EECS240 – Spring 2008Lecture 7: Noise and FeedbackElad AlonDept. of EECSEECS240 Lecture 7 2Noise and Feedback• Ideal feedback:• No increase of input referred noise• No decrease of SNR at output• Practical feedback: increased noise• Noise from feedback network• Noise gain from elements outside feedback loopEECS240 Lecture 7 3Ideal Feedback and Noise• Ideal (noiseless) feedback network:• Noise doesn’t change • Real feedback elements have noise though…EECS240 Lecture 7 4Real Feedback• Conceptually identical to standard two port calculations• Use Rs = 0 to find vi,eq2Rs = ∞ to find ii,eq2• Calculations get tedious…EECS240 Lecture 7 5Practical Feedback Analysis• Quick approximation method:• Consider loading of feedback network on the input• Add a noise source associated with this element. • Example: shunt feedback• Loading at input is RFÆ ii2= in2+ 4kT∆f/RFEECS240 Lecture 7 6Example #2: Series-Shunt Feedback• Loading is RF||RE• So, noise voltage becomes:• vi2= vn2+ 4kT(RF||RE)∆fEECS240 Lecture 7 7Implications: Non-Inverting Ampa = infR1R2in1in2vnViVovx= vi-vn• Minimum power from feedback Æ large R1+R2• Example: • Av= 10, R2 = 100kΩ, R1 = R2(Av0-1) = 900kΩ• vnfb2= 40nV/√Hz (very high)• Only way to lower noise is increase power…EECS240 Lecture 7 8Example: Inverting AmplifierinfR2R1vnViVo{02121122222 2 2121 1212 2 011voi nAieq n n nvRRRvv vRRRRR RRvv v vRR R A−+=− +⎛⎞⎛⎞⎛⎞++===+⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠• Ignoring noise from R1, R2:• “Ideal” feedback, why is vi,eq2> vn2?EECS240 Lecture 7 9“Complete” Noise Example• Effect of cascode device noise on common-source feedback amplifier• Simplified model:• Lump parasitic caps• Neglect roEECS240 Lecture 7 10Example (cont.)()22122: : 0: with oLtotomxnxxxmgmxnggoFFtotvsCFCvgvivsCvgvgvivvFvCFCC+=++++===+• Calculate noise TF to amplifier output:CxCLVovxvgCtotCFgm2vxgm1vgin22EECS240 Lecture 7 11Example (cont.)()()()222111222121111xmonLtotxmLtotmmmponmoosC gviCFCCFgCFCssgF gFgsvissFgQωωω=++++=++After some algebra …CxCLVovxvgCtotCFgm2vxgm1vgin22• Low frequency:• in2doesn’t reach output• High frequency:• Cxacts as a shortEECS240 Lecture 7 12Example (cont.)()()()()()()()()222221211222121441ooon mpmmx mon mm L tot L totmxonLtotLtotQvkTgFgFg C FgvkTggCFC CFCFgCkTvCFC CFCωωγωγγ==++⎡⎤=⎢⎥++⎢⎥⎣⎦After some algebra …CxCLVovxvgCtotCFgm2vxgm1vgin22• Total
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