EE 247B/ME 218: Introduction to MEMS Design Lecture 26m1: Noise & MDS CTN 4/25/17. Copyright 2017 Regents of the University of California

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1 EE 47B/ME 18: Introduction to MEMS Design Lecture 6m1: & MDS CTN 4/5/17 Thermal Sources Thermal in Electronics: (Johnson noise, Nyquist noise) Produced as a result of the thermally excited random motion of free e s in a conducting medium Path of e s randomly oriented due to collisions Thermal in Mechanics: (Brownian motion noise) Thermal noise is associated with all dissipatie processes that couple to the thermal domain Any damping generates thermal noise, including gas damping, internal losses, etc. Properties: Thermal noise is white (i.e., constant w/ fruency) Proportional to temperature Not associated with current Present in any real physical resistor EEC47B/MEC18: Introduction to MEMS Design 1 EEC47B/MEC18: Introduction to MEMS Design 13 epresentation of Thermal Thermal can be shown to be represented by a series oltage generator or a shunt current generator actual Note: These are onesided meansquare spectral densities! To make them sided, must diide by. i i kt 4 f noiseless EEC47B/MEC18: Introduction to MEMS Design 14 or 4 kt f 0 where 4kT 1.66x10 V C and where these are spectral densities. i noiseless in Capacitors and Inductors? esistors generate thermal noise Capacitors and inductors are noiseless why? + Now, add a resistor: L L C C + Can oscillate foreer t Decays to zero EEC47B/MEC18: Introduction to MEMS Design 15 t But this iolates the laws of thermodynamics, which ruire that things be in constant motion at finite temperature Need to add a forcing function, like a noise oltage to keep the motion going and this noise source is associated with Copyright 017 egents of the Uniersity of California 1

2 EE 47B/ME 18: Introduction to MEMS Design Lecture 6m1: & MDS CTN 4/5/17 MEMSBased Tuning Fork Gyroscope z Tuning Tuning Drie Electrode () Current Back to Determining esolution Drie Voltage Drie Drie Oscillation Sustaining (+) Current Differential Trans [Zaman, Ayazi, et al, MEMS 06] 3 EEC47B/MEC18: Introduction to MEMS Design Drie Axis Equialent 180o 1: e io lx cx rx 4 Drie/ esponse Spectra: x d ii Co 180o x d d xd Drie Voltage Drie Mode Drie Oscillation Sustaining Drie esponse esponse fo (@ T1) Drien Velocity x s s xs x s Generates drie displacement elocity xd to which the Coriolis force is proportional EEC47B/MEC18: Introduction to MEMS Design Drieto Transfer Function e:1 xd Co1 Amplitude EEC47B/MEC18: Introduction to MEMS Design To (for synchronization) Velocity Mode 5 Copyright 017 egents of the Uniersity of California EEC47B/MEC18: Introduction to MEMS Design 6

3 EE 47B/ME 18: Introduction to MEMS Design Lecture 6m1: & MDS CTN 4/5/17 F ma c F c c l x c x Gyro eadout Equialent (for a single tine) Sources m( x ) f rx r x e :1 i o x i 0 ia C + p Gyro Element d EEC47B/MEC18: Introduction to MEMS Design 7 ia f i f Conditioning (Transresistance ) Easiest to analyze if all noise sources are summed at a common node Minimum Detectable (MDS) Minimum Detectable (MDS): Input signal leel when the signaltonoise ratio (SN) is ual to unity d Scale Factor Gain Conditioning Includes desired output plus noise The sensor scale factor is goerned by the sensor type The effect of noise is best determined ia analysis of the uialent circuit for the system EEC47B/MEC18: Introduction to MEMS Design 8 Moe Sources to a Common Point Moe noise sources so that all sum at the input to the amplifier circuit (i.e., at the output of the sense element) Then, can compare the output of the sensed signal directly to the noise at this node to get the MDS d Scale Factor Gain Equialent Inputeferred Voltage and Current Sources Input eferred Conditioning Includes desired output plus noise EEC47B/MEC18: Introduction to MEMS Design 9 EEC47B/MEC18: Introduction to MEMS Design 30 Copyright 017 egents of the Uniersity of California 3

4 EE 47B/ME 18: Introduction to MEMS Design Lecture 6m1: & MDS CTN 4/5/17 Equialent Input, i Generators Calculation of and i Take a noisy port network and represent it by a noiseless network with input and i noise generators that generate the same total output noise a) To get for a twoport: Case I Case II I emarks: 1. Works for linear timeinariant networks. and i are generally correlated (since they are deried from the same sources) 3. In many practical circuits, one of and i dominates, which remoes the need to address correlation 4. If correlation is important easier to return to original network with internal noise sources EEC47B/MEC18: Introduction to MEMS Design 31 i 1) Short input, find (or ) ) For. network, short input, find I (or i I ) I f f i I 3) Set sole for (or ) EEC47B/MEC18: Introduction to MEMS Design 3 i i Calculation of and (cont) Cases Where Correlation Is Not Important b) To get i for a port: I There are two common cases where correlation can be ignored: 1. Source resistance s is small compared to input resistance i i.e., oltage source input. Source resistance s is large compared to input resistance i i.e., current source input 1) S = small (ideally = 0 for an ideal oltage source): i 1) Open input, find (or ) ) Open input for. circuit, find I (or i I ) 3) Set sole for (or ) i I i0 I ii i Once the uialent inputreferred noise generators are found, noise calculations become straightforward as long as the noise generators can be treated as uncorrelated EEC47B/MEC18: Introduction to MEMS Design 33 S S EEC47B/MEC18: Introduction to MEMS Design 34 Current shorted out! For S = small, can be neglected only is important! (Thus, we need not deal with correlation) Copyright 017 egents of the Uniersity of California 4

5 EE 47B/ME 18: Introduction to MEMS Design Lecture 6m1: & MDS CTN 4/5/17 Cases Where Correlation Is Not Important ) S = large (Ideally = for an ideal current source) i S S Voltage effectiely opened out! in in i in 0! For S = large, can be neglected! only i is important! ( and again, we need not deal with correlation) EEC47B/MEC18: Introduction to MEMS Design 35 Copyright 017 egents of the Uniersity of California 5