Harmonic Balance of Nonlinear RF Circuits

Transcription

1 MICROWAE AND RF DESIGN Harmonc Balance of Nonlnear RF Crcuts Presented by Mchael Steer Readng: Chapter 19, Secton 19. Index: HB Based on materal n Mcrowave and RF Desgn: A Systems Approach, nd Edton, by Mchael Steer. ScTech Publshng, 013. Presentaton copyrght Mchael Steer

2 Harmonc Balance of Nonlnear RF Crcuts 1 1 Lnear subcrcut v 1 v Nonlnear subcrcut Sldes copyrght 013 M. Steer. ADA 1

3 Steady-State Analyss Assume that sgnal can be modeled as the sum of dscrete tones. Solve for phasors of these tones n the crcut. Everywhere or Just at nonlnear elements. Note Cannot consder actual dgtally modulated sgnals.

4 Modelng Problem + v - R t Output t Output Resstor wth passve conventon t Input v t Input v v characterstc of a lnear resstor. v characterstc of a dode. 3

5 Propertes of RF Sgnals Modulated sgnals wth very narrow modulaton bandwdth E.G. 5 MHz WCDMA on a GHz carrer. The ampltude and phase of the carrer change very slowly n tme wth one symbol transton every 400 RF cycles. Based crcuts can take a long tme to reach steady-state Requre hgh dynamc range n smulaton Communcatons about 100 db Radar about 160 db. 4

6 What About Transent Smulaton? Take a very long tme to smulate meanngful dstorton metrcs. E.G. 5 MHz WCDMA on a GHz carrer. In transent smulaton must have tme steps about 1/0 th the perod of the hghest frequency component. Perod of a GHz sgnal s 500 ps. Need Dt < 5ps, usually however = 1 ps. Symbol nterval s 00 ns. So to look at meanngful sgnal dstorton statstcs requres mllons of tme ponts. Even worse when consderng dynamc range of at least 100 db requred. Based crcuts can take a long tme to reach steadystate. Smply not practcal to a tradtonal SPICE smulaton 5

7 Modelng of Nonlnear Mcrowave Crcuts Two Commercally Avalable Approaches: Harmonc Balance Smulaton Assume that the sgnals n a crcut are a sum of snusods Perodc Steady-State Smulaton (PSS) Spce based Assume that there s one large perodc sgnal Determne dynamc state of the crcut 6

8 Harmonc Balance (HB) Analyss Assume that the sgnals n a crcut are a sum of snusods 1 1 Lnear subcrcut v 1 v Nonlnear subcrcut The harmonc balance method parttons the crcut nto lnear and nonlnear subcrcuts. 7

9 Example: HB Analyss 1/7 Assume that the sgnals n a crcut are a sum of snusods e R s = 1 v Lnear subcrcut e Nonlnear subcrcut v t () vt () [ vt ()] vt () cos( t) cos( t) 0 1 I 0 0 I E I 1 1 I I I

10 Example: HB Analyss /7 Lnear subcrcut e Nonlnear subcrcut v I 0 0 I E I 1 1 I I I KCL error s F f0 f1 f f I I f I I f I I Newton teraton: f0 1 1 J 1 f1 f J s jacoban of I wth respect to. 9

11 Example: HB Analyss 3/7 Newton teraton: f0 1 1 J 1 f1 f J s Jacoban of KCL error wth respect to

12 Example: HB Analyss 4/7 Now each element of the Jacoban s affected by both the lnear and nonlnear subcrcuts, so, f I I I

13 Example: HB Analyss 5/7 Smlarly 1

14 Example: HB Analyss 6/7 Enough equatons to solve: f0 1 1 J 1 f1 f 13

15 Example: HB Analyss 7/7 Lnear subcrcut Nonlnear subcrcut e v 14

16 Users Gude to HB Analyss Three major factors lmt accuracy: The number of tones ncluded n the analyss. The alasng errors due to a fnte transform spectrum. Ths error can be reduced by consderng many tones. The alasng error s a numercally ntroduced error. Ths sets an upper lmt on resoluton. The fnal value of the harmonc balance error. The major lmtng factor here s how closely the Jacoban descrbes the actual error functon. Both the error functon and the Jacoban have truncaton error so deally the Jacoban evaluaton reflects the same truncaton errors as the error functon evaluaton. In the end ths comes down to the accuracy of the models. 15

17 Perodc Steady-State (PSS) Outlne: Analyss Use SPICE analyss for one perod of a large tone. Develop lnearzed dynamc crcut. Consder other tones as operatng on dynamc crcut. Detal: Smulator guesses the ntal values of voltages at all termnals, charges on capactors, and currents through all nductors. Then the crcut s smulated usng transent analyss for one perod of the exctng waveform. The state varables updated f requred. From soluton, a model akn to a converson matrx descrbng the dynamc crcut s establshed. An advantage of the PSS technque s that a conventonal Spce smulator, and the all mportant transstor models, can be used.

18 Summary Analyss s based on assumng a fnte number of tones. Not the same as a dgtally modulated sgnal. 1 1 Lnear subcrcut v 1 v Nonlnear subcrcut 17