Types of Noise Thermal Noise (Johnson Noise) Caused by thermal random motion of the current carriers Spectral Density: ()4vSf kTR= Noise Voltage: ()24nvBVSfdfkTRB==∫ where 2nV is the mean-squared thermal noise, T is the absolute temperature in K, B is the bandwidth, and R is the real part of the impedance. Example 21 kΩ100 KHz300 K1.3 VnRBTVµ===⇒= Flicker Noise (1f noise) ()nvfmVSf Kf= In semiconductors this noise is mostly due to random trapping and detrapping of charges at the Si-SiO2 interface and associated changes in carrier mobility due to Coulombic scattering. Proposed Hooge’s formula ()2HvVSfNfα=Shot Noise Shot noise is proportional to the current through the device and is caused by the random passage of electrons and holes through a potential barrier. 2,2nshotiqBI= where 2,n shoti is the root-mean-squared shot noise current, B is the bandwidth, and I is the current through the device. Example: Photodiode 221 Milli Ampere100 KHz300 K5.6nA5.6dcnnIBTivVµ===⇒== Noise Bandwidth ()20nvinVSfdf+∞=∫ For a system with transfer function H () ( )2202nvoutVSfHjfdfπ+∞=∫ () ( ) () ()220020BNvvSfHj f df SfH dfπ+∞∫∫ If white noise (()vSf is constant), ()()220120BN H j f dfHπ+∞=∫Flicker Noise in MOSFET Two related mechanisms: • Random trapping/detrapping of carrier at Si-SiO2 interface • Change in bulk carrier mobility due to trapped charges and hence additional Coulombic scattering Assuming uniform trap density at the interface, exponential electron wave decay in the oxide, n-MOSFET, and ignoring trap states far from EFn ()()222() 1gVtFnoxkTqSfNNEfWLCαµγ=+ ()*4211 1 1BtFnnox nmhNEπγαµµ µ µ=Φ=+ =+ oxWidth of the channelLength of the channelElectron mobility without oxide charge scatteringElectron mobility limited by oxide charge scattering( ) Noise Power Spectral DensityAttenuatiognVWLSfµµγ======8-1B-15n function of electron wave in oxide 10 cm* Effective mass of carrier in oxideTunneling barrier height at the interface Plank's constantScattering coefficient 1*10 VsTotal number of cmhNα≈=Φ===≈= hannel carriers per unit areaNumber of interface trapsElectron Quasi-fermi leveltFnNE== For complete derivation see Hung, Ko, Hu, and Cheng, “A Unified Model for the Flicker Noise in Metal-Oxide-Semiconductor Field Effect Transistors”, IEEE Trans. Elec. Dev., March 1990Noise Measures Signal to Noise Ratio signal powernoise powerSN= Signal to noise ratio is often expressed in decibels (dB): 1010logdBSSNN⎛⎞ ⎛⎞=⎜⎟ ⎜⎟⎝⎠ ⎝⎠ Noise in Systems ()()()()11iixinputioutput xiiiSSNNFSSNNxGx++=== where x is the signal power in dBm. Noise Factor (Fi) 1010log ( )iiNF F= Effective Noise Temperature (Ti) ()290 1iiTF=− System i Gain Gi (in dB) Noise Figure NFi(in dB)Input xi Output xi+1Noise Factor of Cascaded Amplifiers Stage 1Gain G1Noise Figure NF1Stage 2Gain G2Noise Figure NF2Stage NGain GNNoise Figure NFN…x yStage 1Gain G1Noise Figure NF1Stage 2Gain G2Noise Figure NF2Stage NGain GNNoise Figure NFN…x y Friis’ Formula 11211NitotaliijjFFFG−==−=+∑∏ Example (N=3) 32111211totalFFFFGGG−−=+ + Note: G must be its linear value, ie. not expressed in dB! F being the noise factor is also