Workshop WMB. Noise Modeling

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1 Workshop WMB Noise Modeling Manfred Berroth, Markus Grözing, Stefan Heck, Alexander Bräckle University of Stuttgart, Germany WMB (IMS) Parameter Extraction Strategies For Compact Transistor Models IMS 9

2 Outline Motivation Fundamentals Noise Modeling Noise Measurements Parameter Extraction Application Low Noise Amplifier

3 Local network Access point Motivation Mobile phone Headset Mouse Printer Laptop Noise limits transmission distance!

4 PSD/KHz -8 Noise Fundamentals Antenna Noise Power Spectral Density db - max. Noise - Receiver Noise Cosmic Noise -4.. m λ

5 Fundamentals Noise is caused by spontaneous fluctuations. Spontaneous fluctuations limit the accuracy of measurements. The signal-to-noise ratio limits the range of any communications system. Three types of noise are present in electronic circuits: - Thermal noise - Shot noise - Flicker noise

6 Probability dp that the value of a fluctuating quantity is between x and x + dx Fundamentals Probability distribution ( ) dx Probability distribution function f(x): dp f x Average value of the n-th moment xn x n dp True fluctuating quantity: Most important average value real mean square: Example: Normal distribution p ( ξ) x f ( x) e σ σ π σ p ( ξ ) x x ξ u u σ ξ u u σ

7 Fundamentals Definition of Correlation x, y mean-free fluctuating quantities Uncorrelated: xy xy x if y x Correlation coefficient c x xy y c c uncorrelated completely correlated < c < partly correlated

8 Fundamentals Fourier Analysis Noise signal x(t) w(f) spectral intensity of the noise X w( f) df Amplifier example: Y ( t) h ( t) x ( t) ( time domain) y * ( f) g ( f) X ( f) ( frequency domain) y g ( f) w( f) df

9 Thermal Noise Available noise power in the frequency interval df at a resistance R at temperature T. P 4 with u R S p i 4 i ( f,t) R e kt p 4 kt ( f) p( f, T) R hf kt hf kt ( f,t) df (Planck's correction factor) at room temperature (3 K) termal noise is flat up to ~6 THz

10 Thermal Noise White Noise Sources S ir Diffusion Noise S ig 4 k T R 4 k Te G (all resistive parts of the circuit) (channel noise) f << τ Shot Noise S ij q I (e.g. pn-junctions) T absolute temperature T e electron gas temperature

11 Channel Noise Inversion Charge Model t ds id N L R 4kT (f) S + Wang et.al [7] + 3 D ox eff id ) ( ) ( L I W C 4kTµ (f) S inv eff ds Q µ R + Wang et.al [7] + DSeff DSeff T GS C eff ox 3 DSeff DSeff T GS DSeff T GS ) ( L E µ 4kTWC 3 ) ( ) (

12 BSiM Channel Noise S 4kT dseff 4 ktθtnoi (gm + I R + g DSeff id (f) + βtnoi(gm + gmbs) I D R ds d ds mbs ) θ TNOI R nb + T nb L gs E C L β TNOI R na + T na L gs E C L

13 Flicker Noise i f K f I f A E f f df Example MOSFET : S id K I f C f f d ( f) with A E f E A ' X L f f

14 Unified Model (Hung) Flicker- Noise S id (f) ktq µ α γ fc eff ' ox I d L d kti + L γ fwl N Aln N L A+ BN + N + N L + CN ( N ) L N + + B L ( ) ( N N + N N ) L C L

15 Amplifier Noise Power Spectral Density S i (f) -6 A /Hz I II f a I f µ f obs K K K M M f c Hz III M G f o f

16 Noisy Two-Port Noise Factor F S S i /N /N i Noise Figure NF log (F)

17 Noisy Two-Port P T n e i i i T T B G T k N B S T k S N S N S N F + k B G P T n e ( ) e T T k B G N +

18 Noisy Two-Port Interaction of Different Noise Sources e e e e e e a W W W W W e e e e e e a W W W W W e e e e e e a u u u u u u u + + +

19 Noisy Two-Port I U A I Noiseless Two-Port Z S U U S U I A Z U I A A U U + + A A I I + + I U A A F S N i i N S + U A + Z S I A / ( 8 kt f Re { Z }) S F 4R Z Γ n S opt Fmin + Z + Γ opt ZS

20 ector Network Analyzer Noise Test Setup Device Driver HP EE MATLAB Port Port Test Set IEEE 488. PC Noise Figure Metre Noise Source NPT 8 Tuner Γ NS Γ S Γ D Γ rcvr DUT NPT 8 Tuner Parameter Analyzer

21 Noise Hyperbolic of the used MOSFET 6 5 w µm l.35 µm 4 F 3 8 U ds, U GHz I d 9,7 ma F min.8 db

22 Minimum Noise Figure ersus Operating oltage 6 db F min U DS 3 5,8,4,6 4, U GS

23 Correlation Matrices ABCD Noiseless Two-Port C Trans A kt NF R n NF min R Y min R nyopt Rn Yopt n * opt Trans Trans C Z TAZC A T + AZ T: Transformation Matrix T + : Hermitian Conjugate Complex int Trans C C C Z,transistor Z,transistor Z,Rs Trans Trans C Y TZYC A T + ZY

24 Intrinsic Transistor Noise Model i > < g Admittance Noiseless Two-Port * < ig id > Series resistances already subtracted by correlation matrices * * Cross correlation between gate : and channel noise C < igig > < igid > B idig idi < > < d > Y * *

25 Device Parasitics Γ s, e Γ s, i Noise of Lossy Substrate

26 MOSFET Substrate Modeling Polysilicon Gate Drain Bulk Source Bulk R s R g R d n + n+ C sb R ch C db R dsb C sub R sb R db C sub

27 High Frequency Modeling of MOSFET Intrinsic Transistor Source and bulk connected!

28 High Frequency Model and Measurement real(ymodel(,)) real(ymeas(,)) real(ymodel(,)) real(ymeas(,)) freq, GHz freq, GHz real(ymodel(,)) real(ymeas(,)) real(ymodel(,)) real(ymeas(,)) freq, GHz freq, GHz

29 High Frequency Noise Model of MOSFETs Contact Pad Contact Pad All resistors generate thermal noise with the spectral density 4kT R

30 Induced Gate Noise Gate noise only induced by capacitive coupering g 4 4kTggsB 3 < 6 i > ktr C 3 ω g gs gs an der Ziel, Noise in Solid-State Devices and Circuits, John Wiley & Sons, 986 Norton equivalent circuit

31 Deembedding with Correlation Matrices Y pad pad C kt Re( Y ) Y Z C Y y y -y y y -y Z z z z z -z -z Transformations Between Correlation Matrices C a -a a -a Equivalent Circuit of Pads Hillbrand und Russer, An efficient method for computer-aided analysis of linear amplifier networks, 976. C Trans A kt NF min R n R Y n opt NF min R R Y n Y opt n * opt ABCD Matrix

32 Parameter Extraction (MOSFET) After Deembedding of pad capacitances and inductances, the series resistances of gate and drain have to be deembedded: [ CZ,T ] [ TZ Y ] [ CA ] [ TA Z ] [ ] Rg C Z, T [ CZ,T ] kt Rd + + Hermitian Conjugation

33 Parameter Extraction (MOSFET) To deembed the substrate admittance, the correlation matrices have to be transformed to the admittance form: [ C ] [ T ] [ C ] [ T ] Y, T Z Y [ C ] [ C ] Y, T Y, T Z, T Z Y kt Re + Y sub

34 Parameter Extraction (MOSFET) To deembed the source resistance, the impedance form of the correlation matrix is required: [ C ] [ T ] [ C ] [ T ] Z, T Y Z Y, T [ ] [ ] int Rs C Z, T C Z, T kt Rs Y Z +

35 Measured Noise Parameters ( ds, gs, W394 µm)

36 Noise Figure of the MOSFET at a Source Impedance of 5 Ω db 8 F measurement simulation with parasitics simulation without parasitics GHz f

37 Noise Parameters ( DS, GS )

38 Minimum Noise Figure of the MOSFET F min, G ass db F min - measurement G ass - measurement F min - simulation GHz f

39 Sensitivity Analysis of all Noise Sources at 5 Ω F 5 9 db channel current noise MOSFET w µm lg.35 µm 3 R g thermal noise sources Rs R gs g ds GHz frequency U ds and U gs R d

40 Noise Circles Noise Matching L g improves the stability Gain Circles Z in gm jω L + + L + jω L jωc C s s g gs gs

41 Low Noise Amplifier

42 Layout 48 µm 69 µm 8 µm LNA 4GHz LNA 5GHz

43 Measurements of Low Noise Amplifier

44 Measurements of Low Noise Amplifier

45 Summary Analytical modeling of the noise spectral density High frequency noise model Noise parameter extraction Application of the model Low noise amplifier

46 References: [] A. van der Ziel, Noise, Prentice Hall, 954 [] H. Hillbrand, P. H. Russer, An Efficient Method for Computer Aided Noise Analysis of Linear Amplifier Networks, IEEE Trans. Circuits and Systems, ol. AS-3, no. 4, 976, pp [3] U. Basaran, Modellierung von Transistoren in CMOS/BiCMOS-Technologie zum Entwurf von rauscharmen erstärkern, Dissertation Universität Stuttgart, 7

47 Questions?

Transistor Noise Lecture 10 High Speed Devices

Transistor Noise Lecture 10 High Speed Devices Transistor Noise 1 Transistor Noise A very brief introduction to circuit and transistor noise. I an not an expert regarding noise Maas: Noise in Linear and Nonlinear Circuits Lee: The Design of CMOS RFIC