General Topology of a single stage microwave amplifier

Transcription

1 General Topology of a ingle tage microwave amplifier Tak of MATCH network (in and out): To preent at the active device uitable impedance Z and Z S Deign Step The deign of a mall ignal microwave amplifier at a ingle frequency i compoed of the following tep: Choice of active device Evaluation of optimum load for the device (Z and Z S ) Synthei of MATCH network

2 Active device repreentation The active device i repreented by mean of it meaured cattering parameter in the pecified bia condition. The reference impedance i typically 50 Ohm S v in S (50Ω) S Z Z Z Z S S Uing uitable formula, it i poible to evaluate the Tranducer Gain and the reflection coefficient at input and output.

3 Evaluation of in, out and G T S (50Ω) All reflection coefficient are defined with repect 50 Ω: in out ZS 50 Z 50 S, Z + 50 Z + 50 S in Z Z in in ( ) 1 1 Z out 50 + out Z out + 50 ( 1 S ) S 1 1 G T (1 S ) (1 ) 1 (1 ) (1 ) S S 1 1

4 Stability Iue A -port network operating a an amplifier mut be table, i.e. the output ignal mut remain of finite amplitude for an input exciting ignal with finite amplitude A -port i aid unconditionally table if, for whatever value of e S, it ha: S S in out 1 1 in + < S out + < 1 S 1 1 If both the condition are not atified the -port i aid potentially intable

5 Stability Condition Given the S parameter, the condition in <1, out <1 are verified for whatever value of S, if: K > 1, Det S 1 1 [ ] < 1 When thee equation are verified (and the port i unconditionally table ) a pair S,opt,,opt doe exit which determine the conjugate matching both at input and output. In thi condition G T i maximum and can be expreed a: G 1, T MAX 1 ( K K ) 1

6 B C g g 1 + Expreion for S,opt,,opt C B B C 1 ( 4 ) * g g g g S, opt C ( 4 ) C B B C C 1 *, opt * ( ) C ( ) g B * 1 1 NOTE: The above equation hold for 1 0. They are the olution of the ytem:, opt * 1 1, opt ( ) +, ( ) in * * 1 1 S, opt, + 1, 1 opt out opt S, opt *

7 Potentially Intable Device When k<1 a pair ( S, ) doe not exit for which G T i maximum. In cae of intability G T become in fact infinity. The admiible value of S, mut however atify the condition + < + < in S 1, out S Thee contraint, reported graphically on the Smith Chart, allow to identify the admiible value of di S e. A a guideline for the choice of G T the maximum table gain can be G conidered: T,max The elected value of G T hould be maller of thi value. 1 1

8 Admiible region for S The equation defining the boundary of thi region i: 1 1 S out + 1 S The equation define a circle with centre and radiu given by: 1 C S * * C r r 1 1 Plane S

9 Admiible region per The equation defining the boundary of thi region i: 1 1 in + 1 The equation define a circle with centre and radiu given by: 1 C * * C r r 1 1 Plane

10 Identification of admiible region The circle een in the previou lide define the boundary between the admiible and not admiible region. To identify which of the two i the table region the value of in ( out ) for ( S )0 mut be oberved. Taking into account that in ( out ) coincide in thi cae with ( ), it ha: The table region for ( S ) i outide the intability circle if: - ( ) <1 and the circle doe not encloe the centre of the chart - ( ) >1 and the circle encloe the centre of the chart The table region for ( S ) i inide the intability circle if : - ( ) >1 and the circle doe not encloe the centre of the chart - ( ) <1 and the circle encloe the centre of the chart

11 Amplifier deign with potentially intable device In thi cae there i not a unique olution. It i however poible: To choice in the table region and compute S for the maximum G T (alo the reulting S mut be inide the table region) To choice S in the table region and compute for the maximum G T (alo the reulting mut be inide the table region) To maximize G T the conjugate matching condition mut be impoed, i.e: ( ) in * * Cae 1 ( ) out * S 1 S * Cae

12 Circle with contant G p From the definition of Power Gain G p the following expreion i derived: G p (1 ) ( ) ( ) 1 * 1 + Re Note that G p doe not depend on S. Moreover it alway larger than or equal to G T ; it i equal when the input i matched: in ( ) *. Drawing the previou equation in the plane, we found a curve on thi plane where G p i contant; thi curve i a circle with the following center and radiu (g p G p / 1 ): C p * * ( ) ( ) ( ) 1 k gp + gp ( ) p gp, r 1+ g 1+ g p p 1

13 Deign with aigned G p Select an active device with the requeted G T (maximum table gain) Draw the circle G p G T on the Smith Chart repreenting Select a point on thi circle in the table region; thi i the elected,opt Compute S,opt by impoing the matching at the input. Verify that alo S,opt i in the table region of S., opt + 1 1, opt 1, opt Note: Once S,opt i aigned to the ource, the input i matched and, a a conequence, the tranducer power gain coincide numerically with the impoed power gain * S,opt Intability region of the ource Circle G p cot,opt Intability region of the load

14 Circle with contant G a From the definition of Available Power Gain G a the following expreion i derived : G a (1 ) ( ) S ( ) 1 * 1 +S Re S Note that G a doe not depend on. Moreover it alway larger than or equal to G T ; it i equal when the output i matched: out ( ) *. Drawing the previou equation in the plane S, we found a curve on thi plane where G a i contant; thi curve i a circle with the following center and radiu (g a G a / 1 ): C a a * * ( ) g, r ( ) ( ) 1 k ga + ga ( ) a a 1+ g 1+ g a 1

15 Deign with aigned Gp Select an active device with the requeted G T (maximum table gain) Draw the circle G a G T on the Smith Chart repreenting S Select a point on thi circle in the table region; thi i the elected S,opt Compute,opt by impoing the matching at output. Verify that alo,opt i in the table region of., opt S, opt 1 S, opt Note: Once,opt i aigned to the load, the output i matched and, a a conequence, the tranducer power gain coincide numerically with the impoed available power gain *,opt Intability region of the load Cerchio a G a cot S,opt Intability region of the ource

16 Deign reult Once the value of,opt and S,opt have been obtained with once of the method preented, we have: Cae 1 (Aigned Gp) Traduced Gain impoed Input Matched (NOT the output) Cae (Aigned Ga) Traduced Gain impoed Output Matched (NOT the input) NOTE: If lole network are ued for realized,opt and S,opt, alo the input or the output of the amplifier i matched

17 Example: Deign of a 1 GHz Amplifier Active device NEC70000 (GaA Mefet ) Max Gain at 1 GHz: 13.4 db Amplifier requirement Frequency band: GHz Tranducer gain in band: 1.5 ± 0.5 db Output Matching: < -15 db Topology: Subtrate ε r 9.8 H 0.6 mm t 50 µm Rho (reitivity normalized to Gold) 1 50 Ω In Out 50 Ω V in out

18 Biaing network of the active device V GS Bia V DS Bia RF Short Circuit RF Open Circuit NOTE: The S parameter delivered by the manufacturer refer to the red ection. After the biaing network ha been aigned, the S parameter change to the one referred to the black ection Input reference ection Block Capacitor (DC) Output reference ection

19 Scattering parameter of the biaed tranitor S parameter at 1 GHz S (Mag, Phae deg) 0.704, S1 (Mag, Phae deg) 0.099, -5.7 S1 (Mag, Phae deg).067, S (Mag, Phae deg) 0.467, Stability Coefficient: Potentially Intable K 1 S S + SS S1S1 < S S Maximum Stable Gain (db): S S 1 10 log

20 Evaluation of and S Aigned Ga : 1.5 db Choice of S Evaluation of ( out ) * Matching network (ingle tub topology) X

21 Input Network TIN E1.9 Deg F01.e4 MHz PORT RES R50 Ohm TSC E35.54 Deg F01.e4 MHz S ine : Φ β 1.91 Stub admittance: j B -j.475 -j cotan(β S ) Stub length (.c.) : Φ S tan

22 Output Network TIN E131.6 Deg F01.e4 MHz PORT RES R50 Ohm TSC E4.51 Deg F01.e4 MHz ine : Φ β Stub admittance: j B -j.193 -j cotan(β S ) Stub length (.c.) : 1 1 Φ S tan

23 Simulated repone 14 Ampli Initial Repone S S S DB( S(1,1) ) (R) Ampli Ottimizzato DB( S(,1) ) () Ampli Ottimizzato DB( S(,) ) (R) Ampli Ottimizzato Frequency (MHz) PORT P1 Z50 Ohm TIN IDT1 Z050 Ohm EFI1 Deg F0f0 MHz SUBCKT IDS1 NET"nec7000pola" 1 TIN IDT Z050 Ohm EFI3 Deg F0f0 MHz PORT P Z50 Ohm TSC IDT3 Z050 Ohm EFI Deg F0f0 MHz TSC IDT4 Z050 Ohm EFI4 Deg F0f0 MHz

24 Optimized Repone Ampli Optimized Repone S S S DB( S(1,1) ) (R) Ampli Ottimizzato DB( S(,1) ) () Ampli Ottimizzato DB( S(,) ) (R) Ampli Ottimizzato Frequency (MHz)