PowerPoint PresentationWhat Does Stability Mean?Criteria for Unconditional StabilityUnconditional Stability: Rollett FactorStabilization MethodsStabilization Using Series Resistance or Shunt ConductanceStabilization Method: Smith ChartConstant Gain: Unilateral Design (S12= 0)Unilateral Power Gain EquationsUnilateral Gain CirclesSlide 11Gain Circle ObservationsInput Matching Network Gain CirclesBilateral Amplifier Design (S12 included)Bilateral Conjugate MatchOptimum Bilateral MatchingDesign Procedure for RF BJT AmpsSlide 18Slide 19Slide 20RF Shunt-Shunt Feedback Amp DesignDistortion: 1 dB CompressionDistortion: 3rd Order Intermodulation DistortionDistortion: 3rd Order IMDELEC 412 - Lecture 20 1ELEC 412 RF & Microwave EngineeringFall 2004Lecture 20ELEC 412 - Lecture 20 2What Does Stability Mean?•Stability circles determine what load or source impedances should be avoided for stable or non-oscillatory amplifier behavior •Because reactive loads are being added to amp the conditions for oscillation must be determined•So the Output Stability Circle determine the L or load impedance (looking into matching network from output of amp) that may cause oscillation•Input Stability Circle determine the S or impedance (looking into matching network from input of amp) that may cause oscillationELEC 412 - Lecture 20 3Criteria for Unconditional Stability•Unconditional Stability when amplifier remains stable throughout the entire domain of the Smith Chart at the operating bias and frequency. Applies to input and output ports. •For |S11| < 1 and |S22| < 1, the stability circles reside completely outside the |S| = 1 and |L| = 1 circles.ELEC 412 - Lecture 20 4Unconditional Stability: Rollett Factor•|Cin| – rin | >1 and |Cout| – rout | >1 •Stability or Rollett factor k: 2 2 211 2212 21112S SkS S- - +D= >with |S11| < 1 or |S22| < 1and 11 22 12 211S S S SD = - <ELEC 412 - Lecture 20 5Stabilization Methods•Stabilization methods can be used to for operation of BJT or FET found to be unstable at operating bias and frequency•One method is to add series or shunt conductance to the input or output of the active device in the RF signal path to “move” the source or load impedances out of the unstable regions as defined by the Stability CirclesELEC 412 - Lecture 20 6Stabilization Using Series Resistance or Shunt ConductanceELEC 412 - Lecture 20 7Stabilization Method: Smith ChartELEC 412 - Lecture 20 8Constant Gain: Unilateral Design (S12= 0)•Need to obtain desired gain performance•Basically we can “detune” the amp matching networks for desired gain•Unilateral power gain GTU implies S12 = 0ELEC 412 - Lecture 20 9Unilateral Power Gain Equations•Unilateral Power gain 2 2221 02 211 221 11 1S LTU S LS LG S G G GS S- G - G= =- G - G•Individual blocks are: 2 220 212 211 221 11 1S LS LS LG ; G S ; GS S- G - G= = =- G - G•GTU (dB) = GS(dB) + G0(dB) +GL(dB)ELEC 412 - Lecture 20 10Unilateral Gain Circlesmax max2 211 221 11 1S LG ; GS S= =- -•If |S11| < 1 and |S22 |< 1 maximum unilateral power gain GTUmax when S = S11* and L = S22* •Normalized GS w.r.t. maximum: ( )22112max11111SSSSSGg SGS- G= = -- GELEC 412 - Lecture 20 11Unilateral Gain Circles•Results in circles with center and radii:( )22222max22111LLLLLGg SGS- G= = -- G•Normalized GL w.r.t. maximums:( )( )( )22 21 11 1 1 1i ii iii iig gii i ii ig Sg Sd ; rS g S g- -= =- - - -ii = 11 or 22 depending on i = S or LELEC 412 - Lecture 20 12Gain Circle Observations•Gi max when i = Sii* and dgi = Sii* of radius rgi = 0•Constant gain circles all have centers on line connecting the origin to Sii* •For the special case i = 0 the normalized gain is: gi = 1 - | Sii |2 and dgi = rgi = | Sii |/(1 + | Sii |2) •This implies that Gi = 1 (0dB) circle always passes through origin of i - planeELEC 412 - Lecture 20 13Input Matching Network Gain CirclesS is detuned implying the matching network is detunedELEC 412 - Lecture 20 14Bilateral Amplifier Design (S12 included)•Complete equations required taking into account S12: Thus S*  S11 and L*  S22 12 21 111122 221 1*L LSL LS S SSS SG - G DG = + =- G - G12 21 222211 111 1*S SLS SS S SSS SG - G DG = + =- G - GELEC 412 - Lecture 20 15Bilateral Conjugate Match•Matched source reflection coefficient21 1 11 1 1142 2*MSB B CC C C� �G = - -� �� �2 2 21 11 22 1 22 111*C S S ; B S S= - D = - - D +•Matched load reflection coefficient22 2 22 2 2142 2*MLB B CC C C� �G = - -� �� �2 2 22 22 11 2 11 221*C S S ; B S S= - D = - - D +ELEC 412 - Lecture 20 16Optimum Bilateral Matching12 2111221MS*MLMLS SSSGG = +- G12 2122111ML*MSMSS SSSGG = +- GELEC 412 - Lecture 20 17Design Procedure for RF BJT Amps•Bias the circuit as specified by data sheet with available S-Parameters•Determine S-Parameters at bias conditions and operating frequency•Calculate stability |k| > 1 and | | < 1?•If unconditionally stable, design for gain•If |k|  1 and || 1 then draw Stability Circles on Smith Chart by finding rout, Cout, rin, and Cin radii and distances for the circlesELEC 412 - Lecture 20 18Design Procedure for RF BJT Amps•Determine if L ( S22* for conjugate match) lies in unstable region – do same for S •If stable, no worries. •If unstable, add small shunt or series resistance to move effective S22* into stable region – use max outer edge real part of circle as resistance or conductance (do same for input side)•Can adjust gain by detuning L or SELEC 412 - Lecture 20 19Design Procedure for RF BJT Amps•To design for specified gain, must be less than GTU max (max unilateral gain small S12)•Recall that (know G0 = |S21|2)GTU [dB] = GS [dB] + G0 [dB] + GL [dB]•Detune either S or L •Draw gain circles for GS (or GL) for detuned S (or L) matching network•Overall gain is reduced when designed for (a) Stability and (b) detuned matching netw0rkELEC 412 - Lecture 20 20Design Procedure for RF BJT Amps•Further circles on the Smith Chart include noise circles and constant VSWR circles•Broadband amps often are feedback ampsELEC 412 - Lecture 20 21RF Shunt-Shunt Feedback Amp Design( )1 0 211R Z S= -02211mZRR g= -CmTIgV=S21 calculated from desired gain GELEC 412 - Lecture 20 22Distortion: 1 dB CompressionELEC 412 - Lecture 20 23Distortion: 3rd Order Intermodulation DistortionELEC 412 - Lecture 20 24Distortion: 3rd Order IMD[ ]( )[ ] [ ]2 2 13 dB dBm (2 ) dBmout outIMD