MEMS技术 第六讲 噪声与器件的性能精讲

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Ps ,max DR 10log Pnoise vs2,max 10log 2 vn v 20log s ,max v n,rms
Signal and Noise waveforms
Sinusoid with amplitude normalized to 1
MOSFET Noise sources
When biased in saturation, (VDS>VDS,sat), the noise can be represented by an input noise voltage and an input noise current
Origin of 1/f noise in MOSFETs: surface states
• Assume noise sources are uncorrelated
2 i 1. For n1 replace w/a deterministic source of value
in1
2 in 1 1H z f
Systematic Noise Calculation Procedure
SNR and DR, Defined
Signal-to-noise ratio = SNR
Ps SNR 10log Pn v2 s 10log 2 vn v 20log s 2 vn vs 20log v n,rms
thermal noise (johnson noise) shot noise (散粒噪声) 1/f noise
Mechanical (Brownian) Noise
Impinging molecules give rise to a Brownian noise force:
f n2 4k B Tbf
Equivalent MOSFET small-signal model with input-referred noise sources
Crossover frequency between thermal and flicker noise can range from 1 kHz to 1 MHz
v
2 m
K f f 2 1 4k B T f 3 gm WLCox f
inverse dependence on gate area large transistors have lower 1/f noise
channel resistance in saturation
2. Calculate on1 in1 H j (treating it like a deterministic signal) 2 2 2 3. Determine on1 in1 H j 2 2 2 in , v , v 4. Repeat for each noise source: 1 n2 n3 5. Add noise power (mean square values)
MEMS和微系统设计
课程的基本目的
• 掌握MEMS设计的基本过程 • 掌握mems机电及其耦合分析的基本理论 • 掌握机电结构微器件的性能分析方法 • 了解热、流体的基本理论 • 了解MEMS的发展前沿知识 • 培养对MEMS的兴趣
课程内容
• • • • • • • •
MEMS概述及MEMS设计的概述 工艺简要回顾 系统设计、工艺设计及版图设计 主要的机械、电子元件及其设计基础 多域耦合设计:以机电耦合为例子 器件性能的估计 简单的其他域的元件及其简要设计要点 设计实例
i
2 m
2 2 Cgs 2 g m
KI D (neglecting DC gate 2 1 4k B T f f current and it’s shot 3 gm f noise
MOSFET Noise source (cont.)
Note 1: Pnoise is calculated over a limited bandwidth Note 2: Vn,rms is taken as the minimum detectable signal, in the absence of special coding or signal processing Dynamic range = DR
Circuit Noise Calculations
• Deterministic:
0 j H j i j
* 2
• Random: S0 H j H j Si H j Si
S0 H j Si
Flicker (1/f) Noise
Noise mechanism requirea a DC current, in contrast to thermal noise Origin of 1/f noise in MOSFETs: surface states
2 in
KI a f f
Near DC, the noise current diverges!
i
2 n
Example: R=1kΩ, T=300 K, BW=1MHz
4k B T / f R
i
2 n
4kBT BW 4 A R
Resistor Noise in MEMS
Interconnect resistance Rint to capacitive position sensors > routing in poly Si0 can lead to a high resistances, due to relatively high sheet resistance of this layer > inertial MEMS often have compliant suspensions large number of squares in polySi1 and significant contribution to Rint
本章提纲
• 噪声处理的基本知识和类型 • 器件的分辨率 • 系统的分辨率
• Noise: Random fluctuation of a • • • •
Noise
given parameter I(t) In addition, a noise waveform has a zero average value We can’t handle noise at instantaneous times But we can handle some of the averaged effects of random fluctuations by giving noise a power spectral density representation Thus, represent noise by its mean-square value:
2 2 2 2 2 vonTOT von v v v 1 on 2 on3 on 4
2 2 2 2 vonTOT von v v v 1 on 2 on 3 on 4
Total RMS value
噪声源
• 干扰噪声(理论可消除:隔离和共地) • 机械噪声(thermal noise : brownian noise) • 电噪声
3 Z n f 4k B T / 0 kQ 4k BT / 0 mQ (8) The signal response is 2 Z s f f / f 0 G f Ys (9) but 2 Ys is the magnitude of the input acceleration, a s (in meters per square second per root hertz), so 2 Z s f as G f / 0 (10) G f 1 in the accelerometer limit. The signal-to-noise ratio (SNR) at any frequency is then Z s / Z n as2 mQ / 4k B T 0 (11)
b M 1 / Q damping coefficient
Noise force applied to M-k-b system results in random Brownian motion with a frequency-depenndent power spectrum:
Handling Noise Deterministically
• Can do this for noise in a tiny bandwidth (e.g., 1 Hz) • Can approximate this by a S f S f B
2 n1
Gaussian noise with rms level normalized to 1; note that peak-peak noise level is occasionally as high as 6!
本章提纲
• 噪声处理的基本知识和类型 • 器件的分辨率 • 系统的分辨率
对简单模型加速度计噪声的估计
Let
i t I t I D
i I ID
2
2 i ( t ) 0, while i 0
Then
2
ቤተ መጻሕፍቲ ባይዱ
1 T 2 lim I I D dt T T 0
Noise Spectral Density
• We can plot the spectral density of this mean-square value:
f
1
n1
1
simusoidal voltage generator (especially for small B, say 1 Hz)
[This is actually the principle by which oscillators work oscillators are just noise going through a tiny bandwidth filter]
Why? Neither the amplitude nor the phase of a signal can change appreciably within a time period 1/B.
Systematic Noise calculation procedure
General Circuit with Several Noise Source
x
2 n

4k B Tbf f 1 f / f1 2 Qf 1
2 2
Implications: f<<f1
Electronic Noise Sources
1. Thermal noise in resistors
generated by random motion of electrons or holes white spectral density (up to 10 THz)
Z n f 4kBTRG f / k m/ Hz
Where
2 2 G f 1/ 1 f / f 0 f / f 0 / Q 2 6 2 and 4 2 f 02 0 k / m, In the accelerometer limit (f f 0 ), the noise displacement becomes Z n f 4k B TR / k (7) 2
2 vn 4k B TR f
spectral density
2 vn / f 4k B TR
Example: R=1kΩ, T=300 K
2 vn / f 4nV / Hz
vrms
2 vn 4mV
Thermal Noise (cont.)
Thermal noise current: find Norton equivalent
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