A Simplified Method for Phase Noise Calculation

Transcription

1 Poster: T-18 Simplified Method for Phase Noise Calculatio Massoud Tohidia, li Fotowat hmady* ad Mahmoud Kamarei Uiversity of Tehra, *Sharif Uiversity of Techology, Tehra, Ira

2 Outlie Itroductio Prelimiary ssumptios Noise pproximatio Noise Frequecy Traslatio PM ad M Noise Separatio Output Phase Noise Spectra Phase Noise Calculatio Method The Proposed Method Compariso with Hajimiri s ISF Method Experimetal Results Coclusio

3 Leeso s Equatio [1] Itroductio heuristic ad historical model for phase oise of LC oscillators Hajimiri s ISF Method [] Geeral ccurate Impulse Sesitivity Fuctio (ISF) L Trasiet-time simulatio ktr 4 m F V Qm 3

4 Noise pproximatio oise sigal is approximated by a series of several siusoidal sigals [3]. Noise Source Spectra Δ... Noise pproximatio Radom Phase Equal Power... 4

5 Noise Frequecy Traslatio t α t α t α Y ) cos( 3 ) cos( cos X α X α X α Y ) cos( ) cos( t t X Cosider a geeral oliear system Iput: carrier + oise Output: traslated oise (eglectig the carrier ad small terms) 5

6 Noise Source Spectra Output Spectra Promiet Frequecies Oly promiet frequecies traslate to aroud the carrier i- i+ 6

7 PM ad M Noise Separatio sigle toe oise at a promiet frequecy geerates two oise toes aroud the carrier. These two carriers geerally modulate both Phase (PM) ad mplitude (M) of the carrier. + s V V - s PM - s + s M Output Spectra Phasor Represetatio 7

8 PM ad M Noise Separatio The output oise ca be separated ito PM ad M oise. PM M 1 1 cos cos M V + s - s PM V - s + s Pure PM Noise Pure M Noise 8

9 Output Phase Noise Spectra Leeso s equatio: Phase oise skirt aroud the carrier sigal falls with db/dec for a white oise source [1]. Geeral phase oise equatio: total oise traslatio gai oise curret L m P 1 log 1 log V oise Psig m Z i s carrier amplitude phase oise offset frequecy frequecy at which Z is simulated 9

10 Noise Source Spectra Output Spectra Noise Traslatio Gai The traslatio gais are calculable usig simulatio Z i VPM, i / ii, i, i i i V PM, i / i i, i, i i s s - s + s i- i i- i+ 1

11 Noise Sources Statioary Noise Sources Resistors, costat curret source, etc. Noise source is modeled with a sigle toe (ST) source. i Cyclostatioary Noise Sources Modulated sources, switchig trasistors, etc. Noise source is modeled with a sigle toe source with amplitude modulatio i d i out =f(i d,i ) i 11

12 Proposed ST Simulatio Method Calculate the oise traslatio gai pplyig the ST oise source at promiet frequecies, simulatig the circuit ad measurig the output spectrum aroud the carrier. PM compoet: Partial traslatio gai: Total oise traslatio gai of the oise source: The total output phase oise cotributio of the oise source Z PM cos 1 1log s m m V i Z L i i PM i i i V,, / 1

13 Compariso with ISF Method Liear Time-Variat Model [] i(t) i(t) h ( t, ) (t) (t) max. charge of the ode ISF t h It ca be show that the oise traslatio gais are covertible to ISF ad vice versa. i t, q V c q V c q u t c cosi c max i max i1 max i i L t i m 1log qmax m ISF Fourier series coefficiets i c 13

14 ST vs. ISF ST Method Directly calculates oise cotributio i frequecy domai. The domiat oise sources ad oise frequecies are foud. Separately calculates the Phase ad mplitude Noise. Simulatio Speed ccurate ISF requires several trasiet time simulatios (time cosumig). ST method has improved the simulatio speed usig Harmoic- Balaced simulatio (HB) for just some few promiet frequecies. Flicker oise upcoversio ca be predicted by just oe simulatio (cosiderig ). 14

15 Experimetal Results Case Study: QVCO desiged for GPS applicatio [4]. V DD V DD L 1 L L 3 L 4 R 1 C 1 C R R 3 C 3 C 4 R 4 I p I Q p Q Q p Q I I p I bias M sw1 M sw M sw3 M sw4 Mcp1 M cp M cp3 M cp4 M bias M tail C bp 15

16 Experimetal Results Measured output phase oise spectra Die micrograph fabricated i TSMC 1P6M+.18-µm CMOS 16

17 Phase Noise Frequecy Cotributio Simulated phase oise frequecy 1MH The two methods almost predict the same results Time-domai ISF for M tail DC + Fourth Harmoic Normalied ISF pi/ pi 1.5*pi *pi Output Phase (rad) Output Phase Noise (dbc/h) Output Phase Noise (dbc/h) Noise Source Frequecy (carrier hamoic idex) Noise Source Frequecy (carrier hamoic idex) Msw1 Mcp1 Mtail Mbias R1 Msw1 Mcp1 Mtail Mbias R1 17 ST method ISF method

18 Compariso Noise cotributios are i good agreemet for all simulatios methods ad measuremet. Noise Source Noise Type Method Sigle Toe ISF SpectreRF Thermal M sw1-4 Flicker Thermal M cp1-4 Flicker Thermal M tail Flicker Thermal M bias Flicker R Other Sources eglected eglected -18. Total Measuremet Result Phase 1MH offset 18

19 Coclusio faster method usig oliear frequecy domai simulatio ST directly shows the oise frequecy traslatio Facilitates more ituitive desig of high purity oscillators by cosiderig substatial oise frequecies Separate predictio of Phase ad mplitude Noise Simulatio results show good agreemet with other methods ad measuremets 19

20 Refereces [1] D. B. Leeso, simple model of feedback oscillator oise spectrum, Proc. IEEE, pp , Feb []. Hajimiri ad T. H. Lee, geeral theory of phase oise i electrical oscillators, IEEE J. Solid-State Circuits, vol. 33, pp , [3] W.P. Robis, Phase Noise i Sigal Sources, Peter Peregrius Ltd., Lodo, 198, pp [4] F. Behbahai, et al., " fully itegrated low-if CMOS GPS radio with o-chip aalog image rejectio," IEEE J. Solid-State Circuits, vol.37, o.1, pp , Dec.