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CMRR • One important measure of the goodness of an opamp or an opamp circuit is the common mode rejection ratio (CMRR) • Ideally, opamps are expected to amplify the differences between v1 and v2 with nearly infinite gain • Due to transistor nonidealities, some small amount of amplification occurs due to the common signal of both inputs open loop gain common mode gain v1 v2 vcm vo vo A = ----------------v2 – v1 vo vo A cm = --------v cm A CMRR = ---------A cm Lecture 8-1 CMRR • We would like to have an infinite CMRR v id = v 2 – v 1 v1 v2 + v1 v Icm = ----------------2 v2 v o = Av id + Acm v Icm • A typical CMRR is 80-100dB at low frequency • Would the CMRR improve, or get smaller with increasing frequency? Lecture 8-2 CMRR • Not really a problem for inverting amplifier configurations --- why? R2 R1 Vo Vin • But definitely a problem for noninverting amplifier configurations --- why? R2 R1 Vo Vin Lecture 8-3 Difference Amplifier • Also a problem for difference amplifiers R2 R1 Vo Va Vb Lecture 8-4 Difference Amplifier • We have to scale the voltage vb to achieve balanced amplification of vb-va R2 R1 R1 Va Vb Vo R2 Lecture 8-5 CMRR • Opamp data sheets specify the CMRR for the opamp itself, but the opamp differential amplifier circuit also has a CMRR Rf Even with ideal opamp model you will see some common mode gain if there is a mismatch in the resistor values Rs vo vin vp R1 R2 Lecture 8-6 Input-Currents and -Resistances • There is some small dc current flowing into/out of the inputs at all times -- input bias current v1 _ v id v2 + IB1 IB2 • There is also a component of input current that changes with input voltage (both common mode and differential) --- input resistances v Icm Rcm v1 _ v id v2 + Rid Lecture 8-7 Input Resistance • These resistances are generally quite large: Rcm ~ 100MΩ, and Rid ~ 1MΩ • These resistances are even larger for MOS opamps 1 2Rcm Rid 2 2Rcm Lecture 8-8 Input Resistance • These opamp input resistances do not affect an inverting amplifier configuration as long as R1 is much less than Rid and Rcm R2 R1 Vo Vin • But these resistances are what determines the input resistance of a non- inverting amplifier configuration R2 R1 Vo Vin Lecture 8-9 Input Resistances • The resistors R1 and R2 should be kept significantly smaller than the input resistances for the gain to be close to ideal R2 R1 v1 2Rcm vo Rid iin v2 + 2Rcm A ( v2 – v1 ) vin Rin _ Lecture 8-10 Input Resistances R2 R1 v1 2Rcm vo Rid iin v2 + 2Rcm A ( v2 – v1 ) vin Rin _ Lecture 8-11 Nonzero Output Resistance • We also have to keep in mind that the opamp output cannot source an infinite amount of current --- so we can’t drive arbitrarily small resistance loads • This is modeled by an output resistance, Ro R2 if vin < 0 R1 iL Ro A ( v 2 – v1 ) RL note that vo definition is changed when output resistance is added to the model Lecture 8-12 Measuring Output Resistance R2 R1 Ro A ( v2 – v1 ) Lecture 8-13 Modeling Output Resistance • Since the open loop gain depends on frequency, so does the opamp circuit output impedance Lecture 8-14 Input Bias Current • The input bias current is not frequency dependent, but can cause an unwanted dc output response R2 R1 IB1 IB2 Lecture 8-15 Compensating for IB • In practice, a resistor is added so that the bias current drops are compensated properly between the two ports Rf Rs vo vin Rcomp Lecture 8-16 Compensating for IB R2 R1 R3 IB1 IB2 Lecture 8-17 dc Offset Voltage • Another unwanted dc output signal is due to the dc offset voltage • A dc differential input is required for a real opamp to zero the output • This offset is due to mismatch in transistor parameters, and is temperature dependent --- more on this later in the course VOS ~ 1-5mV 1 2 VOS Lecture 8-18 dc Input Offset Voltage • Calculate output voltage due to dc input offset voltage Rf Rs vo vin VOS Lecture 8-19 ac Coupling • We can avoid this offset voltage at the output by using ac coupling Rf CC Rs vo vin VOS Lecture 8-20