ( 0) 12S 0( ) Bilateral (Operating power gain) (Available power gain) 4 8. (Operating Power-Gain Circle) pG 1.8 inΓ 1.9 pG inΓ pG 1.13 2 21p pG S g= ⋅ pg (Normalized gain factor) 0 1 1pg = pG 21S pg pG pg pg LΓ ( LΓ ) pG 1.6
  12. 12. 11 ( )2 2 21 2 212 211 22 22 1 1 1 1 L p p L L L S G S g S S S − Γ = = ⋅  − ∆Γ  − − Γ  − Γ   • Unconditionally stable bilateral case: ( ) ( ) 2 2 2 2 2 2 2 2 22 11 11 22 2 1 1 1 1 2Re L L p L L L L g S S S S C − Γ − Γ = = − Γ − − ∆Γ − + Γ − ∆ − Γ 2 22 11C S S∗ = − ∆ Gp and gp are the functions of the device S parameters and ΓL. The values of ΓL that produce a constant gp are shown to lie on a circle, known as an operating power- gain circle. L p pC rΓ − = ( ) 2 2 2 221 p p p g C C g S ∗ = + − ∆ ( ) 2 2 12 21 12 21 2 2 22 1 2 1 p p p p K S S g S S g r g S − + = + − ∆ Center Radius where • Operating Power-Gain Circle: 1.13 pg 0 1 0.5pg = LΓ 0.5pg = LΓ 0.5pg = ( 1pg = ) 3 dB −3 dB 0.6pg = LΓ 0.8pg = LΓ 1pg = LΓ 0 pg pg 1.13 ( ) 1.14 1.13 1pg = ( ,g optΓ ) 1.14 ,maxpG ( ,max 11.38 dBpG = ) ,g optΓ 9 dBpG = 2.38 dB 2.38 dB 0.578pg = − = 9 dBpG = LΓ 9 dBpG = LΓ 1.15
  13. 13. 12 optΓ optΓ pg pg pg optΓ ( 4.38 dB 0.364pg = − = ) ( ,g optΓ , ,maxpG ) 1.15 gp = 0 dB gp = −2.38 dB ΓL -Plane Γg,opt 1.14 gp = 0 dB gp = −4.38 dB ΓL -Plane Γg,opt Γopt Maximum output power 1.15
  14. 14. 13 ( )2 2 21 2 212 222 11 11 1 1 1 1 s A a s s s S G S g S S S − Γ = = ⋅  − ∆Γ  − − Γ  − Γ   • Unconditionally stable bilateral case: ( ) ( ) 2 2 2 2 2 2 21 22 11 1 1 1 2Re sA a s s G g S S S C − Γ = = − + Γ − ∆ − Γ 1 11 22C S S∗ = − ∆ Ga and ga are the functions of the device S parameters and Γs. The values of Γs that produce a constant ga are shown to lie on a circle, known as an available power-gain circle. s a aC rΓ − = ( ) 1 2 2 111 a a a g C C g S ∗ = + − ∆ ( ) 2 2 12 21 12 21 2 2 11 1 2 1 a a a a K S S g S S g r g S − + = + − ∆ Center Radius • Available Power-Gain Circle: where 1.16 9. (Available Power-Gain Circle) AG 1.8 outΓ AG outΓ AG 1.16 2 21A aG S g= ⋅ ag 0 1 1ag = ag sΓ ( sΓ ) AG 1.7 ( 1.14 1.15 sΓ ,g optΓ ,a optΓ pG AG optΓ sΓ ) 10. (
  15. 15. 14 ) ( ) 1.17 9 dBpG = A C D B ( ) A C D C D A C D ΓL -Plane Unstable region Stable region Output stability circle A B C D 1.17 1.3 1. Gonzalez Microwave Transistor Amplifier Analysis and Design Example 3.3.2 800 MHz 11 0.65 95S = ∠ − 12 0.035 40S = ∠ 21 5 115S = ∠ 22 0.8 35S = ∠ − K (Maximum stable gain, MSG) 20 dB 18 dB 16 dB
  16. 16. 15 2. amp1900 Data Display circles.dds Data Display 1111 0.65 95S a S= = ∠ − 1212 0.035 40S a S= = ∠ 2121 5 115S a S= = ∠ 2222 0.8 35S a S= = ∠ − 1.18 CL rL C rs ( circle( ) ) ADS l_stab_circle(S,points) s_stab_circle(S,points) S points l_stab_circle_center_radius(S, “x”) s_stab_circle_center_radius(S, “x”) (x center) (x radius) l_stab_region(S) s_stab_region(S) ADS stab_fact() mu() mu_prime() U unilateral_figure() 1.19 Eqn S11a=polar(0.65,-94) Eqn S12a=polar(0.035,40) Eqn S21a=polar(5,115) Eqn S22a=polar(0.8,-35) Eqn Delta=S11a*S22a-S12a*S21a Eqn CL=conj(S22a-Delta*conj(S11a))/(abs(S22a)**2-abs(Delta)**2) Eqn rL=abs(S12a*S21a/(abs(S22a)**2-abs(Delta)**2)) Eqn Sa={{S11a,S12a},{S21a,S22a}} Sa Sa(1,1) Sa(1,2) Sa(2,1) Sa(2,2) 0.650 / -94.000 0.035 / 40.000 5.000 / 115.000 0.800 / -35.000 CL 1.310 / 47.706 rL 0.457 Eqn In_stable_circle=s_stab_circle(Sa,51) indep(In_stable_circle) (0.000 to 51.000) In_stable_circle indep(Out_stable_circle) (0.000 to 51.000) Out_stable_circle (0.000 to 0.000) CL Cs Eqn Cs=conj(S11a-Delta*conj(S22a))/(abs(S11a)**2-abs(Delta)**2) Eqn rs=abs(S12a*S21a/(abs(S11a)**2-abs(Delta)**2)) Cs 1.815 / 120.890 rs 1.057 Eqn Out_stable_circle=l_stab_circle(Sa,51) Eqn Cs_cal=s_stab_circle_center_radius(Sa,"center") Eqn rs_cal=s_stab_circle_center_radius(Sa,"radius") CL_cal 1.310 / 47.706 rL_cal 0.457 Eqn CL_cal=l_stab_circle_center_radius(Sa,"center") Eqn rL_cal=l_stab_circle_center_radius(Sa,"radius") Cs_cal 1.815 / 120.890 rs_cal 1.057 Eqn In_stable_region=s_stab_region(Sa) Eqn Out_stable_region=l_stab_region(Sa) In_stable_region Outside Out_stable_region Outside Draw the stability circles: see Example 3.3.2 in Gonzalez’s Textbook Transistor parameter Make Sa as a “Matrix” Calculate CL, rL, Cs, and rs by equations You can also calculate CL, rL, Cs, and rs by ADS build-in functions. Input stability circle Output stability circle 1.18
  17. 17. 16 Eqn K=stab_fact(Sa) K 0.556 Mu_load 0.853 Mu_source 0.757 Eqn U=unilateral_figure(Sa) U 0.438 Eqn Mu_load=mu(Sa) Eqn Mu_source=mu_prime(Sa) Numerical Stability Factors and Unilateral Figure 1.19 Eqn Gmax1=10*log((abs(S21a)/abs(S12a))) Gmax1 21.549 Gmax2 21.549 Eqn Gp_circle_20dB=gp_circle(Sa,20,51) cir_pts (0.000 to 51.000) Gp_circle_20dB Gp_circle_18dB Gp_circle_16dB indep(Out_stable_circle) (0.000 to 51.000) Out_stable_circle Eqn Gmax2=max_gain(Sa) Eqn Gp_circle_18dB=gp_circle(Sa,18,51) Eqn Gp_circle_16dB=gp_circle(Sa,16,51) Constant Operating Power-Gain Circles: Maximum stable gain (MSG) Calculate MSG using built-in function Use gp_circle() function to get constant gain circles. 1.20 3. ADS gp_circle() 1.20 max_gain() MSG Gmax2 MSG Gmax1 Gmax1 Gmax2 MSG MSG MSG MSG 21.549 dB gp_circle(Sa, 21.549, 51) Sa 21.549 51 51 21.549 23 25 28 ADS ( )
  18. 18. 17 gp_circle() 1.21 gp_circle(Sa, [20, 18, 16], 51) 20 dB 18 dB 16 dB gp_circle(Sa, , 51, 3, 2) MSG 2 dB 3 gp_circle() Eqn Gp_circles=gp_circle(Sa,[20,18,16],51) indep(Out_stable_circle) (0.000 to 51.000) Out_stable_circle cir_pts (0.000 to 51.000) Gp_circles Eqn Gp_circles_step=gp_circle(Sa, ,51,3,2) indep(Out_stable_circle) (0.000 to 51.000) Out_stable_circle cir_pts (0.000 to 51.000) Gp_circles_step Assign constant-gain sequence to get a series of circles Constant Operating Power-Gain Circles: Draw 3 circles every 2 dB lower than MSG. 1.21 Eqn Ga_circle_20dB=ga_circle(Sa,20,51) Eqn Ga_circle_18dB=ga_circle(Sa,18,51) Eqn Ga_circle_16dB=ga_circle(Sa,16,51) cir_pts (0.000 to 51.000) Ga_circle_20dB Ga_circle_18dB Ga_circle_16dB indep(In_stable_circle) (0.000 to 51.000) In_stable_circle Constant Available Power-Gain Circles: Use ga_circle() function to get constant gain circles. 1.22
  19. 19. 18 4. ADS ga_circle() 1.22 5. S_Param 1.23 1.24 Data Display Ideal amplifier behavioral model MuPrime MuPrime2 MuPrime2=mu_prime(S) MuPrime MuPrime MuPrime1 MuPrime1=mu_prime(S) MuPrime Mu Mu1 Mu1=mu(S) Mu GaCircle GaCircle1 GaCircle1=ga_circle(S,[20,18,16],51) GaCircle GpCircle GpCircle1 GpCircle1=gp_circle(S,[20,18,16],51) GpCircle L_StabCircle L_StabCircle1 L_StabCircle1=l_stab_circle(S,51) LStabCircle S_StabCircle S_StabCircle1 S_StabCircle1=s_stab_circle(S,51) SStabCircle S_Param SP1 Step=1.0 MHz Stop=800 MHz Start=800 MHz S-PARAMETERS Amplif ier2 AMP1 S12=polar(0.035,40) S22=polar(0.8,-35) S11=polar(0.65,-95) S21=polar(5,115) Term Term2 Z=50 Ohm Num=2 Term Term1 Z=50 Ohm Num=1 You can just use the measuring components in S_Param palette within schematic. 1.23 cir_pts (0.000 to 51.000) GaCircle1 indep(S_StabCircle1) (0.000 to 51.000) S_StabCircle1 cir_pts (0.000 to 51.000) GpCircle1 indep(L_StabCircle1) (0.000 to 51.000) L_StabCircle1 Constant Operating Power-Gain Circles Output Stability Circle Constant Available Power-Gain Circles Output Stability Circle 1.24
  20. 20. 19 1.4 ADS
  21. 21. 20 2.1 (Infineon) SiGe BJT BFP640ESD 2.4 GHz ~ 2.5 GHz 13 dB 1.5 dB 2.2 1. Johnson Nyquist Johnson Noise ( ) (mean-square) (root-mean-square) (Available noise power) NAP kTB= k (Boltzman’s constant) ( )23 1.38 10 J K− × T B NAP kTB= kT (Power spectrum density, PSD) B PSD W/Hz( dBm/Hz) B NAP PSD (White noise) 2.1 PSD kT ( PSD )
  22. 22. 21 PSD (dBm/Hz) Frequency (Hz) Bandwidth B (Hz) kT 2.1 2. ( ) NAP kTB= ( )o 17 C 290 K= 1 Hz ( )21 4 10 W 174 dBm− × = − PSD 174 dBm Hz− 2.2 PSD (dBm/Hz) Frequency (Hz) −174 2.2 ( )290 K (Spectrum analyzer, SA) SA (Resolution bandwidth, RBW) RBW RBW SA NAP kTB= B PSD( 174 dBm Hz− ) B ( ) SA (Noise floor) RBW SA RBW 1 Hz SA 174 dBm− ( 1Hz) RBW 1 kHz 174 dBm 30 dB 144 dBm− + = − ( 1 kHz 1 Hz 1000 ) 144 dBm 1 kHz− 1 kHz RBW 10
  23. 23. 22 kHz 144 dBm 10 dB 134 dBm− + = − ( 10 kHz 1 kHz 10 ) RBW 100 kHz 134 dBm 10 dB 124 dBm− + = − ( 100 kHz 10 kHz 10 ) 2.3 y P dBm P (dBm) Frequency (Hz) −174 Noise Floor of Spectrum Analyzer −144 −134 −124 30 dB 10 dB 10 dB Noise floor@RBW = 1 Hz Noise floor@RBW = 1 kHz Noise floor@RBW = 10 kHz Noise floor@RBW = 100 kHz 2.3 ( )290 K RBW RBW SA 2.4 SA RBW 1 kHz 144 dBm 1 kHz− 2.5 SA 2.6 RBW 1 kHz A 136 dBm− B 127 dBm− A 136 dBm− B 127 dBm− ( SA RBW RBW 1 kHz ) SA
  24. 24. 23 P (dBm) Frequency (Hz) Noise Floor of Spectrum Analyzer −144 −136 Noise floor@RBW = 1 kHz Noise floor@RBW = 1 kHz Only white noise White noise + other noise 2.4 P (dBm) Frequency (Hz) Spectrum Analyzer −136 Noise floor@RBW = 1 kHz above floor: measurable below floor: unmeasurable 2.5 P (dBm) Frequency (Hz) Spectrum Analyzer A −136 Noise floor@RBW = 1 kHz P (dBm) Frequency (Hz) Spectrum Analyzer B −127 Noise floor@RBW = 1 kHz 2.6 3. ( ) 2.7 80 MHz 95 dBm− 80 dBm−
  25. 25. 24 (Signal-to-Noise Ratio, SNR) 15 dB 15 dB SNR SNR ( ) −174 dBm/Hz noise B = 80 MHz Noise floor = −95 dBm 2.7 4. p-n (Shot noise Schottky noise) (Flicker noise Pink noise 1 f noise) (Popcorn noise Burst noise Bistable noise random telegraph signals, RTS) BJT FET ( FET ) FET BJT
  26. 26. 25 5. NAP kTB= 2.8 R NAP kTB= 2 , 4n rmsv kTBR= , 4n rmsv kTBR= ( )2 , 4n rmsv B kTR= 2 V Hz ( ), 4n rmsv B kTR= V Hz 2.9 R Thermal noise source (Noisy resistor) R + − ,n rmsv R Matched load Noise-free resistor Noise source 2 , 1 2 n rms NA v P kTB R      = = 2 , 4n rmsv kTBR=Mean-square open-circuited noise voltage: For a 1 kΩ resistor over 1 Hz bandwidth: , 4 4 nVn rmsv kTR= ≃ At room temperature For a 50 Ω resistor over 1 Hz bandwidth: , 4 0.9 nVn rmsv kTR= ≃ Thus, said, the rms-noise spectral density: For a 1 kΩ resistor over 1 Hz bandwidth: , 4 4 nV Hzn rmsv kTR= ≃ For a 50 Ω resistor over 1 Hz bandwidth: , 4 0.9 nV Hzn rmsv kTR= ≃ Or, said, the mean-square noise spectral density: For a 1 kΩ resistor over 1 Hz bandwidth: 2 2 , 4 16 nV Hzn rmsv kTR= ≃ For a 50 Ω resistor over 1 Hz bandwidth: 2 2 , 4 0.81 nV Hzn rmsv kTR= ≃ 2.8 R Thermal noise source (Noisy resistor) R + − ,n rmsv Noise-free resistor R,n rmsi Noise-free resistor 2 , 4n rmsv kTBR= 2 ,2 , 4 4n rms n rms v kTB i kTGB R R   = = =    Thevenin’s Equivalent Circuit Norton’s Equivalent Circuit 2.9
  27. 27. 26 6. oN 0 eqN kT B= oN ( )eq oT N kB= eqT K 2.10 (Cold) (Hot) For one-port components to acts as noise sources under impedance matched condition: o eq N T kB = eqT 2.10 (Input-referred noise) aG 2.11 0N 0 K( iN 0) oN 2.11 oN oN iN aG i o a eqN N G kT B= = eq i o aT N kB N G kB= = eqT
  28. 28. 27 aG aG o a eqN G kT B= i o eq a N N T kB G kB = = i eqN kT B= 2.11 7. (Y ) o a i a eqN G N G kT B= = oN 2.11 0 K 0 ( ) (Excess noise ratio, ENR) ENR 0 290 KT = ENR ( 0 290 KT = ) 0 290 KT = 0 290 KT = 0 290 KT = 21 0 4 10 JkT − = × ENR ( ) ( ) ( ) ( )0 0 0 0dB 10log 10log 10log 290 290s s sENR N N N T T T T     = − = − = −      0 0N kT B= 0 290 KT = sN sT B ENR B ENR B ENR ( ) ENR 20 dB 40 dB ENR ENR
  29. 29. 28 ENR ENR ENR ENR 6 dB ENR 16 dB 16 dB 15 dB ENR 25 dB Y 2.12 ( ) ( ) Y Y eqT Y Y-factor Method Noise source ON Noise source Off 1 1a a eqN G kT B G kT B= + 2 2a a eqN G kT B G kT B= + 11 1 2 2 2 1 1 eqON eq Off eq T TN N T YT Y T N N T T Y + − = = = ≥ ⇒ = + − , ,a eqG T B 2.12 Y 8. F NF F(Noise factor) NF(Noise figure) NF F dB ( )10log dBNF F= aG iN a iG N oN
  30. 30. 29 a iG N addN _o a i o addN G N N= + _o addN eT ( ) _o add a eN G kT B= _i add eN kT B= iN 290 K 0iN kT B= oN ( )0 _ 0o a a i add a eN G kT B G N G kB T T= + ⋅ = + ( )o a iF N G N= ( ) ( ) ( ) ( )0 0 01 1 290a e a e eF G kB T T G kBT T T T= + = + = + F 1 o a iN G N= F 1 o a iN G N> 1.2F = 1 a iG N 0.2 a iG N F dB NF ( ) ( )10log 1.2 0.79 dBNF = = a iG N 0.79 dB ( 0 dBNF = ) F (Signal-to-noise ratio, SNR) ( ) _ _ 0 _ 1 1 i i a i a i add i addi i i e o a io a i i o a i o add S S G N G N NSNR N N T F S G SSNR G N N T N G N N + = = = = = + = + + 2.13 −60 dBm −100 dBm SNRi 40 dB 20 dB 20 dB −40 dBm −80 dBm −72 dBm 8 dB 8 dB SNR SNRo 32 dB ( ) ( )dB dB 40 32 8 dBi oNF SNR SNR= − = − =
  31. 31. 30 P (dBm) Frequency (Hz) −100 −60 SNRi = 40 dB P (dBm) Frequency (Hz) −80 −40 SNRo= 32 dB −72 Gain = 20 dB NF = ? NF = 8 dB Amplifier 2.13 SNR 9. ( ) 2.14 ADS ( ) ( ) 2 2 2 min min n n s opt s opt s opt s s R R F F Y Y F G G B B G G  = + − = + − + −   s s sY G jB= + : Source admittance opt opt optY G jB= + : Optimum source admittance for minimum F (or NF) minF : Minimum noise factor nR : Equivalent noise resistance Noise factor of a two-port amplifier Constant Noise Circle 0 11 1 s s s Y Z − Γ = + Γ 0 11 1 opt opt opt Y Z − Γ = + Γ ( ) ( ) 2 min 22 0 4 1 1 s optn s s opt R F F Z Γ − Γ Γ = + − Γ + Γ 2.14
  32. 32. 31 2.3 1. (Datasheet) (Infineon) SiGe BJT Infineon BFP640 BFP640 BFP640ESD BFP640 BFP640ESD ADS BFP640ESD BFP640 ADS Datasheet BFP640 (Reference design) (Datasheet) Datasheet 2.15 BFP640ESD (SiGe) 21 dBm 6 mA 1.5 GHz 2.4 GHz 0.65 dB 0.7 dB 2.15 Infineon BFP640ESD SiGe BJT abstract
  33. 33. 32 2.16 Datasheet 4.7 V 180 50 mA Datasheet Maximum Ratings 2.17 2.4 GHz VCE=3 V IC = 6 mA 0.7 dB (Associated gain, Gass) 20 dB ( , 6 mA) ( , 30 mA) 18 dB 20 dB 21 dB 23 dB 2.4 GHz 20 dB ( ) 1 dB 23 dB 23 dB ( ) ( ) Datasheet IC ( ) Datasheet 2.4 GHz 0.7 dB 0.3 dB 0.4 dB BFP640ESD Datasheet Datasheet Datasheet
  34. 34. 33 2.16 BFP640ESD 2.17 BFP640ESD 2. ADS BFP640ESD Infineon BFP640ESD_spar10GHz_noisepar10GHz_spice10GHz_ADS_MWO.zip s2p SPICE AWR MWO BFP640ESD_MWO.sch Agilent ADS bfp640esd_ADS.dsn ADS bfp640esd_ADS.dsn
  35. 35. 34 2.4 1. (Project) (1) LNA24G (2) 2.18 Copy Design dsn /network (3) /network bfp640esd_ADS.dsn 2.19 Symbol Symbol Library (4) I-V Curve Copy the transistor model to your project 2.18 bfp640esd_ADS.dsn bfp640esd_ADS X1 Use “Design Parameters…” to assign a symbol for this transistor 2.19 bfp640esd_ADS.dsn (symbol)
  36. 36. 35 2. (1) 2.4 GHz ADS (2) Bias_MinNF.dsn 2.20 I-V Curve 2.4 GHz ( ) NFmin (3) IBB 0 µA 100 µA 10 µA - VCE 0 V 4 V 0.2 V IBB VCE I-V Curve( ) (4) Z0 50 50 2.21 dataset datadisplay S_Param SP1 Freq=2.4 GHz CalcNoise=yes S-PARAMETERS Options Options1 Tnom=25 Temp=16.85 OPTIONS VAR VAR2 Z0=50 VCEstep=0.2 V VCEmax=4 V VCEmin=0 V IBBstep=10 uA IBBmax=100 uA IBBmin=0 uA Eqn Var VAR VAR1 Rload=50 IBB=0 A VCE=0 V Eqn Var DC DC1 Step=VCEstep Stop=VCEmax Start=VCEmin SweepVar="VCE" DC ParamSweep Sweep2 Step=VCEstep Stop=VCEmax Start=VCEmin SimInstanceName[6]= SimInstanceName[5]= SimInstanceName[4]= SimInstanceName[3]= SimInstanceName[2]= SimInstanceName[1]="SP1" SweepVar="VCE" PARAMETER SWEEP Term Term2 Z=50 Ohm Num=2 Term Term1 Z=50 Ohm Num=1 DC_Feed DC_Feed2 DC_Block DC_Block2 DC_Block DC_Block1 DC_Feed DC_Feed1 bfp640esd_ADS X1 BFP640ESD I_Probe IC V_DC SRC1 Vdc=VCE ParamSweep Sweep1 SweepVar="IBB" SimInstanceName[1]="Sweep2" SimInstanceName[2]="DC1" SimInstanceName[3]= SimInstanceName[4]= SimInstanceName[5]= SimInstanceName[6]= Start=IBBmin Stop=IBBmax Step=IBBstep PARAMETER SWEEP I_DC SRC2 Idc=IBB Ideal chokes and bypass caps. DC-biasing voltage Collector current probing DC-biasing base current Frequency is 2.4 GHz and turn on “CalcNoise” to consider noise Use “Options” to set Temp=16.85 according to the standard definition and the room temperature Tnom. Set the ranges and steps you like to run 2.20 (2.4 GHz)
  37. 37. 36 S_Param SP1 Freq=2.4 GHz CalcNoise=yes S-PARAMETERS VAR VAR2 Z0=50 VCEstep=0.2 V VCEmax=4 V VCEmin=0 V IBBstep=10 uA IBBmax=100 uA IBBmin=0 uA Eqn Var Pass the variable Z0 to the dataset 2.21 Z0 dataset (5) Datadisplay dB(S21[0]) NFmin[0] 2.22 IBB VCE S21 NFmin S21[0] NFmin[0] [0] 2.4 GHz 0 S21[0] NFmin[0] 2.4 GHz S21 S21[0] NFmin[0] 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 -20 -15 -10 -5 0 5 10 15 -25 20 IBB=0.000 IBB=10.0u IBB=20.0uIBB=30.0uIBB=40.0uIBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u VCE dB(S21[0]) m1 m1 VCE= dB(S21[0])=19.172 IBB=0.000050 1.800 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 2 4 6 8 10 0 12 IBB=0.000 IBB=10.0uIBB=20.0uIBB=30.0uIBB=40.0uIBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u VCE NFmin[0] m2 m2 VCE= NFmin[0]=600.9052m IBB=0.000010 1.200000 BJT OFF BJT OFF S21 is around 15 dB to 20 dB Minimum NF is around 0.6 dB to 1 dB 2.22 S21 NFmin (6) 2.22 BJT S21 15 dB 20 dB 0.6 dB 1 dB VCE 1 V S21 NF ( ) ( ) I-V Curve S21 NF (7) 2.23 IC VCE maker m3 I-V Curve m3
  38. 38. 37 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 5.00m 10.0m 15.0m 20.0m 0.000 25.0m IBB=0.000 IBB=10.0u IBB=20.0u IBB=30.0u IBB=40.0u IBB=50.0u IBB=60.0u IBB=70.0u IBB=80.0u IBB=90.0u IBB=100.u VCE IC.i,A m3 m3 VCE= IC.i=5.406418m IBB=0.000020 2.800000 Eqn frequency=SP.freq[0,0,0] Eqn ICindex=find_index(IC[VCEindex],m3) Eqn VCEindex=find_index(DC.VCE[0,::],indep(m3)) Eqn IC=-SRC1.i Eqn DC_power=m3*indep(m3) Eqn NFmin_at_bias_pt=NFmin[ICindex,VCEindex,0] Collector DC current Find index for the swept variable VCE and ICE according to marker "m3" x-axis. Minimum noise figure at the m3 bias point. DC power comsumption when biased at marker "m3" (base current is ignored) Basic information at the bias point m3. These equations are used to find out the DC consumption power and the minimum NF according to the biased-point I-V Curves Put a maker “m3” to select a biased-point indep(m3) 3.0000 m3[0] 5.4174 m DC_power[0] 16.252 m ...min_at_bias_pt 651.19 m frequency 2.400 G DC pow er (W)ICVCE NFmin@biased-point List a table and move maker “m3,” and you will see the parameters varies for different biased-point. 2.23 m3 (8) NFmin 2.24 Maker m3 VCE( 3-V) VCE IC NFmin 2.25 maker m3 ( VCE ) NFmin m3 ( VCE) NFmin ( ) 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 5.00m 10.0m 15.0m 20.0m 0.000 25.0m IBB=0.000 IBB=10.0u IBB=20.0u IBB=30.0u IBB=40.0u IBB=50.0u IBB=60.0u IBB=70.0u IBB=80.0u IBB=90.0u IBB=100.u VCE IC.i,A m3 m3 VCE= IC.i=2.902361m IBB=0.000010 3.000000 2.00m 4.00m 6.00m 8.00m 10.0m 12.0m 14.0m 16.0m 18.0m 0.000 20.0m 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.4 2.0 IC NFmin,dB NFmin versus IC, at VCE (set by m3) I-V Curve Eqn VCEindex=find_index(DC.VCE[0,::],indep(m3)) Write an equation to find the index of VCE according to the marker m3 NFmin v.s. IC at a specified VCE 2.24 NFmin 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 5.00m 10.0m 15.0m 20.0m 0.000 25.0m IBB=0.000 IBB=10.0u IBB=20.0u IBB=30.0u IBB=40.0u IBB=50.0u IBB=60.0u IBB=70.0u IBB=80.0u IBB=90.0u IBB=100.u VCE IC.i,A m3 m3 VCE= IC.i=5.406418m IBB=0.000020 2.800000 I-V Curves Move the maker “m3” and observe the variation of NFmin for different biased-points. 2.00m 4.00m 6.00m 8.00m 10.0m 12.0m 14.0m 16.0m 18.0m 0.000 20.0m 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.4 2.2 IC NFmin,dB 2.00m 4.00m 6.00m 8.00m 10.0m 12.0m 14.0m 16.0m 18.0m 0.000 20.0m 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.4 2.2 IC NFmin,dB 2.00m 4.00m 6.00m 8.00m 10.0m 12.0m 14.0m 16.0m 18.0m 0.000 20.0m 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.4 2.2 IC NFmin,dB 2.00m 4.00m 6.00m 8.00m 10.0m 12.0m 14.0m 16.0m 18.0m 20.0m 0.000 22.0m 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.4 2.2 IC NFmin,dB (1) Move “m3” vertically to keep VCE constant (IBB or IC varies) (2) Move “m3” horizontally to keep IC constant (VCE varies) 2.25 NFmin ( m3 )
  39. 39. 38 (9) m3 VCE NFmin IC VCE NFmin IC IC NFmin VCE VCE IC NFmin (10) NFmin 2.24 IBBstep 1 uA NFmin (11) 2.26 m3 K µ K 1 ( MSG) µ 1 ( MSG) µ 1 ( MAG) µ dB(S_11) -6.7279 dB(S_12) -23.460 dB(S_21) 17.996 dB(S_22) -7.0302 Transistor S-parameter at bias point m3 Use these equations to find S-parameters, stability factor, and maximum available gain at certain biased-point. 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 -10 -5 0 5 10 15 20 -15 25 IBB=0.000 IBB=10.0u IBB=20.0u IBB=30.0uIBB=40.0uIBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u VCE MAG,dB Maximum Available Gain versus IBB and VCE 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 -25 -20 -15 -10 -5 -30 0 IBB=0.000 IBB=10.0u IBB=20.0u IBB=30.0uIBB=40.0uIBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u VCE dB(S12) dB(S12) versus IBB and VCE m1 VCE= dB(S21[0])=15.888 IBB=0.000010 2.000 Transistor dB(S21) versus IBB and VCE 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 -20 -15 -10 -5 0 5 10 15 -25 20 IBB=0.000 IBB=10.0u IBB=20.0uIBB=30.0uIBB=40.0uIBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u VCE dB(S21) m1 m1 VCE= dB(S21[0])=15.888 IBB=0.000010 2.000 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 -14 -12 -10 -8 -6 -4 -2 -16 0 IBB=0.000 IBB=10.0u IBB=20.0u IBB=30.0u IBB=40.0u IBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u VCE dB(S11[0]) IBB=0.000 IBB=10.0u IBB=20.0u IBB=30.0u IBB=40.0u IBB=50.0u IBB=60.0u IBB=70.0u IBB=80.0uIBB=90.0uIBB=100.u dB(S22[0]) dB(S11) and dB(S22) versus IBB and VCE You can also observe the swept S21, S12, S11, S22, and MAG 2.00m 4.00m 6.00m 8.00m 10.0m 12.0m 14.0m 16.0m 18.0m 0.000 20.0m -15 -10 -5 0 5 10 15 -20 20 IC dB(S21) dB(S21) versus IC, at VCE (set by m3) You can also observe how the dB(S21) varies with respect to the biased current IC at certain VCE K 0.6776 Stability Factor MuL 0.7081 MuL 0.7081 Characteristics Impedance Z0[0,0,0] 50.0000 Eqn MAG=max_gain(S) Maximum available/stable gain at all frequencies Eqn S_11=S_bp(1,1) Eqn S_12=S_bp(1,2) Eqn S_21=S_bp(2,1) Eqn S_22=S_bp(2,2) Eqn K=stab_fact(S_bp) Eqn S_bp=S[ICindex,VCEindex,0] S-parameters at the bias point specified by marker m3. Stability factors at the bias point m3. Eqn MuL=mu(S_bp) Eqn MuS=mu_prime(S_bp) MAG[ICindex,VCEindex,0] 20.7283 Max Avaliable/Stable Gain (dB) 2.26 m3 3. (1) ADS 2.27 Pgain_assoc (Associated power gain)
  40. 40. 39 (2) 2.27 m3 NFmin_at_bias_pt source Sopt_at_bias_pt Zopt Zload_wSopt Pgain_assoc_at_bias_pt Eqn S_22p_at_bias=S_22p[ICindex,VCEindex] Eqn Zload_wSopt=zopt(conj(S_22p_at_bias),Z0[0,0,0]) Eqn S_22p=S22[0]+(S12[0]*S21[0]*Sopt[0])/(1-S11[0]*Sopt[0]) Eqn GammaL_wSopt=conj(S_22p_at_bias) S_22p : ref lection looking into the output of the dev ice, when the source is optimal f or minimum noise f igure. GammaL_wSopt is the complex conjugate of S22_p, and is the optimal load ref lection coef f icient when Sopt is the source ref lection coef f icient. Zload_wSopt is the corresponding impedance. Output Conjugately Matching Impdeance Calculation (when input is noise matched) Eqn Zopt=zopt(Sopt_at_bias_pt,Z0[0,0,0]) Source impedance for minimum noise figure at the bias point specified by marker m3. Eqn Sopt_at_bias_pt=Sopt[ICindex,VCEindex,0] Source reflection coefficient for minimum noise figure at frequency specified by marker m3. Sopt is the s-parameter for optimum noise performance. Optimum reflection coefficient(impedance) for minimum noise at the bias point m3. Eqn Pgain_assoc_at_bias=Pgain_assoc[ICindex,VCEindex] Eqn Pgain_assoc=pwr_gain(S[0],zopt(Sopt[0],Z0[0,0,0]),zopt(conj(S_22p),Z0[0,0,0]),Z0[0,0,0]) Transducer power gain with the source reflection coefficient Sopt for minimum noise figure, and the load then conjugately matched. zopt() is just used to convert a reflection coefficient to an impedance. Matching for Noise Figure NFmin_at_bias_pt 0.6512 Minimum Noise Figure (dB) Sopt_at_bias_pt 0.2799 / 57.8169 Soure Ref lection Coef f . f or NFmin Zopt 59.0670 + j30.3691 Zopt f or NFmin Zload_wSopt 31.8982 + j31.7136 Conjugate Matched Load (f or input matched to NFmin) Zopt Zload_wSopt DUT* Pgain_assoc_at_bias 18.6761 Power Gain (dB) at this noise matched condition 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 -10 -5 0 5 10 15 20 -15 25 IBB=0.000 IBB=10.0u IBB=20.0u IBB=30.0u IBB=40.0u IBB=50.0uIBB=60.0uIBB=70.0uIBB=80.0uIBB=90.0uIBB=100.u VCE Pgain_assoc m4 m4 VCE= Pgain_assoc=18.676 IBB=0.000020 3.000 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 5.00m 10.0m 15.0m 20.0m 0.000 25.0m IBB=0.000 IBB=10.0u IBB=20.0u IBB=30.0u IBB=40.0u IBB=50.0u IBB=60.0u IBB=70.0u IBB=80.0u IBB=90.0u IBB=100.u VCE IC.i,A m3 m3 VCE= IC.i=5.417352m IBB=0.000020 3.000000 Use these equations to find the matching result (associated gain) for minimum NF at certain biased-point. Example: Move maker m3 to VCE=3V, IBB=20uA Move maker m4 to VCE=3V, IBB=20uA You can find the associated gain is 18.676 dB You can list out all parameters of interest, such as Nfmin, optimum source reflection coefficient and impedance, conjugate matched load impedance, and the associated gain for this minimum NF matching at biased-point m3. 2.27 m3 (3) ( ) 2.28 ADS m3 Smith Chart ( 50 ) K<1 m3 (4) 2.29 page
  41. 41. 40 Eqn GammaS_at_bias_pt=sm_gamma1(S_bp) Eqn GammaL_at_bias_pt=sm_gamma2(S_bp) Zsource and Zload are the source and load impedances to present to the device for simultaneous conjugate matching, at the bias point m3. These are not defined and return 0 if K<1. Simultaneous conjugate match source and load reflection coefficients at bias point m3. These are not defined and return 0 if K<1. Eqn Zsource=sm_z1(S_bp,Z0[0,0,0]) Eqn Zload=sm_z2(S_bp,Z0[0,0,0]) Input/Output Simultaneously Conjugate Matched (input is NOT noise matched) 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 5.00m 10.0m 15.0m 20.0m 0.000 25.0m IBB=0.000 IBB=10.0u IBB=20.0u IBB=30.0u IBB=40.0u IBB=50.0u IBB=60.0u IBB=70.0u IBB=80.0u IBB=90.0u IBB=100.u VCE IC.i,A m3 m3 VCE= IC.i=5.417352m IBB=0.000020 3.000000 K 0.6776 Stability Factor Matching for Gain Zsource Zload DUT* max_gain(S_bp) 20.7283 Max Avaliable Gain (dB) Zsource 50.0000 Zload 50.0000 Simultaneous Match (0.000 to 0.000) Sopt_at_bias_pt GammaS_at_bias_pt GammaL_at_bias_pt GammaL_wSopt Optimal Source Reflection Coefficients for Mininum NF, Simultaneous Conjugate Matching, and Load Reflection Coefficient for Simultaneous Conjugate Matching, and with source matched for NFmin Note: if the device (or circuit) is unstable at the bias point, the simultaneous conjugate matching impedances are undefined and GammaL_at_bias_pt and GammaS_at_bias_pt default to 0. Also, MAG is set equal to the maximum stable gain, |S21|/|S12|. Gamma_S (NFmin) Gamma_L when NFmin 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 5.00m 10.0m 15.0m 20.0m 0.000 25.0m IBB=0.000 IBB=10.0u IBB=20.0u IBB=30.0u IBB=40.0u IBB=50.0u IBB=60.0u IBB=70.0u IBB=80.0u IBB=90.0u IBB=100.u VCE IC.i,A m3 m3 VCE= IC.i=13.18580m IBB=0.000060 600.0000m K 1.1081 Stability Factor Matching for Gain Zsource Zload DUT* max_gain(S_bp) 16.1195 Max Avaliable Gain (dB) Zsource 9.0268 / -46.0973 Zload 44.0380 / 56.7293 Simultaneous Match (0.000 to 0.000)Sopt_at_bias_pt GammaS_at_bias_pt GammaL_at_bias_pt GammaL_wSopt Gamma_S (NFmin) Gamma_L when NFmin Use these equations to find the simultaneously conjugate matching condition. Noted that if such a biased condition is not unconditionally stable, the simultaneous matching is impossible and thus Zsource and Zload can’t be defined. Example: Biased@VCE=3V, IBB=20uA, K < 1 Example: Biased@VCE=0.6V, IBB=60uA, K > 1 Zsource and Zload can’t be found Zsource and Zload are not defined Gamma_L@NFmin Optimum Gamma_S@NFmin Zsource and Zload can be found For noise matching For maximum gain matching Max Available/Stable Gain (dB) Max Available/Stable Gain (dB) 2.28 m3 Arrange all the equations, tables, and draws we’ve done, and rename this datadisplay page as “Noise Condition.” Now, you can move maker m3 to any biased-point and observe all the information you need. m2 VCE= NFm in[0]=595.2716m IBB=0.000010 3.000000 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 2 4 6 8 10 0 12 I BB=0. 000 I BB=10. 0uI BB=20. 0u I BB=30. 0uI BB=40. 0uI BB=50. 0uI BB=60. 0uI BB=70. 0uI BB=80. 0u I BB=90. 0uI BB=100. u VCE NFmin[0] m2 m2 VCE= NFm in[0]=595.2716m IBB=0.000010 3.000000 m 1 VCE= dB(S21[0])=16.007 IBB=0.000010 3.000 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 -20 -15 -10 -5 0 5 10 15 -25 20 I BB=0. 000 I BB=10. 0u I BB=20. 0uI BB=30. 0uI BB=40. 0uI BB=50. 0uI BB=60. 0uI BB=70. 0uI BB=80. 0uI BB=90. 0uI BB=100. u VCE dB(S21[0]) m1 m 1 VCE= dB(S21[0])=16.007 IBB=0.000010 3.000 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 -14 -12 -10 -8 -6 -4 -2 -16 0 I BB=0. 000 I BB=10. 0u I BB=20. 0u I BB=30. 0u I BB=40. 0u I BB=50. 0u I BB=60. 0uI BB=70. 0uI BB=80. 0u I BB=90. 0uI BB=100. u VCE dB(S11[0]) I BB=0. 000 I BB=10. 0u I BB=20. 0u I BB=30. 0u I BB=40. 0u I BB=50. 0u I BB=60. 0u I BB=70. 0uI BB=80. 0u I BB=90. 0u I BB=100. u dB(S22[0]) 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 -25 -20 -15 -10 -5 -30 0 I BB=0. 000 I BB=10. 0u I BB=20. 0u I BB=30. 0u I BB=40. 0uI BB=50. 0uI BB=60. 0u I BB=70. 0uI BB=80. 0uI BB=90. 0uI BB=100. u VCE dB(S12) 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 -10 -5 0 5 10 15 20 -15 25 I BB=0. 000 I BB=10. 0u I BB=20. 0u I BB=30. 0u I BB=40. 0uI BB=50. 0uI BB=60. 0uI BB=70. 0uI BB=80. 0uI BB=90. 0uI BB=100. u VCE MAG,dB M inim um Nois e Figure v ers us IBB and VCETrans is tor dB(S21) v ers us IBB and VCE Max im um Av ailable Gain v ers us IBB and VCE dB(S12) vers us IBB and VCE dB(S11) and dB(S22) v ers us IBB and VCE m 4 VCE= Pgain_as soc =-2.051 IBB=0.000000 1.200 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 3. 50. 0 4. 0 - 10 - 5 0 5 10 15 20 - 15 25 I B B = 0 . 0 0 0 I B B = 1 0 . 0 u I B B = 2 0 . 0 u I B B = 3 0 . 0 uI B B = 4 0 . 0 u I B B = 5 0 . 0 uI B B = 6 0 . 0 uI B B = 7 0 . 0 uI B B = 8 0 . 0 uI B B = 9 0 . 0 uI B B = 1 0 0 . u VCE Pgain_assoc m 4 m 4 VCE= Pgain_as soc =-2.051 IBB=0.000000 1.200 As s oc iated Power Gain (input matc hed for NFm in, output then c onjugately m atc hed) v ers us IBB and VCE Eqn M AG =m ax_gain( S) M ax im um av ailable/s table gain at all frequenc ies Eqn f r equency=SP. f r eq[ 0, 0, 0] Eqn I Cindex=f ind_index( I C[ VCEindex] , m 3) Eqn VCEindex=f ind_index( DC. VCE[ 0, : : ] , indep( m3) ) Eqn I C=- SRC1. i Eqn DC_power =m3*indep( m 3) Eqn G amm aS_at _bias_pt =sm _gam ma1( S_bp) Eqn G amm aL_at _bias_pt =sm _gam ma2( S_bp) Eqn Zopt=zopt ( Sopt _at _bias_pt , Z0[ 0,0, 0] ) Eqn S_11=S_bp( 1, 1) Eqn S_12=S_bp( 1, 2) Eqn S_21=S_bp( 2, 1) Eqn S_22=S_bp( 2, 2) Eqn S_22p_at _bias=S_22p[ I Cindex, VCEindex] Eqn Pgain_assoc_at _bias=Pgain_assoc[ ICindex, VCEindex] Eqn Zload_wSopt =zopt ( conj( S_22p_at _bias) , Z0[ 0, 0, 0] ) Eqn K=st ab_f act ( S_bp) Eqn Pgain_assoc=pwr _gain( S[ 0] , zopt ( Sopt [ 0] , Z0[ 0, 0, 0] ) , zopt ( conj( S_22p) , Z0[ 0, 0, 0] ) , Z0[ 0, 0, 0] ) Eqn S_22p=S22[ 0] +( S12[ 0] *S21[ 0] *Sopt [ 0] ) / ( 1- S11[ 0] *Sopt [ 0] ) Eqn G amm aL_wSopt =conj( S_22p_at _bias) Eqn S_bp=S[ I Cindex, VCEindex, 0] Eqn NFm in_at _bias_pt =NFm in[ I Cindex, VCEindex, 0] S-param eters at the bias point s pec ified by m arker m 3. Sourc e impedanc e for m inim um nois e figure at the bias point s pec ified by m ark er m 3. Stability fac tors at the bias point m 3. Zs ourc e and Zload are the s ourc e and load im pedanc es to pres ent to the dev ic e for s im ultaneous c onjugate m atc hing, at the bias point m3. These are not defined and return 0 if K<1. S_22p : reflec tion look ing into the output of the dev ic e, when the s ourc e is optim al for m inim um nois e figure. Gam m aL_wSopt is the c om plex c onjugate of S22_p, and is the optimal load reflec tion c oeffic ient when Sopt is the s ourc e reflec tion c oeffic ient. Zload_wSopt is the c orres ponding impedanc e. Sim ultaneous c onjugate m atc h s ource and load reflec tion c oeffic ients at bias point m 3. Thes e are not defined and return 0 if K<1. Trans duc er power gain with the s ourc e reflec tion c oeffic ient Sopt for m inim um noise figure, and the load then c onjugately matc hed. z opt() is jus t us ed to c onv ert a reflec tion c oeffic ient to an im pedanc e. Collec tor DC c urrent Find index for the s wept v ariable VCE and ICE ac c ording to m ark er "m3" x -ax is . M inim um nois e figure at the m 3 bias point. DC power c om s um ption when bias ed at m ark er "m 3" (bas e c urrent is ignored) m 3 VCE= IC.i=5.417352m IBB=0.000020 3.000000 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 5.00m 10.0m 15.0m 20.0m 0.000 25.0m I BB=0. 000 I BB=10. 0u I BB=20. 0u I BB=30. 0u I BB=40. 0u I BB=50. 0u I BB=60. 0u I BB=70. 0u I BB=80. 0u I BB=90. 0u I BB=100. u VCE IC.i,A m3 m 3 VCE= IC.i=5.417352m IBB=0.000020 3.000000 I/V Curv e (Selec t Bias ing Point v ia m ak er m 3) Eqn Sopt_at _bias_pt =Sopt [ I Cindex, VCEindex, 0] Eqn Zsour ce=sm _z1( S_bp, Z0[ 0, 0, 0] ) Eqn Zload=sm _z2( S_bp, Z0[ 0, 0, 0] ) Source reflec tion c oeffic ient for m inimum nois e figure at frequenc y s pec ified by m ark er m 3. Sopt is the s -param eter for optim um nois e perform anc e. (1) (2) Bas ic inform ation at the bias point m 3. Optimum reflec tion c oeffic ient(im pedanc e) for m inim um nois e at the bias point m 3. Output Conjugately M atc hing Im pdeanc e Calc ulation (when input is nois e m atc hed) Input/Output Sim ultaneous ly Conjugate M atc hed (input is NOT nois e matc hed) Move marker m3 to selectbias point. All listings and impedances on Smith Chartwill be updated. Matching for Gain Zs ourc e Zload DUT* (0.000 to 0.000) Sopt_at_bias_pt GammaS_at_bias_pt GammaL_at_bias_pt GammaL_wSopt Optim al Sourc e Reflec tion Coeffic ients for M ininum NF, Simultaneous Conjugate M atc hing, and Load Reflec tion Coeffic ient for Sim ultaneous Conjugate M atc hing, and with s ourc e m atc hed for NFm in Note: if the dev ic e (or c irc uit) is uns table at the bias point, the s im ultaneous c onjugate m atc hing im pedances are undefined and Gam m aL_at_bias _pt and Gam m aS_at_bias _pt default to 0. Als o, M AG is s et equal to the m ax im um stable gain, |S21|/|S12|. 2.00m 4.00m 6.00m 8.00m 10.0m 12.0m 14.0m 16.0m 18.0m 0.000 20.0m 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.4 2.0 IC NFmin,dB NFmin versus IC, at VCE (set by m3) 2.00m 4.00m 6.00m 8.00m 10.0m 12.0m 14.0m 16.0m 18.0m 0.000 20.0m -15 -10 -5 0 5 10 15 -20 20 IC dB(S21) dB(S21) v ers us IC, at VCE (s et by m 3) indep( m 3) 3. 0000 m3[ 0] 5. 4174 m DC_power [0] 16. 252 m f r equency 2. 400 G VCE IC DC power (W) dB( S_11) - 6. 7279 dB( S_12) - 23. 460 dB( S_21) 17. 996 dB( S_22) - 7. 0302 Trans is tor S-param eter at bias point m 3 K 0. 6776 Stability Fac tor Z0[ 0, 0, 0] 50. 0000 Charac teris tic s Im pedanc e m ax_gain( S_bp) 20. 7283 M ax Av aliable/Stable Gain (dB)Zsour ce 50. 0000 Zload 50. 0000 Sim ultaneous M atc h Matching for Noise Figure NFm in_at _bias_pt 0. 6512 M inimum Nois e Figure (dB) Sopt _at _bias_pt 0. 2799 / 57. 8169 Soure Reflec tion Coeff. for NFm in Zopt 59. 0670 + j30. 3691 Zopt for NFm in Zload_wSopt 31. 8982 + j31. 7136 Conjugate M atc hed Load (for input m atc hed to NFm in) Zopt Zload_wSopt DUT* Pgain_assoc_at _bias 18. 6761 Power Gain (dB) at this nois e m atc hed c ondition Gam ma_S (NFm in) Gam ma_L when NFm in Bias Point Selector Updated Information according to the Bias Point m3 Eqn M uL=m u( S_bp) Eqn M uS=m u_pr im e( S_bp) M uL 0. 7081 M uL 0. 7081 M AG [ I Cindex, VCEindex, 0] 20. 7283 M ax Av aliable/Stable Gain (dB) 2.29 Datadisplay page
  42. 42. 41 4. (1) Bias_MinNF.dsn Bias_MinNF.dds Bias_MinNF_choose.dsn Bias_MinNF_choose.dds 2.30 IBB IBBstep VAR VAR2 Z0=50 VCEstep=0.2 V VCEmax=4 V VCEmin=0 V IBBstep=1 uA IBBmax=30 uA IBBmin=0 uA Eqn Var Rload=50 IBB=0 A DC DC1 Step=VCEstep Stop=VCEmax Start=VCEmin SweepVar="VCE" DC ParamSweep Sweep2 SimInstanceName[4]= SimInstanceName[3]= SimInstanceName[2]= SimInstanceName[1]="SP1" SweepVar="VCE" PARAMETER SWEEP ParamSweep Sweep1 SweepVar="IBB" SimInstanceName[1]="Sweep2" SimInstanceName[2]="DC1" SimInstanceName[3]= SimInstanceName[4]= PARAMETER SWEEP Simulating with finer step and range. 2.30 I-V (2) 2.31 NFmin Pgain_assc MAG VCE 3 IC 6.12 mA VCE IC NFmin (a) 20 mW 18.89 mW ( ) 16 mW (b) ( IC NFmin ) NF NF NF NF 1.5 dB NF 1.5 dB NF NF (c) ( ) 15 dB Pgain_assoc 15 dB Pgain_assoc MAG NF (d) Smith Chart
  43. 43. 42 S11 S22 (−5 dB ~ −3 dB) 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0 4.0 1.00m 2.00m 3.00m 4.00m 5.00m 6.00m 7.00m 0.000 8.00m IBB=0.000 IBB=1.00u IBB=2.00u IBB=3.00u IBB=4.00u IBB=5.00u IBB=6.00u IBB=7.00u IBB=8.00u IBB=9.00u IBB=10.0u IBB=11.0u IBB=12.0u IBB=13.0u IBB=14.0u IBB=15.0u IBB=16.0u IBB=17.0u IBB=18.0u IBB=19.0u IBB=20.0u IBB=21.0u IBB=22.0u IBB=23.0u IBB=24.0u IBB=25.0u IBB=26.0u IBB=27.0u IBB=28.0u IBB=29.0u IBB=30.0u VCE IC.i,A m3 m3 VCE= IC.i=6.120396m IBB=0.000023 3.000000 1.00m 2.00m 3.00m 4.00m 5.00m 6.00m 7.00m 0.000 8.00m 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.4 2.0 IC NFmin,dB m5 m5 indep(m5)= vs(NFmin[VCEindex,0],IC.i[VCEindex])=0.670226 0.006120 NFmin versus IC, at VCE (set by m3) MuL 0.7391 MuL 0.7391 K 0.7203 Stability Factor indep(m3) 3.0000 m3[0] 6.1204 m DC_power[0] 18.361 m DC power (W)ICVCE NFmin_at_bias_pt 0.6702 Minimum Noise Figure (dB) 1.00m 2.00m 3.00m 4.00m 5.00m 6.00m 7.00m 0.000 8.00m 0 5 10 15 20 -5 25 IC MAG[VCEindex,0] m6 Pgain_assoc[VCEindex] m7 m6 indep(m6)= vs(MAG[VCEindex,0],IC.i[VCEindex])=21.044851 0.006120 m7 indep(m7)= plot_vs(Pgain_assoc[VCEindex], IC.i[VCEindex])=18.892510 0.006120 MAG[ICindex,VCEindex,0] 21.0449 Max Avaliable/Stable Gain (dB) Pgain_assoc_at_bias 18.8925 Power Gain (dB) at this noise matched condition Select a biasing point that has a reasonable gain, NF, and power consumption (constrained by spec.) 2.31 I-V Curve NFmin Pgain_assc MAG 5. (1) IBB = 23 uA VCE = 3 V IC = 6.12 mA 18.36 mW 0.67 dB 18.89 dB 1 MSG 21.04 dB ( 0 ~ 10 GHz 0 ~ 16 GHz 20 GHz 40 GHz )
  44. 44. 43 (2) Bias_MinNF_choose.dsn Bias_MinNF_stability_BW.dsn 2.32 Options Options1 Tnom=25 Temp=16.85 OPTIONS S_Param SP1 Freq= CalcNoise=y es Step=50 MHz Stop=10 GHz Start=0.05 GHz S-PARAMETERS DC DC1 Step= Stop= Start= SweepVar= DC VAR VAR1 Z0=50 Rload=50 IBB=23 uA VCE=3 V Eqn Var Term Term2 Z=50 Ohm Num=2DC_Block DC_Block2 DC_Feed DC_Feed1 I_DC SRC2 Idc=IBB DC_Block DC_Block1 DC_Feed DC_Feed2Term Term1 Z=50 Ohm Num=1 bf p640esd_ADS X1 BFP640ESD I_Probe IC V_DC SRC1 Vdc=VCE Sweep frequency for a fixed biased-point 2.32 (3) Datadisplay m1 freq= NFmin=670.2263m 2.400000GHz 1 2 3 4 5 6 7 8 90 10 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.4 2.0 freq, GHz NFmin,dB m1 m1 freq= NFmin=670.2263m 2.400000GHz 1 2 3 4 5 6 7 8 90 10 5 10 15 20 25 0 30 freq, GHz dB(S21) 1 2 3 4 5 6 7 8 90 10 -50 -45 -40 -35 -30 -25 -20 -55 -15 freq, GHz dB(S12) 1 2 3 4 5 6 7 8 90 10 15 20 25 30 35 10 40 freq, GHz MAG,dB Minimum Noise Figure versus frequencyTransistor dB(S21) versus frequency Maximum Available(Stable) Gain versus frequency dB(S12) versus frequency m2 freq= Pgain_assoc=18.893 2.400GHz 1 2 3 4 5 6 7 8 90 10 10 15 20 25 30 35 40 45 5 50 freq, GHz Pgain_assoc m2 m2 freq= Pgain_assoc=18.893 2.400GHz Associated Power Gain (input matched for NFmin, output then conjugately matched) v ersus f requency m3 freq= MuS=0.746 2.400GHz 1 2 3 4 5 6 7 8 90 10 1 -1 2 freq, GHz MuS m3 MuL m3 freq= MuS=0.746 2.400GHz 1 2 3 4 5 6 7 8 90 10 -7 -6 -5 -4 -3 -2 -1 -8 0 freq, GHz dB(S11) dB(S11) versus frequency 1 2 3 4 5 6 7 8 90 10 -12 -10 -8 -6 -4 -2 -14 0 freq, GHz dB(S22) dB(S22) versus frequency Stability factor Transistor S-parameter Eqn MAG=max_gain(S) Maximum available(stable) gain at all frequencies Eqn frequency=SP.freq Eqn GammaS_all_freq=sm_gamma1(S) Eqn GammaL_all_freq=sm_gamma2(S) Eqn Zopt=zopt(Sopt,Z0) Eqn Zload_wSopt=zopt(conj(S_22p),Z0) Eqn K=stab_fact(S) Eqn Pgain_assoc=pwr_gain(S,zopt(Sopt,Z0),zopt(conj(S_22p),Z0),Z0) Eqn S_22p=S22+(S12*S21*Sopt)/(1-S11*Sopt) Eqn GammaL_wSopt=conj(S_22p) S-parameters, stabilityfactors, and MAG at all frequencies Source impedance for minimum noise figure Stabilityfactor at all frequencies Zsource and Zload are the source and load impedances to present to the device for simultaneous conjugate matching. These are not defined and return 0 if K<1. S_22p : reflection looking into the output of the device, when the source is optimal for minimum noise figure. GammaL_wSopt is the complexconjugate of S22_p, and is the optimal load reflection coefficient when Sopt is the source reflection coefficient. Zload_wSopt is the corresponding impedance. Simultaneous conjugate match source and load reflection coefficients at bias point m3. These are not defined and return 0 if K<1. Transducer power gain with the source reflection coefficient Sopt for minimum noise figure, and the load then conjugatelymatched. zopt() is just used to convert a reflection coefficient to an impedance. Eqn Zsource=sm_z1(S,Z0) Eqn Zload=sm_z2(S,Z0) Optimum reflection coefficient(impedance) for minimum noise at all frequencies Output ConjugatelyMatching Impdeance Calculation (when input is noise matched) Input/Output SimultaneouslyConjugate Matched (input is NOT noise matched) Eqn MuL=mu(S) Eqn MuS=mu_prime(S) 2.32
  45. 45. 44 (4) 2.33 2.4 GHz Eqn Source_stabcir1=s_stab_circle(S,51) Eqn Load_stabcir1=l_stab_circle(S,51) indep(Source_stabcir1) (0.000 to 51.000) Source_stabcir1 indep(Load_stabcir1) (0.000 to 51.000) Load_stabcir1 2.33 (5) Datadisplay Rectangular plot Trace Expression 2.34 maker fm1 fm1 2.4 GHz fm1 datadisplay Move marker fm1 to desiredfrequency point. Frequency Point Selector fm1 indep(fm1)= plot_vs([0::sweep_size(frequency)-1],frequency)=47.00000 2.400000G 1.0E9 2.0E9 3.0E9 4.0E9 5.0E9 6.0E9 7.0E9 8.0E9 9.0E90.0 1.0E10 0.0 1.0E6 frequency fm1 fm1 indep(fm1)= plot_vs([0::sweep_size(frequency)-1],frequency)=47.00000 2.400000G 2.34 (6) Datadisplay Smith Chart 2.35 rhos Smith Chart 2000 ( ) Smith Chart
  46. 46. 45 Eqn tindex=[0::2000] Eqn rhos=sqrt(tindex/2000)*exp(j*2*sqrt(pi*tindex)) tindex is a vector of numbers 0,1,2,3,...,2000. rhos are 2001 complex reflection coefficients. Show 2000 points on Smith Chart indep(rhos) (0.000 to 2000.000) rhos indep(rhos) (0.000 to 2000.000) rhos indep(rhos) (0.000 to 2000.000) rhos indep(rhos) (0.000 to 2000.000) rhos Scatter type Use lighter symbol color Copy Smith Chart 1Smith Chart 2 Preparing 2 Smith Charts for input and output stability circles Plot equation “rhos” on a Smith Chart 2.35 Smith Chart (7) 2.36 Smith Chart AutoScale Smith Chart 1 list Smith Chart 2.4 GHz (8) 2.37 (Shunt) (Series) BJT CE FET CS (Degeneration) CE CS
  47. 47. 46 indep(Source_stabcir) (0.000 to 51.000) Source_stabcir indep(rhos) (0.000 to 2000.000) rhos indep(Load_stabcir) (0.000 to 51.000) Load_stabcir indep(rhos) (0.000 to 2000.000) rhos indep(Source_stabcir) (0.000 to 51.000) Source_stabcir indep(Load_stabcir) (0.000 to 51.000) Load_stabcir Outside Source Stable Region Outside Load Stable Region Source Stability Circle Load Stability Circle Source Stability Circle Load Stability Circle Set Smith Chart Radius < 1 Show the Stable region Stable Stable Unstable Unstable Eqn Source_stabcir=s_stab_circle(S[fm1],51) Eqn Load_stabcir=l_stab_circle(S[fm1],51) Source and Load Stability Circles Draw the stability circles at frequency “fm1” 2.36 2.4 GHz 1R 2R 6R 5R 3R 4R • Stabilization methods described below are used to stabilize the transistor unconditionally. Stabilization of input port through series or shunt resistance, eg., R1, R2. Stabilization of output port through series or shunt resistance, eg., R3, R4. Stabilization using series or shunt negative feedback, eg., R5, R6. Inductances and capacitances are also commonly used as feedback elements. Stabilization results in a loss of gain and an increase in noise figure. shunt negative feedback series negative feedback (degeneration) 2.37
  48. 48. 47 (9) 2.37 2.38 ( ) 2.39 DC block 2.40 1R 3R 2R 4R 1R 3R 1R 4R 2R 3R 2R 4R Case (a): Input series Case (b): Input parallel Case (c): Output series Case (d): Output parallel Case (e) Input series / Output series Case (f) Input series / Output parallel Case (g) Input parallel/ Output series Case (h) Input parallel/ Output parallel 2.38 2R 4R Blocks are needed to prevent DC biasing current flow through the stabilizing resistors. 2.39 DC block 1R 3R VBias VBiasDon’t block your bias 1R 3R VBias VBias 2.40
  49. 49. 48 (10) 2.38(a) Smith Chart ( Gonzalez 3.3 Stability Considerations ) 2.41 Datadisplay maker Smith Chart r ( maker g) 7.7 9 (11) 2.41 MAG MSG 0.5 dB 18.9 dB 16.5 dB 2.5 dB MAG 19.9 dB Pgain_assoc 3.4 dB 3.4 dB 2.4 GHz indep(Source_stabcir) (0.000 to 51.000) Source_stabcir indep(rhos) (0.000 to 2000.000) rhos m4 m4 indep(m4)= rhos=0.733 / 179.349 impedance = Z0 * (0.154 + j0.006) 1075 Input series resistance = 0.154*50 Ohm = 7.7 Ohm 1R Case (a): Input series R R1 R=9 Ohm DC_Block DC_Block2 I_DC SRC2 Idc=IBB DC_Feed DC_Feed2 bf p640esd_ADS X1 BFP640ESD I_Probe IC indep(Source_stabcir) (0.000 to 51.000) Source_stabcir indep(rhos) (0.000 to 2000.000) rhos Inside Source Stable Region Stable Unstable 1 2 3 4 5 6 7 8 90 10 1 -1 2 freq, GHz MuS m3 MuL m3 freq= MuS=1.036 2.400GHz Unstable Stable Stabilization at 2.4 GHz / Input Series R Mu=0.746, MAG/MSG= 21 dB, NFmin = 0.67 dB, Pgain_assoc=18.9 dB Mu=1.036, MAG/MSG= 19.9 dB, NFmin = 1.16 dB, Pgain_assoc=16.5 dB Before stabilizing After stabilizing Draw a circle to roughly evaluate the input series stabilizing resistance Not whole band stable It is stable at 2.4 GHz 2.41
  50. 50. 49 (12) 2.37 ( ) 2.42 g indep(Source_stabcir) (0.000 to 51.000) Source_stabcir indep(rhos) (0.000 to 2000.000) rhos 2R Case (b): Input parallel Input parallel stabilize is impossible Mu= -, MAG/MSG= -, NFmin = -, Pgain_assoc= - Stabilization at 2.4 GHz / Input Parallel R Stabilizing can’t be achieved 2.42 (13) 2.43 2.44 (10) (11) m4 indep(m4)= rhos=0.614 / -179.141 impedance = Z0 * (0.239 - j0.007) 755 indep(Load_stabcir) (0.000 to 51.000) Load_stabcir indep(rhos) (0.000 to 2000.000) rhos m4 m4 indep(m4)= rhos=0.614 / -179.141 impedance = Z0 * (0.239 - j0.007) 755 Output series R = 0.239*50 Ohm = 11.95 Ohm 3R Case (c): Output series R R1 R=20 Ohm DC_Block DC_Block2 bf p640esd_ADS X1 BFP640ESD I_Probe IC Mu=0.746, MAG/MSG= 21 dB, NFmin = 0.67 dB, Pgain_assoc=18.9 dB MuL=1.028, MAG/MSG= 19.96 dB, NFmin = 0.7 dB, Pgain_assoc=16.9 dB indep(Load_stabcir) (0.000 to 51.000) Load_stabcir indep(rhos) (0.000 to 2000.000) rhos Outside Load Stable Region 1 2 3 4 5 6 7 8 90 10 1 -1 2 freq, GHz MuS m3 MuL m4 m3 freq= MuS=1.024 2.400GHz m4 freq= MuL=1.028 2.400GHz Unstable Stable Stable Unstable Stabilization at 2.4 GHz / Output Series R Draw a circle to roughly evaluate the output series stabilizing resistance Before stabilizing After stabilizing Not whole band stable It is stable at 2.4 GHz 2.43
  51. 51. 50 m4 indep(m4)= rhos=0.555 / 1.014 impedance = Z0 * (3.491 + j0.099) 616 indep(Load_stabcir) (0.000 to 51.000) Load_stabcir indep(rhos) (0.000 to 2000.000) rhos m4 m4 indep(m4)= rhos=0.555 / 1.014 impedance = Z0 * (3.491 + j0.099) 616 Output parallel R= 1/(0.286/50) Ohm = 174.8 Ohm Mu=0.746, MAG/MSG= 21 dB, NFmin = 0.67 dB, Pgain_assoc=18.9 dB 4R Case (d): Output parallel Mu=1.015, MAG/MSG= 20.25 dB, NFmin = 0.69 dB, Pgain_assoc=17.32 dB R R1 R=140 Ohm DC_Block DC_Block3 DC_Block DC_Block2 bf p640esd_ADS X1 BFP640ESD I_Probe IC indep(Load_stabcir) (0.000 to 51.000) Load_stabcir indep(rhos) (0.000 to 2000.000) rhos Outside Load Stable Region Stable Unstable 1 2 3 4 5 6 7 8 90 10 1 -1 2 freq, GHz MuS m3 MuL m4 m3 freq= MuS=1.012 2.400GHz m4 freq= MuL=1.015 2.400GHz Unstable Stable Before stabilizing After stabilizing Stabilization at 2.4 GHz / Output Parallel R Not whole band stable It is stable at 2.4 GHz 2.44 (14) 2.45 2.38 case(e)~(h) ADS tuning 1R 4R Case (f) Input series / Output parallel MuS=1.62, MuL= 1.67, MAG/MSG= 14.8 dB, NFmin = 1.24 dB, Pgain_assoc=13.3 dB 1 2 3 4 5 6 7 8 90 10 2 3 4 5 1 6 freq, GHz MuS m3 MuL m4 m3 freq= MuS=1.620 2.400GHz m4 freq= MuL=1.667 2.400GHz R R1 R=47 OhmR R2 R=9 Ohm DC_Block DC_Block3 DC_Block DC_Block2 bf p640esd_ADS X1 BFP640ESD I_Probe IC Mu=0.746, MAG/MSG= 21 dB, NFmin = 0.67 dB, Pgain_assoc=18.9 dB Before stabilizing After stabilizing Stabilization at 2.4 GHz / Input Series R and Output Parallel R Whole band stable 2.45
  52. 52. 51 (15) (9) 2.38 10 GHz ( ) 2.46 Smith Chart ( ) (2.4 GHz ) MAG NFmin Pgain_assoc (a) (b) S11 S22 (c) S11 S22 indep(rhos) (0.000 to 2000.000) rhos Minimum series resistance 1 1 GHzf = 1 1.5 GHzf =1 2 GHzf = 1 3 GHzf = 1 5 GHzf = Increasing frequency 2.46 (16) (15) (15) (17) (15) L C 2.47
  53. 53. 52 2.48 2.49 RLC (18) 2.48 2.49 (2.4 GHz ) MAG NFmin Pgain_assoc 1Z 3Z High-band Stabilization 2Z 4Z 2.47 1Z 3Z Low-band Stabilization 2Z 4Z 2.48 1Z 3Z Band-pass Stabilization 2Z 4Z 2.49
  54. 54. 53 (19) 2.50 ( ) 2.50 (2.4 GHz ) MAG NFmin Pgain_assoc R R1 R=? Ohm Term Term2 Z=50 Ohm Num=2 bfp640esd_ADS X1 BFP640ESD Term Term1 Z=50 Ohm Num=1 DC_Feed DC_Feed2 DC_Block DC_Block2 DC_Block DC_Block1 DC_Feed DC_Feed1 I_Probe IC V_DC SRC1 Vdc=VCE I_DC SRC2 Idc=IBB R R1 R=? Ohm DC_Block DC_Block3 Term Term2 Z=50 Ohm Num=2 bfp640esd_ADS X1 BFP640ESD Term Term1 Z=50 Ohm Num=1 DC_Feed DC_Feed2 DC_Block DC_Block2 DC_Block DC_Block1 DC_Feed DC_Feed1 I_Probe IC V_DC SRC1 Vdc=VCE I_DC SRC2 Idc=IBB Shunt Feedback Stabilization Feedback Resistance Isolated from DC network 2.50 (20) (17) 2.51 L L3 R= R R6 DC_Block DC_Block6 C C4 L L2 R= DC_Block DC_Block5 R R5 DC_Block DC_Block4 C C3 R R4 C C2 R R3 R R2 C C1 DC_Block DC_Block3 L L1 R= R R1 Term Term2 Z=50 Ohm Num=2 bfp640esd_ADS X1 BFP640ESD Term Term1 Z=50 Ohm Num=1 DC_Feed DC_Feed2 DC_Block DC_Block2 DC_Block DC_Block1 DC_Feed DC_Feed1 I_Probe IC V_DC SRC1 Vdc=VCE I_DC SRC2 Idc=IBB Frequency-selective Shunt Feedback Stabilization 2.51
  55. 55. 54 (21) 2.52 BJT 50 ( 50 IC ) R R7 Term Term2 Z=50 Ohm Num=2 bfp640esd_ADS X1 BFP640ESD Term Term1 Z=50 Ohm Num=1 DC_Feed DC_Feed2 DC_Block DC_Block2 DC_Block DC_Block1 DC_Feed DC_Feed1 I_Probe IC V_DC SRC1 Vdc=VCE I_DC SRC2 Idc=IBB C C5 R R7 Term Term2 Z=50 Ohm Num=2 bfp640esd_ADS X1 BFP640ESD Term Term1 Z=50 Ohm Num=1 DC_Feed DC_Feed2 DC_Block DC_Block2 DC_Block DC_Block1 DC_Feed DC_Feed1 I_Probe IC V_DC SRC1 Vdc=VCE I_DC SRC2 Idc=IBB L L4 R= Term Term2 Z=50 Ohm Num=2 bfp640esd_ADS X1 BFP640ESD Term Term1 Z=50 Ohm Num=1 DC_Feed DC_Feed2 DC_Block DC_Block2 DC_Block DC_Block1 DC_Feed DC_Feed1 I_Probe IC V_DC SRC1 Vdc=VCE I_DC SRC2 Idc=IBB Series Feedback Stabilization (Degeneration) C C1 L L4 R= R R2 Term Term2 Z=50 Ohm Num=2 bfp640esd_ADS X1 BFP640ESD Term Term1 Z=50 Ohm Num=1 DC_Feed DC_Feed2 DC_Block DC_Block2 DC_Block DC_Block1 DC_Feed DC_Feed1 I_Probe IC V_DC SRC1 Vdc=VCE I_DC SRC2 Idc=IBB Considered with bias Considered with bias Bypass to increase AC gain No DC disturb High frequency degeneration No DC disturb Bandpass degeneration DC path 2.52
  56. 56. 55 (22) ( ) (23) 2.53 ( Smith Chart ) (1k Ohm) 2.4 GHz 1.2 dB MAG 19.56 dB 18.2 dB S11 S22 −10 dB −15 dB 1 GHz 6 GHz Smith Chart MuS=1.012, MuL= 1.014, MAG/MSG= 19.56 dB, NFmin = 1.2 dB, Pgain_assoc=18.2dB 1 2 3 4 5 6 7 8 90 10 1.05 1.10 1.15 1.20 1.25 1.00 1.30 freq, GHz MuS m3 MuL m4 m3 freq= MuS=1.012 2.400GHz m4 freq= MuL=1.014 2.400GHz Stabilization at 2.4 GHz / Input Parallel R and Shunt Feedback Mu=0.746, MAG/MSG= 21 dB, NFmin = 0.67 dB, Pgain_assoc=18.9 dB Before stabilizing After stabilizing R R2 R=1 kOhm R R1 R=800 Ohm DC_Block DC_Block5 DC_Block DC_Block4 DC_Block DC_Block2 Term Term2 Z=50 Ohm Num=2 DC_Feed DC_Feed1 I_DC SRC2 Idc=IBB DC_Block DC_Block1 DC_Feed DC_Feed2Term Term1 Z=50 Ohm Num=1 bf p640esd_ADS X1 BFP640ESD I_Probe IC V_DC SRC1 Vdc=VCE 2.53
  57. 57. 56 (24) DC Block 2.54 (50 ) 1/10 1/20 1/20 26 pF 27 pF SRF 2.4 GHz SRF block 2.4 GHz 1/10 SRF C C2 C=27 pF C C1 C=27 pF R R2 R=1 kOhm R R1 R=800 Ohm DC_Block DC_Block2 Term Term2 Z=50 Ohm Num=2 DC_Feed DC_Feed1 I_DC SRC2 Idc=IBB DC_Block DC_Block1 DC_Feed DC_Feed2Term Term1 Z=50 Ohm Num=1 bf p640esd_ADS X1 BFP640ESD I_Probe IC V_DC SRC1 Vdc=VCE Put a practical value of capacitance Put a practical value of capacitance ω < 01 20 Z j C > 26 pFC @2.4 GHz 2.54 DC Block (25) 100 GHz 10 20 30 40 50 60 70 80 900 100 1.05 1.10 1.15 1.20 1.25 1.30 1.00 1.35 freq, GHz MuS m3 MuL m4 m3 freq= MuS=1.013 2.550GHz m4 freq= MuL=1.016 2.550GHz Check the stability at higher frequencies 2.55
  58. 58. 57 6. (1) 2.56 ( choke) (2) RF choke RF choke 2.57 choke RF (VCC) ( 3 GHz ) SRF choke λ/4 RF short( bypass ) RF open choke SMD RF λ/4 RF open RF short λ/4 RF short RF open choke RF λ/4 SMD choke R R7 bf p640esd_ADS X4 BFP640ESD R R9 R R8 R R15 bfp640esd_ADS X6 BFP640ESD R R16 R R17 R R14R R10 R R11 bfp640esd_ADS X5 BFP640ESD R R12 R R13R R3 R R4 bf p640esd_ADS X2 BFP640ESD R R6 bf p640esd_ADS X3 BFP640ESD R R5 Common Passive Biasing Circuits VCE IC VCC 2.56
  59. 59. 58 MLIN TL5 R R24 R R25 bfp640esd_ADS X10 BFP640ESD MRSTUB Stub1 bfp640esd_ADS X8 BFP640ESD R R21 R R20 MLIN TL1 C C3 bfp640esd_ADS X9 BFP640ESD R R23 R R22 MLIN TL3 MLOC TL2 L L1 R= R R18 R R19 bfp640esd_ADS X7 BFP640ESD RF Chokes Inductor as RF choke λ/4 transmission line as RF choke RF short RF bypass RF open RF open λ/4 transmission line as RF choke λ/4 open stub RF short RF open Radial open stub RF short RF open RF open 2.57 choke 7. LNA (1) Datadisplay Bias_MinNF_Matching.dsn Bias_MinNF_Matching.dds 2.58 S_Param SP1 Freq= CalcNoise=yes Step=50 MHz Stop=3 GHz Start=2 GHz S-PARAMETERS VAR VAR1 Z0=50 Rload=50 VCC=3.3 V Eqn Var Options Options1 Tnom=25 Temp=16.85 OPTIONS DC DC1 Step= Stop= Start= SweepVar= DC DC_Block DC_Block2 DC_Block DC_Block1 Term Term1 Z=50 Ohm Num=1 R R4 R=96 kOhm R R2 R=1 kOhm C C2 C=27 pF R R1 R=800 Ohm C C1 C=27 pF I_Probe IB R R3 R=50 Ohm L L1 R= L=18 nH V_DC SRC1 Vdc=VCC I_Probe IC bfp640esd_ADS X1 BFP640ESD Term Term2 Z=50 Ohm Num=2 Stabilizing Ckt Voltage feedback biasing Use VCC Here, we use a 3.3 V supply voltage Sweep from 2 GHz ~ 3 GHz 2.58 LNA
  60. 60. 59 (2) 2.58 ADS ADS (3) 2.58 2.59 2.4 GHz~2.5 GHz 1.2 dB 18 dB ~ 17.8 dB Smith Chart (Sopt ) (Gamma_L_wSopt ) 2 GHz 3 GHz 1 GHz Smith Chart m1 freq= NFmin=1.203725 2.400000GHz 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.92.0 3.0 1.190 1.195 1.200 1.205 1.210 1.215 1.185 1.220 freq, GHz NFmin,dB m1 m1 freq= NFmin=1.203725 2.400000GHz 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.92.0 3.0 16.4 16.6 16.8 17.0 17.2 17.4 17.6 17.8 18.0 16.2 18.2 freq, GHz dB(S21) 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.92.0 3.0 -23.0 -22.8 -22.6 -22.4 -23.2 -22.2 freq, GHz dB(S12) m5 freq= MAG=18.937 2.400GHz 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.92.0 3.0 18.2 18.4 18.6 18.8 19.0 19.2 18.0 19.4 freq, GHz MAG,dB m5 m5 freq= MAG=18.937 2.400GHz MinimumNoise Figure versus frequencyTransistordB(S21) versus frequency Maximum Available(Stable) Gain versus frequency dB(S12) versus frequency m2 freq= Pgain_assoc=17.981 2.400GHz 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.92.0 3.0 17.2 17.4 17.6 17.8 18.0 18.2 18.4 17.0 18.6 freq, GHz Pgain_assoc m2 m2 freq= Pgain_assoc=17.981 2.400GHz Associated PowerGain (input matched for NFmin, output then conjugately matched) versus frequency Eqn M AG=m ax _gain(S) Maximumavailable(stable) gain at all frequencies Eqn frequency =SP.freq Eqn Gam m aS_all_freq=s m _gamm a1(S) Eqn Gam m aL_all_freq=s m _gamm a2(S) Eqn Zopt=zopt(Sopt,Z0) Eqn Zload_wSopt=z opt(c onj(S_22p),Z0) Eqn K=stab_fac t(S) Eqn Pgain_as s oc=pwr_gain(S,z opt(Sopt,Z0),z opt(c onj(S_22p),Z0),Z0) Eqn S_22p=S22+(S12*S21*Sopt)/(1-S11*Sopt) Eqn Gam m aL_wSopt=conj(S_22p) S-parameters at the bias point specified by marker fm. Source impedance for minimum noise figure Stability factor at all frequencies Zsource and Zload are the source and load impedances to present to the device for simultaneous conjugate matching. These are not defined and return 0 if K<1. S_22p : reflection looking into the output of the device, when the source is optimal for minimumnoise figure. GammaL_wSopt is the complex conjugate of S22_p, and is the optimal load reflection coefficient when Sopt is the source reflection coefficient. Zload_wSopt is the corresponding impedance. Simultaneous conjugate match source and load reflection coefficients at bias point m3. These are not defined and return 0 if K<1. Transducer powergain with the source reflection coefficient Sopt forminimumnoise figure, and the load then conjugately matched. zopt()is just used to convert a reflection coefficient to an impedance. Eqn Zsource=s m_z 1(S,Z0) Eqn Zload=s m _z2(S,Z0) Optimumreflection coefficient(impedance)for minimum noise at all frequencies Output Conjugately Matching Impdeance Calculation (when input is noise matched) Input/Output Simultaneously Conjugate Matched (input is NOTnoise matched) m11 freq= Sopt=0.171 / 138.227 impedance =Z0 * (0.755 + j0.178) 2.400GHz m12 freq= GammaL_wSopt=0.171 / 52.058 impedance =Z0 * (1.185 + j0.329) 2.450GHz freq (2.000GHz to 3.000GHz) Sopt m11 GammaS_all_freq GammaL_all_freq GammaL_wSopt m12 m11 freq= Sopt=0.171 / 138.227 impedance =Z0 * (0.755 + j0.178) 2.400GHz m12 freq= GammaL_wSopt=0.171 / 52.058 impedance =Z0 * (1.185 + j0.329) 2.450GHz Optimal Source Reflection Coefficients for MininumNF,Simultaneous Conjugate Matching, and Load Reflection Coefficientfor Simultaneous Conjugate Matching,and with source matched for NFmin Note: if the device (orcircuit) is unstable at the bias point, the simultaneous conjugate matching impedances are undefined and GammaL_at_bias_pt and GammaS_at_bias_pt default to 0. Also, MAG is set equal to the maximum stable gain, |S21|/|S12|. Gamma_S (NFmin) Gamma_L when NFmin fm1 indep(fm1)= plot_vs([0::sweep_size(frequency)-1],frequency)=8.000000 2.400000G 2.1E9 2.2E9 2.3E9 2.4E9 2.5E9 2.6E9 2.7E9 2.8E9 2.9E92.0E9 3.0E9 0.0 1.0E6 frequenc y fm1 fm1 indep(fm1)= plot_vs([0::sweep_size(frequency)-1],frequency)=8.000000 2.400000G Eqn MuL=mu(S) m3 freq= MuS=1.050 2.400GHz m4 freq= MuL=1.073 2.400GHz 2. 1 2. 2 2. 3 2. 4 2. 5 2. 6 2. 7 2. 8 2. 92. 0 3. 0 1. 04 1. 05 1. 06 1. 07 1. 08 1. 09 1. 03 1. 10 freq, GHz MuS m3 MuL m4 m3 freq= MuS=1.050 2.400GHz m4 freq= MuL=1.073 2.400GHz Eqn MuS=mu_prime(S) m9 freq= dB(S(1,1))=-8.693 2.400GHz 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.92.0 3.0 -9.0 -8.8 -8.6 -8.4 -8.2 -8.0 -9.2 -7.8 freq, GHz dB(S11) m9 m9 freq= dB(S(1,1))=-8.693 2.400GHz dB(S11)versus frequency m10 freq= dB(S(2,2))=-18.825 2.500GHz 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.92.0 3.0 -19.6 -19.4 -19.2 -19.0 -18.8 -18.6 -18.4 -18.2 -18.0 -19.8 -17.8 freq, GHz dB(S22) m10 m10 freq= dB(S(2,2))=-18.825 2.500GHz dB(S22)versus frequency m11 freq= Sopt=0.171 / 138.227 impedance = Z0 * (0.755 + j0.178) 2.400GHz m12 freq= GammaL_wSopt=0.171 / 52.058 impedance = Z0 * (1.185 + j0.329) 2.450GHz freq (2.000GHz to 3.000GHz) Sopt m11 GammaS_all_freq GammaL_all_freq GammaL_wSopt m12 m11 freq= Sopt=0.171 / 138.227 impedance = Z0 * (0.755 + j0.178) 2.400GHz m12 freq= GammaL_wSopt=0.171 / 52.058 impedance = Z0 * (1.185 + j0.329) 2.450GHz Gamma_S (NFmin) Gamma_L when NFmin NFmin Sweep from 2 GHz ~ 3 GHz : The optimum noise point and the corresponding Gamma_L are close to 50 Ohm. 2.59 LNA (4) [A] [B] [C] [D]
  61. 61. 60 (5) [A] [D] 2.60 ”rhos” Smith Chart GammaS GammaL maker Case [A] Case [B] maker fm1 Case [C] GammaS ( Smith Chart 1 maker) GammaS GammaLopt NF_at_GammaS Case [D] GammaL ( Smith Chart 2 maker) GammaL GammaSopt NF_at_GammaSopt Eqn GammaLopt=conj(S22[fm1] +S12[fm1]*S21[fm1]*GammaS/(1-S11[fm1]*GammaS)) Eqn GammaLopt_NFmin=GammaL_w Sopt[fm1] (C) Optimal Gamma_L w hen the Gamma_S is at "maker GammaS" (A) Optimal Gamma_L w hen the Gamma_S is at Sopt (optimal for minimum noise figure.) Eqn GammaSopt=conj(S11[fm1]+S12[fm1]*S21[fm1]*GammaL/(1-S22[fm1]*GammaL)) (D) Optimal Gamma_S w hen the Gamma_L at "maker GammaL" Source reflection coefficientEqn GammaS_ConjMatch=GammaS_all_freq[fm1] Zsource is the impedance at marker GammaS.Eqn Zsource2=Z0*(1+GammaS)/(1-GammaS) (B) Gamma_S for simultaneous conjugate matching at fm1 Reflection Coefficients Calculation indep(rhos) (0.000 to 2000.000) rhos indep(rhos) (0.000 to 2000.000) rhos GammaS GammaL Smith Chart 1 Smith Chart 2 Eqn NF_lin_at_GammaS=NFmin_lin+4*(Rn[fm1]/Z0[fm1])*mag(GammaS-Sopt[fm1])**2/((1-mag(GammaS)**2)*mag(1+Sopt[fm1])**2) Eqn NFmin_lin=10**(NFmin[fm1]/10) Eqn NF_at_GammaS=10*log(NF_lin_at_GammaS) Eqn NF_at_GammaS_ConjMatch=if (stab_fact(S[fm1]) >1) then 10*log(NF_lin_at_GammaS_ConjMatch) else 1000 Eqn NF_lin_at_GammaS_ConjMatch=NFmin_lin+4*(Rn[fm1]/Z0[fm1])*mag(GammaS_ConjMatch-Sopt[fm1])**2/((1-mag(GammaS_ConjMatch)**2)*mag(1+Sopt[fm1])**2 +1e-20) (C) Noise figure for an arbitray Gamma_S (marker GammaS) (B) Noise figure for simultaneously conjugate matching. (Only defined if K is >1. Otherwise the noise figure is set to 1000.) (D) Noise figure for an arbitray Gamma_L (the source reflection coefficient is at GammaSopt) Eqn NF_lin_at_GammaSopt=NFmin_lin+4*(Rn[fm1]/Z0[fm1])*mag(GammaSopt-Sopt[fm1])**2/((1-mag(GammaSopt)**2)*mag(1+Sopt[fm1])**2) Eqn NF_at_GammaSopt=10*log(NF_lin_at_GammaSopt) Noise Figure Calculation (A) NFmin_lin (Miminum noise factor) Create two Smith Charts with “rhos” on them, and separately put makers named “GammaS” and “GammaL” on them. Find reflection coefficients for case [A] to [D] Calculate NF for case [B] to [D] 2.60 Case[A] [D] (6) 2.61 Case[A] [D] (7) 2.62 ADS GA Gp ADS ns_circle()
  62. 62. 61 Eqn Gt_num=mag(S21[fm1])**2 *(1-mag(GammaS)**2) *(1-mag(GammaLopt)**2) Eqn Gt_den=mag((1-S11[fm1]*GammaS)*(1-S22[fm1]*GammaLopt) -S21[fm1]*S12[fm1]*GammaS*GammaLopt)**2 Eqn Gt_num_NFmin=mag(S21[fm1])**2 *(1-mag(Sopt[fm1])**2) *(1-mag(GammaLopt_NFmin)**2) Eqn Gt_den_NFmin=mag((1-S11[fm1]*Sopt[fm1])*(1-S22[fm1]*GammaLopt_NFmin) -S21[fm1]*S12[fm1]*Sopt[fm1]*GammaLopt_NFmin)**2 Eqn Gtrans_power_NFmin=10*log(Gt_num_NFmin/Gt_den_NFmin) (C) Gtrans_power: transducer power gain with the source reflection coefficient at marker GammaS, and the load then conjugately matched. (A) Gtrans_power_NFmin: transducer power gain with the source reflection coefficient Sopt for minimum noise figure, and the load then conjugately matched. Eqn Gtload_num=mag(S21[fm1])**2 *(1-mag(GammaSopt)**2) *(1-mag(GammaL)**2) Eqn Gtload_den=mag((1-S11[fm1]*GammaSopt)*(1-S22[fm1]*GammaL) -S21[fm1]*S12[fm1]*GammaSopt*GammaL)**2 Eqn Gtrans_power_load=if (Gtload_num>0) then 10*log(Gtload_num/Gtload_den) else 1e6 (D) Gtrans_load : transducer power gain with the load reflection coefficient at marker GammaL, and the source then optimumly noise matched. Eqn Gtrans_power=if (Gt_num>0) then 10*log(Gt_num/Gt_den) else 1e6 Transducer Power Gain Calculation (B) Max. transducer power gain is equal to MAG(or MSG) when simulyaneously matched. Transducer gain for case [A] to [D] 2.61 Case[A] [D] Eqn Noise_circleMin=ns_circle(NFmin[fm1],NFmin[fm1],Sopt[fm1],Rn[fm1]/Z0[fm1],51) Eqn Noise_circles=ns_circle(NFmin[fm1]+NFstep_size*[1::num_NFcircles],NFmin[fm1],Sopt[fm1],Rn[fm1]/Z0[fm1],51) Eqn GAcircleMax=ga_circle(S[fm1],max_gain(S[fm1])) Eqn GAcircles=ga_circle(S[fm1],max_gain(S[fm1])-GAstep_size*[0::num_GAcircles]) Eqn GPcircles=gp_circle(S[fm1],max_gain(S[fm1])-GPstep_size*[0::num_GPcircles]) Equations to Plot Noise and Gain Circles Noise Circle Available Power Gain Circle Operating Power Gain Circle Eqn num_NFcircles=3 Eqn NFstep_size=0.2 Eqn GAstep_size=1 Eqn num_GAcircles=3 Eqn num_GPcircles=3 Eqn GPstep_size=1 Set step size and number of circles to plot Plot the transistor GA, Gp, and Noise Circles on the Smith Chart. 2.62 GA Gp (8) list Case[A] Case[B] list Case[A] 1.2 dB 17.98 dB 50 (37.76 + j8.89) (59.8 + j15.87) Case[B] NF_at_GammaS_ConjMatch 2.1526 sm_z1(S[fm1],Z0[fm1]) 9.1969 + j7.2047 sm_z2(S[fm1],Z0[fm1]) 48.1343 + j70.9704 max_gain(S[fm1]) 18.9366 NF with Zsource (valid for K>1) Simultaneous Conjugate Matched (valid for K>1) Zsource Zload MAG (or MSG for K<1) (B) Matching Condition for Simultaneously Conjugate Matched NFmin[fm1] 1.2037 NFmin (dB) zopt(Sopt[fm1],Z0[fm1]) 37.7643 + j8.8868 Source Impedance Zopt at NFmin zin(GammaLopt_NFmin,Z0[fm1]) 59.8045 + j15.8659 Optiomal Load Impedance for source Zopt at NFmin Transducer Power Gain (dB) Gtrans_power_NFmin 17.9810 (A) Matching Condition for Minimum Noise Figure 2.63 Case[A] [B]
  63. 63. 62 (9) 2.64 Smith Chart 1 GA GAcircles Noise_circles ( ) ( ) maker GammaS 2.64 list GammaS GammaS ( ) list 2.63 Case[A] ( GammaS Case[A] ) GammaS GammaS indep(GammaS)= rhos=-0.11872 + j0.12612 impedance = 38.26607 + j9.95049 60 indep(rhos) (0.000 to 2000.000) rhos GammaSgain=18.937 gain=17.937 gain=16.937 gain=15.937 cir_pts (0.000 to 51.000) GAcircles indep(GammaLopt) (60.000 to 60.000) GammaLopt ns figure=1.404ns figure=1.604ns figure=1.804 Noise_circles (0.000 to 0.000) Sopt[fm1] GammaLopt_NFmin GammaS indep(GammaS)= rhos=-0.11872 + j0.12612 impedance = 38.26607 + j9.95049 60 NF at GammaS (dB) NF_at_GammaS 1.2042 Zsource2 38.2661 + j9.9505 Source Impedance at GammaS zin(GammaLopt,Z0[fm1]) 58.7305 + j15.5482 Optiomal Load Impedance at GammaS Transducer Power Gain (dB) Gtrans_power 17.9575 (C) Matching Condition for Arbitray GammaS Gamma_S (NFmin) Gamma_L when NFmin GA = 17.937 dB GA = 16.937 dB GA = 15.937 dB GA = 18.937 dB NF= 1.404 dB NF= 1.604 dB NF= 1.804 dB NFmin= 1.204 dB 2.64 GammaS ( ) (10) maker GammaS GA ( ) list 0.2 dB 0.8 dB
  64. 64. 63 − source stability circle Smith Chart GammaS indep(GammaS)= rhos=-0.45577 + j0.18782 impedance = 17.56757 + j8.71721 486 indep(rhos) (0.000 to 2000.000) rhos GammaS gain=18.937 gain=17.937 gain=16.937 gain=15.937 cir_pts (0.000 to 51.000) GAcircles indep(GammaLopt) (486.000 to 486.000) GammaLopt ns figure=1.404ns figure=1.604ns figure=1.804 Noise_circles (0.000 to 0.000) Sopt[fm1] GammaLopt_NFmin GammaS indep(GammaS)= rhos=-0.45577 + j0.18782 impedance = 17.56757 + j8.71721 486 NF at GammaS (dB) NF_at_GammaS 1.4718 Zsource2 17.5676 + j8.7172 Source Impedance at GammaS zin(GammaLopt,Z0[fm1]) 57.1651 + j46.3908 Optiomal Load Impedance at GammaS Transducer Power Gain (dB) Gtrans_power 18.7382 (C) Matching Condition for Arbitray GammaS Gamma_S (NFmin) Gamma_L when NFmin 2.65 GammaS ( ) (11) 2.66 Smith Chart 2 GP GPcircles ( ) List GammaL Loal-pull
  65. 65. 64 GammaL indep(GammaL)= rhos=0.36056 / 35.02213 impedance = Z0 * (1.61272 + j0.76714) 260 indep(rhos) (0.000 to 2000.000) rhos GammaL gain=18.937 gain=17.937 gain=16.937 gain=15.937 cir_pts (0.000 to 51.000) GPcircles indep(GammaSopt) (260.000 to 260.000) GammaSopt GammaL indep(GammaL)= rhos=0.36056 / 35.02213 impedance = Z0 * (1.61272 + j0.76714) 260 NF_at_GammaSopt 1.6094 ...ammaSopt,Z0[fm1]) 15.0293 + j4.4503 zin(GammaL,Z0[fm1]) 80.6361 + j38.3568 Gtrans_power_load 18.6958 NF with optimal Zsource Optimal Zsource when Zload is at GammaL Zload at GammaL Transducer Power gain (dB) (D) Matching Condition for Arbitray GammaL 2.66 GammaL (12) LNA 2.67 50 2.4 GHz ~ 2.5 GHz 1.2 dB 17.8 dB C C5 C=27 pF Term Term2 Z=50 Ohm Num=2 L L3 R= L=1.68 nH C C4 C=0.27 pF L L2 R= L=6 nH C C3 C=6 pF Term Term1 Z=50 Ohm Num=1 R R4 R=96 kOhm R R2 R=1 kOhm C C2 C=27 pF R R1 R=800 Ohm C C1 C=27 pF I_Probe IB R R3 R=50 Ohm L L1 R= L=18 nH V_DC SRC1 Vdc=VCC I_Probe IC bfp640esd_ADS X1 BFP640ESD 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.492.40 2.50 17.8 18.0 17.6 18.2 freq, GHz Pgain_assoc m2 m2 freq= Pgain_assoc=17.903 2.450GHz 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.492.40 2.50 1.192 1.194 1.196 1.198 1.200 1.202 1.204 1.206 1.208 1.190 1.210 freq, GHz NFmin,dB m1 m1 freq= NFmin=1.202077 2.450000GHz Gamma_S (NFmin) Gamma_L when NFmin freq (2.400GHz to 2.500GHz) Sopt GammaS_all_freq GammaL_all_freq GammaL_wSopt Matched to 50 Ohm 2.67 LNA
  66. 66. 65 8. (1) LNA Pout Pin P1dB IP3 2.5 Datasheet ADS 2.4 GHz ~ 2.5 GHz 17.8 dB 1.2 dB 13 dB 1.5 dB

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