EECS240 – Spring 2009Lecture 5: Electronic NoiseElad AlonDept. of EECSEECS240 Lecture 5 2Electronic Noise• Why is noise important?• Sets minimum signals we can deal with – often sets lower limit on power• Signal-to-noise ratio• Signal Power Psig~ (VDD)2• Noise Power Pnoise~ kBT/C• SNR = Psig/ Pnoise• Technology Scaling• VDDgoes down Æ lower signal• Increase C to compensate Æ increases powerEECS240 Lecture 5 3Types of “Noise”• Interference• Not “fundamental” – deterministic• Signal coupling• Capacitive, inductive, subtrate, etc.• Supply noise• Device noise• Caused by discreteness of charge• “fundamental” – thermal noise• “manufacturing process related” – flicker noiseEECS240 Lecture 5 4Noise in Amplifiers• All amplifiers generate noise• Comes from carrier random thermal motion and discreteness of charge• Noise is random• Has to be treated statistically – can’t predict actual value• Deal with mean (average), variance, spectrumEECS240 Lecture 5 5Thermal Noise of a Resistor• Origin: Brownian Motion• Thermally agitated particles• E.g. ink in water, electrons in a conductor• Available noise power:• Noise power in bandwidth ∆f delivered to a matched load• Example: ∆f = 1Hz Æ PN= 4 x 10-21W = -174 dBm• Reference: J.B. Johnson, “Thermal Agitation of Electricity in conductors,” Phys. Rev., pp. 97-109, July 1928.NBPkT f=∆EECS240 Lecture 5 6Resistor Noise Model24nNBvPkTfR=∆=24nBvkTRf=∆Mean square noise voltage:EECS240 Lecture 5 7Thermal Noise• Present in all dissipative elements• I.e., resistors• Independent of DC current flow• Random fluctuations of v(t) or i(t)• Mean is 0• Distribution (pdf) is Gaussian• Power spectral density is “white”• Up to ~THz frequencies• kBT = 4 x 10-21J (T = 290K = 16.9oC)• Example:R = 1kΩ Æ 4nV/rt-Hz1MHz bandwidth Æ σ = 4uV2244BnB nkTBvkTRB iR==EECS240 Lecture 5 8Noise of Passive Networks• Capacitors and inductors only shape spectrum• Noise calculations• Instantaneous voltages add• Power spectral densities add• RMS voltages do NOTadd• Example: R1+R2in series• Generalization to arbitrary RLC networksEECS240 Lecture 5 9Noise in Diodes• Shot noise• Zero mean, Gaussian pdf, white• Proportional to current• Independent of temperature• Example:ID= 1mA Æ 17.9pA/rt-Hz1MHz bandwidth Æ σ = 17.9nA• Shot noise versus thermal noise• gdiode= Id/(kbT/q)• Thermal noise density: 4kbTgdiode= 4qId• Shot noise half of this (current flow in 1 direction)fqIiDn∆= 22EECS240 Lecture 5 10BJT NoisefqIiffIKfqIifTrkvCcBBbbBb∆=∆+∆=∆=2242122α• Just like diodes: shot noise• Collector and base noise partially correlated• Extrinsic resistors contribute noise• Small signal resistors (e.g., ro) don’t• These aren’t physical resistorsEECS240 Lecture 5 11FET Noise• Channel resistance contributes thermal noise• Channel conductance:• Noise injection is actually distributed across the channel (note γ):()0ds ox GS th mWgCVVgLµ=−=EECS240 Lecture 5 12More Fundamental Expression• More fundamental equation uses channel charge [Tsividis]• When Vds= 0, device is truly a resistor:EECS240 Lecture 5 13• In saturation, drain current noise is• For long channel model, can substitute gmfor the above factor. • In practice, form involving actual inversion charge is more accurate • This is what SPICE/BSIM useStrong Inversion NoiseEECS240 Lecture 5 14Weak Inversion• Weak inversion: BJT Æ shot noise. • Result should be ~ 2qIDS• Get the same result from inversion charge expression:EECS240 Lecture 5 15Thermal Noise for Short Channels• Strong inversion Æ thermal noise• Drain current: gds0is what you really care about• gmmore convenient for input-referred noise• For low field (long L), γ = 2/3 relates gmto gds• For high field, use α to capture increase in noise• High-field noise can be 2-3 times larger than low field• MOS actually has intrinsic gate induced noise (142/242 topic)• Gate leakage Æ shot noiseEECS240 Lecture 5 16FET Noise Model• Model neglects intrinsic gate noise• BSIM3 does not directly include αEECS240 Lecture 5 171/f Noise• Flicker noise• Kf,NMOS= 2.0 x 10-29AFKf,PMOS= 3.5 x 10-30AF• Strongly process dependent• Example: ID= 10µA, L = 1µm,• Cox= 5.3fF/µm2, fhi= 1MHzflo= 1Hz Æ σ = 722pAflo= 1/year Æ σ = 1083pAEECS240 Lecture 5 181/f Noise Corner Frequency• Definition (MOS)• Example:• V* = 200mV, γ = 1NMOS PMOSL = 0.35µm Æ 192kHz 34kHzL = 1.00µm Æ 24kHz 4kHz22144fD fDBr m coox co ox B r mKI KIfkT g f fLC f LC k T gγγ∆=∆ =2*21148mDfgIBr oxfBr oxKkT C LKVkT C Lγγ==EECS240 Lecture 5 19SPICE Noise Analysis100/11000/1050/2EECS240 Lecture 5 20Noise Calculations• Method:1) Create small-signal model2) All inputs = 0 (linear superposition)3) Pick output voor io4) For each noise source vx, ixCalculate Hx(s) = vo(s) / vx(s) (… io, ix)5) Total noise at output is:• Tedious but simple …()()∑==xxjfsxTonfvsHfv2222,)(π()()2,simpler notation: on T nvfSf=EECS240 Lecture 5 21Example: Common SourceEECS240 Lecture 5 22Simulation