ECEN4827/5827 lecture notes Effects of op-amp imperfections on application circuits (part 1) Objectives in this segment of the course are to: 1. Define op-amp static and dynamic characteristics and examine the effects of op-amp imperfections in several circuit application examples. 2. Motivate follow-up discussions about transistor-level op-amp circuit design techniques aimed at improving op-amp characteristics. 3. Review some of the prerequisite circuit and device modeling and analysis techniques required in subsequent course topics. Op-amp imperfections DC and low-frequency small-signal characteristics: • Open-loop low-frequency voltage gain Ao = vo/(v(+) − v(−)) • Output resistance, rout • Input resistance, rin • Supply voltages VDD, −VSS (or VCC, −VEE); supply currents IDD, ISS (or ICC, IEE) • Output saturation limits, VOmin, VOmax; output voltage swing VOmin < VO < VOmax • Maximum output (source or sink) current • Input offset voltage, VOS; temperature drift of the input offset voltage ∆VOS/∆T [mV/oC] • Input bias current, IB = (IB+ + IB−)/2; temperature drift ∆IB/∆T • Input offset current, IOS = IB+ − IB−; temperature drift ∆IOS/∆T • Common-mode rejection ratio CMRR • Power-supply rejection ratio PSRR • Input common-mode voltage range, VCMmin < VCM < VCMmax Dynamic (small-signal and large-signal) characteristics • Open-loop transfer function AOL(s) • Gain-bandwidth product GBW, or unity-gain bandwidth • Input and output impedances, Zin(s), Zout(s) • Slew-rate SR • Frequency-dependent common-mode rejection ratio CMRR(f) • Frequency-dependent power-supply rejection ratio PSRR(f) • Input noise We will introduce the op-amp characteristics and imperfections through application examples.Application circuit examples 1. Basic inverting gain circuit example, effects of finite Ao, finite rin and non-zero rout +_+–VDD−VSSvIR1R2vO Figure 2.1: Basic inverting-gain application circuit Assuming an ideal op-amp, the closed-loop gain of the circuit in Fig. 2.1 is well known: (ACL)ideal = vo/vi = −R2/R1. Analysis of ideal negative-feedback op-amp circuits, such as the example of Fig. 2.1, is usually based on the fact that the ideal op-amp with very large open-loop gain forces the (+) and (−) input voltages to be equal. For example, in the circuit of Fig. 2.1, v(−) = v(+) = 0, and the (−) input of the op-amp is called the virtual ground. Suppose that the op-amp in Figure 2.1 has a finite open-loop gain Ao. It is of interest to find the effect of Ao on the closed-loop gain ACL. A model of the op-amp with finite Ao, and all other characteristics ideal, is shown in Fig. 2.2. +–Ao(v(+)−v(−))−+ Figure 2.2: Model of an op-amp with finite Ao Applying this model in the circuit of Fig. 2.1, we obtain the circuit model in Fig. 2.3.+–Ao(v(+)−v(−))−++–viR1R2vo Figure 2.3: Model of the circuit in Fig. 2.1 using an op-amp with finite Ao. Solving the circuit model in Fig. 2.3, yields the closed-loop gain 211211121RRRARRRARRvvAooioCL+++−==. It is instructive to note that the closed-loop gain is in the form ()TTAAidealCLCL+=1, where T = AoR1/(R1+R2) is the loop-gain in the negative-feedback circuit of Fig. 2.3. Note that the loop gain represents the total gain for a signal starting from a point in the feedback loop to the same point around the loop. Analysis and computation of the loop-gain T will be addressed in more detail later. Comments: • Op-amps are usually constructed with a relatively large open-loop gain Ao, e.g, Ao > 104 (80dB). • The open-loop gain of an op-amp can vary significantly from one component to another, or over temperature, bias or other operating conditions. As a result, op-amp application circuits are rarely based on a precise value of Ao. • The closed-loop gain of a negative-feedback application circuit is close to the ideal value, independent of Ao, as long as the loop gain T is much larger than 1. In other words, as long as Ao is large enough so that T is much larger than 1, the exact value of Ao is not important. • The loop gain T is smaller in an application that requires a larger magnitude of the closed-loop gain, i.e. a larger R2/R1. Therefore, an application circuit with a larger closed-loop gain is more sensitive to variations in the op-amp open-loop gain Ao.Suppose that the op-amp in Figure 2.1 has a finite open-loop gain Ao, a finite input resistance rin, and a non-zero output resistance rout. A model of the op-amp with these imperfections is shown in Fig. 2.4. +–Ao(v(+)−v(−))−+rinrout Figure 2.4: Model of an op-amp with finite Ao Applying this model in the circuit of Fig. 2.1, we obtain the circuit model in Fig. 2.5. +–viR1R2vo+–Ao(v(+)−v(−))−+rinrout Figure 2.5: Model of the circuit in Fig. 2.1 using an op-amp with finite Ao, finite rin, and non-zero rout. A feedback-circuit analysis technique (to be studied later) can be used to obtain the closed-loop gain by inspection: ()TRrrrRRrrTTAAinininoutoutidealCLCL++++++=11||1112, where the loop-gain T is given by outininorRrRrRAT++=211|||| and (ACL)ideal = −R2/R1. You may want to verify the result for ACL using standard circuit-analysis techniques.Comments: • If the loop-gain T is very large, the closed-loop gain is close to the ideal value, independent of Ao, rin, or rout. An op-amp with a very large open-loop gain Ao (so that T is very large) can be used to construct precise negative-feedback application circuits even though it may have significant imperfections in rin or rout. Large gain is the most important characteristic of an op-amp. • Finite rin, and non-zero rout tend to reduce the loop gain in application circuits, requiring a larger Ao to achieve large loop-gain values. • The parameters Ao, rout, rin, are small-signal parameters – they apply to small-signal variations of voltages and currents around a DC operating point. 2. Static transfer characteristic; output voltage swing The ranges of output and input voltages such that an op-amp operates with a large small-signal open-loop gain Ao are constrained by the supply voltages VDD and VSS. On the output side, the saturation voltages Vomin and Vomax define the available output voltage swing. A typical static transfer characteristic of an op-amp is shown in Fig. 2.6. v(+) − v(−)VoVDDVomaxVomin−VSSslope = Aooutput voltage