RF Circuit Linearity Optimization Using a General ... - Semantic Scholar
> TCAS-I 11209
TCAS-I 11209
TCAS-I 112009 < is thhe AC elaaborate and iss given in apppendix I. Notee that traansfer functionn from the currrent in port (kk,s) of transistoor p to the output voltaage and can bbe easily obtaiined by small signal annalysis. IIn summary, since no topoology informaation is involvved in deeriving (3), thee analysis resuult can be reuused in any toppology byy deriving the topology-depeendent AC traansfer functionns. The prresented modeel transforms the circuit diistortion calcuulation that usually is ddone by Volteerra-series intto rather simpple AC traansfer functioon calculationns using a toopology-indepeendent traansformation. When this model is uused for autoomatic syymbolic analyssis of time-invvariant weaklyy nonlinear ciircuits, onnly AC symboolic analysis is required. C. Simplifyinng the transistoor nonlinearity ty model The nonlineaarity model prrovides the possibility to ffurther mplify the MO OS transistor nnonlinearity model given by (1). In sim (3) the resistive and capacitivee coefficients ( and ) are coombined intoo . Then a cutoff freequency / 2 can bee used to esstimate whhether the resiistive nonlineaarity or the caapacitive countterpart is dominant foor certain opeerating frequeencies in a sppecific tecchnology for specific biasinng conditions and transistorr sizes. Hoowever, for ttransistors wiith fixed lenggth (e.g. minnimum lenngth) and widdth that is not close to miniimum width, is fairly independeent of transistoor size (This iss usually true ffor RF This effectivelyy leaves only bbias dependent appplications). T factors in a certaain technologyy. When iss very high, can be rreduced to a purely much having resistive compoonent. Similaarly, for lower than any ssignal frequency, the ccan be seen as purely caapacitive. As a result, evaluaating provvides an approoach to sim mplify the MO OS transistor nonlinearity model m for all of the weeakly nonlineaar RF circuits in the same trransistor technnology. Thhis is differentt from previouus work, as [3, 16] do not taake the caapacitive nonllinearities intto account, w while [17] taakes a traansistor as a black b box and does not distiinguish betweeen the resistive and caapacitive nonliinearities. Mooreover, [3] rem moves m-level insignificant resistive nonlinnearities basedd on a system which makes it topology-deependent, whiile our cirrcuit model, w is mainly ddependent onn bias conditioons and technnology paarameters, annd therefore largely toopology-indepeendent (ap appendix II sshows an exxample for for an NMOS N traansistor). Hennce, the nonlinnearity parameeters only needd to be esstimated oncee for a certaiin technologyy, and can thhen be (ree)used in calcculations or ssimulations using e.g. a loook-up tabble. S process is ussed for In this paper, a commerciall 90nm CMOS deemonstration purposes. p All simulations are a done in S Spectre cirrcuit simulator, using the PS SP compact M MOSFET modeel [18] fittted to our 90nnm CMOS proocess. The PSP P model is knoown to coorrectly fit derivatives up tto the third order [12,13] aand to saatisfy the so-ccalled Gummeel symmetry test (GST) [114,15]. Fiitting derivativves up to the tthird order is essential to reeliably esstimate distortiion levels for all a presented ccircuits in this paper. Paassing the G GST is essenttial for accuurate simulatiion of distortion in thee attenuator cirrcuit in sectionn V. Equation (33) shows thatt the relative importance of the
3 nonnlinearity betw ween different terminals in one transistorr can be determined by evaluuating ∙ / , aand ∙ ∙ / , , ce a are linear tran nsfer ∙ . Sinc , funcctions that ddepend on the actual circcuit topology,, the evalluation of the relative impacct of the nonliinearities betw ween portts can only be used to simplify thee MOS transsistor nonnlinearity moddel for indivvidual circuitss, similar to the situation in [3]. DE AMPLIFIER R LINEARITY OPTIMIZATION III. CASCOD
T The cascode aamplifier topollogy shown inn Fig. 2 is wiidely usedd because of itts superior prooperties over thhe common-soource ampplifier [19-23]]. Typically thhe distortion contribution from casccode transistorr M2 is negleccted [24-28], which is validd for suffficiently largee output impeedance levels of M1. Howeever, CM MOS technoloogy scaling yields relativvely low ouutput resistance for shoort transistors [29]. [ The distoortion contribuution of M2 then can noo longer be neglected.
Fig. 2. Circuit scchematic of the caascode amplifier.
Inn [30-31] only o the efffect of the transconducttance nonnlinearity in M2 is analyzed, while the other o nonnlinearities relaated to the outtput conductannce of M2 (e.gg. the thirdd order outputt conductance nonlinearity , and the cross c term ms and ) are negleccted. In this seection we takee into accoount all nonlinnearities up to the third ordeer and demonsstrate thatt for low supplly voltage andd large gain, , and mayy be dominantt in the total ddistortion. Note that we focuus on the distortion duee to the cascodde transistor, thherefore we iggnore S amplifier andd do not focuus on the input matchinng for the CS goood noise figuree (NF). For sim mulation purppose we put a 50 resistor at the gatee of M1 for inpput matching. A Analysis resultts for output IIM3 and a desscription are given g beloow. The analyysis describedd in the previoous section shhows thatt capacitive noonlinearities arre not significaant for this typpe of circcuits in the loow GHz rangge and can bbe neglected. The firstt-order approxximation (see appendix III ffor the derivaation) of thhe output IM33 of the cascodde amplifier iss 3 4
(5) ,
,
,
,
> TCAS-I 112009
TCAS-I 11209
TCAS-I 11209
TCAS-I 112009
TCAS-I 11209
TCAS-I 112009 < is thhe AC elaaborate and iss given in apppendix I. Notee that traansfer functionn from the currrent in port (kk,s) of transistoor p to the output voltaage and can bbe easily obtaiined by small signal annalysis. IIn summary, since no topoology informaation is involvved in deeriving (3), thee analysis resuult can be reuused in any toppology byy deriving the topology-depeendent AC traansfer functionns. The prresented modeel transforms the circuit diistortion calcuulation that usually is ddone by Volteerra-series intto rather simpple AC traansfer functioon calculationns using a toopology-indepeendent traansformation. When this model is uused for autoomatic syymbolic analyssis of time-invvariant weaklyy nonlinear ciircuits, onnly AC symboolic analysis is required. C. Simplifyinng the transistoor nonlinearity ty model The nonlineaarity model prrovides the possibility to ffurther mplify the MO OS transistor nnonlinearity model given by (1). In sim (3) the resistive and capacitivee coefficients ( and ) are coombined intoo . Then a cutoff freequency / 2 can bee used to esstimate whhether the resiistive nonlineaarity or the caapacitive countterpart is dominant foor certain opeerating frequeencies in a sppecific tecchnology for specific biasinng conditions and transistorr sizes. Hoowever, for ttransistors wiith fixed lenggth (e.g. minnimum lenngth) and widdth that is not close to miniimum width, is fairly independeent of transistoor size (This iss usually true ffor RF This effectivelyy leaves only bbias dependent appplications). T factors in a certaain technologyy. When iss very high, can be rreduced to a purely much having resistive compoonent. Similaarly, for lower than any ssignal frequency, the ccan be seen as purely caapacitive. As a result, evaluaating provvides an approoach to sim mplify the MO OS transistor nonlinearity model m for all of the weeakly nonlineaar RF circuits in the same trransistor technnology. Thhis is differentt from previouus work, as [3, 16] do not taake the caapacitive nonllinearities intto account, w while [17] taakes a traansistor as a black b box and does not distiinguish betweeen the resistive and caapacitive nonliinearities. Mooreover, [3] rem moves m-level insignificant resistive nonlinnearities basedd on a system which makes it topology-deependent, whiile our cirrcuit model, w is mainly ddependent onn bias conditioons and technnology paarameters, annd therefore largely toopology-indepeendent (ap appendix II sshows an exxample for for an NMOS N traansistor). Hennce, the nonlinnearity parameeters only needd to be esstimated oncee for a certaiin technologyy, and can thhen be (ree)used in calcculations or ssimulations using e.g. a loook-up tabble. S process is ussed for In this paper, a commerciall 90nm CMOS deemonstration purposes. p All simulations are a done in S Spectre cirrcuit simulator, using the PS SP compact M MOSFET modeel [18] fittted to our 90nnm CMOS proocess. The PSP P model is knoown to coorrectly fit derivatives up tto the third order [12,13] aand to saatisfy the so-ccalled Gummeel symmetry test (GST) [114,15]. Fiitting derivativves up to the tthird order is essential to reeliably esstimate distortiion levels for all a presented ccircuits in this paper. Paassing the G GST is essenttial for accuurate simulatiion of distortion in thee attenuator cirrcuit in sectionn V. Equation (33) shows thatt the relative importance of the
3 nonnlinearity betw ween different terminals in one transistorr can be determined by evaluuating ∙ / , aand ∙ ∙ / , , ce a are linear tran nsfer ∙ . Sinc , funcctions that ddepend on the actual circcuit topology,, the evalluation of the relative impacct of the nonliinearities betw ween portts can only be used to simplify thee MOS transsistor nonnlinearity moddel for indivvidual circuitss, similar to the situation in [3]. DE AMPLIFIER R LINEARITY OPTIMIZATION III. CASCOD
T The cascode aamplifier topollogy shown inn Fig. 2 is wiidely usedd because of itts superior prooperties over thhe common-soource ampplifier [19-23]]. Typically thhe distortion contribution from casccode transistorr M2 is negleccted [24-28], which is validd for suffficiently largee output impeedance levels of M1. Howeever, CM MOS technoloogy scaling yields relativvely low ouutput resistance for shoort transistors [29]. [ The distoortion contribuution of M2 then can noo longer be neglected.
Fig. 2. Circuit scchematic of the caascode amplifier.
Inn [30-31] only o the efffect of the transconducttance nonnlinearity in M2 is analyzed, while the other o nonnlinearities relaated to the outtput conductannce of M2 (e.gg. the thirdd order outputt conductance nonlinearity , and the cross c term ms and ) are negleccted. In this seection we takee into accoount all nonlinnearities up to the third ordeer and demonsstrate thatt for low supplly voltage andd large gain, , and mayy be dominantt in the total ddistortion. Note that we focuus on the distortion duee to the cascodde transistor, thherefore we iggnore S amplifier andd do not focuus on the input matchinng for the CS goood noise figuree (NF). For sim mulation purppose we put a 50 resistor at the gatee of M1 for inpput matching. A Analysis resultts for output IIM3 and a desscription are given g beloow. The analyysis describedd in the previoous section shhows thatt capacitive noonlinearities arre not significaant for this typpe of circcuits in the loow GHz rangge and can bbe neglected. The firstt-order approxximation (see appendix III ffor the derivaation) of thhe output IM33 of the cascodde amplifier iss 3 4
(5) ,
,
,
,
> TCAS-I 112009
TCAS-I 11209
TCAS-I 11209
TCAS-I 112009
