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
Outline Motivation Fundamentals Noise Modeling Noise Measurements Parameter Extraction Application Low Noise Amplifier
Local network Access point Motivation Mobile phone Headset Mouse Printer Laptop Noise limits transmission distance!
PSD/KHz -8 Noise Fundamentals Antenna Noise Power Spectral Density db - max. Noise - Receiver Noise Cosmic Noise -4.. m λ
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
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
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
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
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
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
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 ) ( ) (
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
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
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
Amplifier Noise Power Spectral Density S i (f) -6 A /Hz -7-8 -9 - - - I II f a I f µ f obs K K K M M f c Hz III M G f o f
Noisy Two-Port Noise Factor F S S i /N /N i Noise Figure NF log (F)
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 +
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 + + +
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
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
Noise Hyperbolic of the used MOSFET 6 5 w 43.75 µm l.35 µm 4 F 3 8 U ds, U gs, @ GHz I d 9,7 ma F min.8 db
Minimum Noise Figure ersus Operating oltage 6 db F min 8 6 4 U DS 3 5,8,4,6 4, U GS
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
Intrinsic Transistor Noise Model i > < i d > < g < i g > Admittance Noiseless < i d > 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 * *
Device Parasitics Γ s, e Γ s, i Noise of Lossy Substrate
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
High Frequency Modeling of MOSFET Intrinsic Transistor Source and bulk connected!
.6.5.4.3. High Frequency Model and Measurement.4.. -. real(ymodel(,)) real(ymeas(,)) real(ymodel(,)) real(ymeas(,)).. -..6.48.36 5 5 5 3 35 4 -.4 5 5 5 3 35 4 freq, GHz freq, GHz..8.6.4. real(ymodel(,)) real(ymeas(,)) real(ymodel(,)) real(ymeas(,)).4.. 5 5 5 3 35 4. 5 5 5 3 35 4 freq, GHz freq, GHz
High Frequency Noise Model of MOSFETs Contact Pad Contact Pad All resistors generate thermal noise with the spectral density < i R > 4kT R
Induced Gate Noise Gate noise only induced by capacitive coupering < i > 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
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
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
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
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 +
Measured Noise Parameters ( ds, gs, W394 µm)
Noise Figure of the MOSFET at a Source Impedance of 5 Ω db 8 F 5 6 4 measurement simulation with parasitics simulation without parasitics 3 4 5 6 7 8 GHz f
Noise Parameters ( DS, GS )
Minimum Noise Figure of the MOSFET F min, G ass db 6 4 8 6 4 F min - measurement G ass - measurement F min - simulation 3 4 5 6 7 8 GHz f
Sensitivity Analysis of all Noise Sources at 5 Ω F 5 9 db 8 7 6 5 4 channel current noise MOSFET w 43.75 µm lg.35 µm 3 R g thermal noise sources Rs R gs g ds 4 6 8 GHz frequency U ds and U gs R d
Noise Circles Noise Matching NFmin@4GHz GA@4GHz L g improves the stability Gain Circles Z in gm jω L + + L + jω L jωc C s s g gs gs
Low Noise Amplifier
Layout 48 µm 69 µm 8 µm LNA 4GHz LNA 5GHz
Measurements of Low Noise Amplifier
Measurements of Low Noise Amplifier
Summary Analytical modeling of the noise spectral density High frequency noise model Noise parameter extraction Application of the model Low noise amplifier
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. 35-38 [3] U. Basaran, Modellierung von Transistoren in CMOS/BiCMOS-Technologie zum Entwurf von rauscharmen erstärkern, Dissertation Universität Stuttgart, 7
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