Operational AmplifiersOp-Amp IntroductionIdeal Op-Amp AssumptionsInverting AmplifierSlide 5Non-Inverting AmplifierSlide 72/1/2005 BAE 5413 1Operational AmplifiersA brief introduction2/1/2005 BAE 5413 2Op-Amp Introduction•Need exists for a circuit element that can perform:–Add, subtract, multiply, divide, differentiate, integrate•Evolved from Analog Computers•Op-Amp properties–Single building block which can be assembled into above functions by adding passive components (R,L,C)–Inexpensive (used in high volume)–Compact•Op-Amp analysis•Use assumptions of “Ideal Op-Amp” to allow low frequency performance to be approximated•Typically have near ideal characteristics but frequency response of an integrator (G(s) = 1/s). (Otherwise, the high bandwidth would be impossibly difficult to manage.)2/1/2005 BAE 5413 3Ideal Op-Amp Assumptions•Differential function•Vout = A•V•Infinite•Intrinsic gain: A = •Input impedance: Zin = •Bandwidth: Vout f()•Zero•Input offset voltage: Vio = 0 for Vout+ Vio= A•V•Input impedance: Zout = 0AV+Vsupply-VsupplyVoutZinZout+-2/1/2005 BAE 5413 4Inverting Amplifier•Consider the circuit configuration to the right•Assuming intrinsic gain of the op-amp is very large for the frequency of interest:–Vout is finite and typically within +15 to -15 V implying V is very small•Assuming ib is very small given the intrinsic input impedance is very large, Vb must be very smallbinRRinVVVV bfRRoutVVVV V+Vsupply-VsupplyVout+-VinRinRfRbibiin_op-ampampopinRRiiifin_outVVA 2/1/2005 BAE 5413 5Inverting Amplifier•Amplifier performance is a function of external components only for ideal assumptions•Input and output impedances of the amplifier can be calculated as approximately:inRinVV fRoutVV finRRii fRinRRVRVfinfoutininRVRVinfinoutRRVVininRZ fininintrinsicoutoutRRRAZZ1_2/1/2005 BAE 5413 6V+Vsupply-VsupplyVout+-VinRinRfibRbbinRRinVVVV bfRRoutVVV bfRbRiii Non-Inverting AmplifierbRinVV inRoutVVVfbfRRii bRfRRVRVbfbfinRRRVVfbfininbfinoutRRVVRRVV 1bfinoutRRVV12/1/2005 BAE 5413 7Non-Inverting Amplifier•Input and output impedances can be calculated as approximately:fininintrinsicininRRRAZZ
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