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RATE SLEW OPERATIONAL AMPLIFIER DYNAMIC LIMITATIONS INEL 5207 - SPRING 2008 - M.TOLEDO TRANSIENT RESPONSE FOLLOWER (NON-INVERTING WITH UNITY GAIN) FREQUENCY RESPONSE 1 A= 1 1 + j ft STEP RESPONSE 1 vO = Vm (1 - exp (-t/ )) = 2ft RISE TIME (TIME TO GO FROM 10% TO 90% OF VM) 0.35 tr = ft CURRENT STARVING VCC IA CC + ! vn Q1 Q2 vp iO1 iO1 vp vn gm Req Q3 Q4 -a2 1 vO VEE EXPONENTIAL & SLEW-RATE LIMITED STEP RESPONSE Volts ! vO + vI + ! tr vO (exponential rsponse) vO(slew-rate limited) t Vm vI HIGHER-ORDER POLES WOULD INTRODUCE "RINGING" - I.E. SMALL OSCILLATIONS ON RESPONSE Volts vO Volts vO S.R. vI t vI S.R. t Expected output: vO,expected = AvI If If dvO,expected dt dvO,expected dt > S.R. then dvO dt = S.R. S.R. then the response is exponential. For an input step, the critical output size Vom,crit beyond which the output becomes slew-rate limited, is vO,expected = Vom (1 - exp (-1/ )) Vom(crit) dvO,max = = S.R. dt S.R. Vom(crit) = S.R. = 2fB where = 1 2fB , fB is the closed-loop bandwidth i.e. = fB ft for unity gain, fB = ft for non-unity gain, where is the noninverting amplifier feedback factor. Vom =| A | Vim where Vim is the size of the input step and A is the (inverting or non-inverting) amplifier gain When the input is a step and Vom > Vom(crit) , initially vO changes linearly vO (t) = SR t t < t1 for t > t1 where t1 is defined by Vom - vO (t1 ) < Vom(crit) the output changes back to a linear response and. VO (t) = Vom - (Vom - vO (t1 )) exp -(t-t1 )/ For an input sinusoid, non-slew-rate limited output signal vO = Vom sin 2f t vO rate of change would be dvO dt = 2f Vom cos2f t dvO dt max maximum rate of change is at t = 0, = 2f Vom thus for Vom = Vom,crit beyond which the output becomes slewrate limited, 2f Vom,crit = S.R. or Vom(crit) = S.R. 2f observe that Vom =| A | Vim where Vim is the size of the input sinusoid and A is the (inverting or non-inverting) amplifier gain Given desired Vom we find the maximum frequency of sinusoid with undistorted output: fmax SR = 2Vom

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