Posted: September 13th, 2017

ECE 303L: Signals and Systems Laboratory: Engineering writers in US

ECE 303L: Signals and Systems Laboratory

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Synthesis of LTIC Transfer Functions using Operational Amplifiers

Purpose:
x Examination*of*the*synthesis*of*common*transfer*functions*using*active*circuits.
x Experimental*evaluation*of*practical*differentiator*and*integrator*circuits.
x Practical*realization*of*the*PI*and*PID*controller.*
Background: In*contrast*to*our*previous*work*where*the*systematic*analysis*of*various*RLC*circuits,*both*
passive*and*active,*preceded*our*experimental*assessment,*we*now*shift*our*perspective*to*the*
synthesis*or*design*of*circuits.*Such*an*approach*is*necessary*if*we*are*to*conceptualize*circuits*as*a*
solution*to*a*design*problem*where*specific*inputJoutput*characteristics*are*desired*and*the*circuit*
topology*or*circuit*realization*must*be*determined*to*meet*those*requirements.*Although*general*design*
techniques*exist*for*practical*circuit*realization
,*perhaps*the*most*direct*approach*is*to*synthesize*using*
commŽŶĐŝƌĐƵŝƚ͞ďƵŝůĚŝŶŐďůŽĐŬƐ͘͟ Operational*amplifiers*make*such*an*approach*possible*since*their*
typical*circuit*application*result*in*nonJinteracting*systems:*circuits*whose*transfer*functions*do*not*
change*when*they*are*connected*to*other*circuits.*This*characteristic*is*a*consequence*of*their*high*
input*impedance*and*low*output*impedance properties.*Note*that*this*is*not*true*of*passive*circuits*ʹ a*
feature*which*we*can readily*demonstrate*in*class.

Signals and Systems Laboratory: Engineering writers in US

Our*preliminary*definition*of*the*transfer*function*of*an*LTIC*system*originates*in*our*
examination*of*the*eigenfunction*response of*an*inputJoutput*differential*equation*model.*Although*we*
will*address*this*definition*again*as*we*develop*a*Laplace*Transform*approach*to*circuit*analysis*and*
design,*our*current*definition*is*sufficient*for*our*present*purposes.*If*we*take*our*familiar*definitions*as*
given,*then*for*an*LTIC*system*model*expressed*in*terms*of*an*inputJoutput*differential*equation,*we*
have*the*following*results:
Model: >Q(