Correlated Noise Modeling - An Implementation into HICUM

Transcription

1 Correlated ose Modelng - An Implementaton nto HICUM A. Chakravorty, M. chroter, P. akalas, J. Herrcht Char for Electron Devces and Integrated Crcuts (CEDIC) Unversty of Technology Dresden Germany Dept. of Electrcal and Computer Engn. Unversty of Calforna at an Dego UA [email protected], [email protected] Atmel, Helbronn (Germany) June 006 AC, M, P, JH 1

2 Outlne Correlated ose n HTs PD matrx : problems wth PICE ystem theoretcal soluton Implementaton challenges Implementaton nto HICUM Results AC, M, P, JH

3 Correlated ose n HTs Presently n HICUM: thermal nose, shot nose, flcker nose ase and collector shot nose sources are actually correlated I 1 I 1 [Y ] I I C bc V r V 1 be C be V be g m.v be nb ose free two-port Correlated nc AC, M, P, JH 3

4 PD matrx: problems wth PICE Output nose power spectral densty YY + ( jϖ ). ( jϖ ) G ( jϖ ) ( jϖ ) = G. xx (jw): nput nose power spectral densty G(jw): transfer functon matrx, G + (jw): complex conjugate of G(jw) XX ( jϖ) = XX nb nc nb nb nc nc Cross-correlated terms Off-dagonal elements not handled by PICE smulators crucal from operatng frequences around and above f Tpeak /10 AC, M, P, JH 4

5 Manpulate nput nose PD matrx XX ystem theoretcal soluton + ( jϖ ). ( jϖ ) T ( jϖ ) ( jϖ ) = T. YY X Cross-correlated terms nsde the transfer functon From matrx element comparson X ( jϖ) = nb T ( jϖ ) = 0 nc t ( jϖ ). T( jϖ ). ( jϖ ) T ( jϖ ) G ( jϖ ) ( jϖ ) = G. X = nb nb ' = t 1 nc nc nb and t 1 = nc nb nb = qi C ( jϖτ qi / 3) = τ jϖ 3 I I C AC, M, P, JH 5

6 ystem theoretcal soluton (cont d) Orgnal nose PD matrx: two correlated nose sources After manpulaton: three uncorrelated nose sources wth dfferent PDs AC, M, P, JH 6

7 Problem at frst look frequency dependent PD at output Implementaton challenges nc = nc ϖτ βdc 3 1 new τ = ϖ 3 β dc nb soluton tme dervatve of nose source: operator "ddt( )" produces "jw" n frequency doman Further problem negatve sgn nsde PD mpossble by smple addton/subtracton of nose sources addton/subtracton of nose PD not possble multplcaton of nose sources not permtted n PICE AC, M, P, JH 7

8 Implementaton nto HICUM One source at nput sde: same as before Two sources at output sde one requres dervatve w.r.t. tme of the nput nose source for the remanng one, followng PD proposed nc = nc βdc ϖτ 1 3 = nc ϖτ 1 βdc 3 β + dc ϖτ 3 Last term reflects the error for ths PD, accurate upto f Tpeak /3 combnng all PDs, accurate upto f Tpeak very small n all practcal purposes AC, M, P, JH 8

9 Implementaton nto HICUM (cont d) I Tme dervatve: capactve Total transt tme used Incorporated nto HICUM smulated wth AD 004A Tested aganst 150GHz HT ource 1: ( b, e) gv. ( b_ n1 ) I = 1 V g ( b _ n1) = qi ource 3: ( c, e) = β kτ ( gv. ( b_ n1) ) f f d dt ource : I β, 1 f n f ( c e) gv. ( b_ n) + ( kτ ) gv. ( b_ ) = ( ) V ( b _ n) = qi C d dt 1 g, g : 1 emens AC, M, P, JH 9

10 Results T=300K,A E =( )μm,V CE =1.5V measurement: symbols, smulaton: lnes AC, M, P, JH 10

11 Results (cont d) T=300K,A E =( )μm measurement: symbols, smulaton: lnes AC, M, P, JH 11

12 Results (cont d) T=300K,A E =( )μm,V CE =1.5V,J C =.74mA/μm measurement: symbols, smulaton: lnes AC, M, P, JH 1

13 Conclusons Relevance of modelng nose correlaton n modern HTs dscussed PEICE-specfc mplementaton problems ponted out A system theoretcal soluton proposed Correspondng Verlog-A mplementaton challenges dscussed Implemented n HICUM and verfed wth measured data from advanced HT (ftpeak=150 GHz) process AC, M, P, JH 13

14 Acknowledgements Jazz emconductors Inc. C. McAndrew (Freescale emconductors) G. Coram (Analog Devces) M. Merznxk (Tburon Inc.) F. Korndoerfer (IHP) Fnancal support from German Research ocety (DFG) AC, M, P, JH 14