HO19_214W09_Translinear_2pp

HO19_214W09_Translinear_2pp - Handout #19 EE 214 Winter...

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Handout #19 EE 214 Winter 2009 Translinear Circuits and Multipliers B. Murmann and B. A. Wooley Stanford University B. A. Wooley, B. Murmann EE214 Winter 2008-09 2
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± “A translinear circuit is one having all inputs and outputs in the form of currents and whose primary function arises from the exploitation of the logarithmic behavior of forward-biased PN junctions arranged in pairs so as to result in fundamentally exact, temperature independent transformations in the amplitude domain” ± Most basic example: 12 BE BE o i TT VV I I Vl n n II = ⎛⎞ = ⎜⎟ ⎝⎠ ss o i I I = 2 1 s oi s I I = B. A. Wooley, B. Murmann EE214 Winter 2008-09 3 Square-Root Circuit 34 BE BE BE BE oo Bi T T V V n n n n + =+ +=+ s s I I = 3 4 s s B I = B. A. Wooley, B. Murmann EE214 Winter 2008-09 4
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Squaring Circuit 15 2 3 4 6 12 2 BE BE BE BE BE BE o Bii BB VV V V V V I II I ++=++ 152 3 46 2 346 1 sss s s s B oi III I I I I = = 2 2 B I B. A. Wooley, B. Murmann EE214 Winter 2008-09 5 Remarks ± Today, most electronic systems rely on digital computation rather than analog function synthesis ± Bio mimetic circuits & systems are one area in which “analog computing” Bio-mimetic circuits & systems are one area in which analog computing remains an active research topic http://www.stanford.edu/group/ brainsinsilicon/index.html K.M. Hynna and K. Boahen, Thermodynamically- Equivalent Silicon Models of Ion Channels, Neural Computation vol 19 no 2 pp 327-350 February 2007 B. A. Wooley, B. Murmann EE214 Winter 2008-09 6 , vol. 19, no. 2, pp. 327 350, February 2007
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Neurons Sodium ion concentration Sodium ion concentration outside the cell inside the cell Barry Gilbert, “Considering Multipliers,” Analog Dialogue 42-11, November 2008 http://www.analog.com/library/analogdialogue/archives/42-11/multipliers.html B. A. Wooley, B. Murmann EE214 Winter 2008-09 7 Practical Applications ± Let’s look at a few circuit schemes that exploit logarithmic device behavior and/or V BE loops in today’s practical applications ± Biasing of class-AB output stages ± Current gain cell ± Voltage multipliers Variable gain amplifie
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HO19_214W09_Translinear_2pp - Handout #19 EE 214 Winter...

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