EE43 Theory: Op-Amps1. ObjectiveThe purpose of these experiments is to introduce the most important of all analog building blocks, the operational amplifier (“op-amp” for short). This handout gives an introduction to these amplifiers and a smattering of the various configurations that they can be used in. Apart from their most common use as amplifiers (both inverting and non-inverting), they also find applications as buffers (load isolators), adders, subtractors, integrators, logarithmic amplifiers, impedance converters, filters (low-pass, high-pass, band-pass, band-reject or notch), and differential amplifiers. So let’s get set for a fun-filled adventure with op-amps!2. Introduction: Amplifier Circuit3. The Operational Amplifier: Ideal Op-Amp Model4. Non-Inverting Amplifier5. Inverting Amplifier6. Operation CircuitFigure 7: Operation circuit7. IntegratorFigure 8: Integrator8. Differentiator9. Differential Amplifier(20)10. Frequency Response of Op-AmpThe bandwidth is the frequency at which the power of the output signal is reduced to half that of the maximum output power. This occurs when the power gain G drops by 3 dB. In Figure 10, the bandwidth is B Hz. For all op-amps, the Gain*Bandwidth product is a constant. Hence, if the gain of an op-amp is decreased, its operational bandwidth increases proportionally. This is an important trade-off consideration in op-amp circuit design. In Sections 3 through 8 above, we assumed that the op-amp has infinite bandwidth.10. More on Op-AmpsEECS 43 Spring 2005 Op AmpsEE43 Theory: Op-Amps1. ObjectiveThe purpose of these experiments is to introduce the most important of all analog building blocks,the operational amplifier (“op-amp” for short). This handout gives an introduction to theseamplifiers and a smattering of the various configurations that they can be used in. Apart from theirmost common use as amplifiers (both inverting and non-inverting), they also find applications asbuffers (load isolators), adders, subtractors, integrators, logarithmic amplifiers, impedanceconverters, filters (low-pass, high-pass, band-pass, band-reject or notch), and differential amplifiers.So let’s get set for a fun-filled adventure with op-amps!2. Introduction: Amplifier CircuitBefore jumping into op-amps, let’s first go over some amplifier fundamentals. An amplifier has an input port and an output port. (A port consists of two terminals, one of which isusually connected to the ground node.) In a linear amplifier, the output signal = A input signal,where A is the amplification factor or “gain.” Depending on the nature of the input and outputsignals, we can have four types of amplifier gain: voltage gain (voltage out / voltage in), current gain(current out / current in), transresistance (voltage out / current in) and transconductance (current out /voltage in). Since most op-amps are used as voltage-to-voltage amplifiers, we will limit thediscussion here to this type of amplifier. The circuit model of an amplifier is shown in Figure 1 (center dashed box, with an input port and anoutput port). The input port plays a passive role, producing no voltage of its own, and is modeled bya resistive element Ri called the input resistance. The output port is modeled by a dependent voltagesource AVi in series with the output resistance Ro, where Vi is the potential difference between theinput port terminals. Figure 1 shows a complete amplifier circuit, which consists of an input voltagesource Vs in series with the source resistance Rs, and an output “load” resistance RL. From thisfigure, it can be seen that we have voltage-divider circuits at both the input port and the output portof the amplifier. This requires us to re-calculate Vi and Vo whenever a different source and/or load isused: sisiiVRRRV(1) iLoLoAVRRRV(2)RSVSViRiA ViRoVoRLS O U R C E A M P L I F I E R L O A D+_+_INPUT PORTOUTPUT PORTFigure 1: Circuit model of an amplifier circuit.1EECS 43 Spring 2005 Op Amps3. The Operational Amplifier: Ideal Op-Amp ModelThe amplifier model shown in Figure 1 is redrawn in Figure 2 showing the standard op-ampnotation. An op-amp is a “differential-to-single-ended” amplifier, i.e., it amplifies the voltagedifference Vp – Vn = Vi at the input port and produces a voltage Vo at the output port that is referencedto the ground node of the circuit in which the op-amp is used.ViRiAViRoVo+_+_+_VpVnipin+_ ViAViVo+_+_+_VpVn+_Figure 2: Standard op-amp Figure 3: Ideal op-ampThe ideal op-amp model was derived to simplify circuit analysis and it is commonly used byengineers for first-order approximate calculations. The ideal model makes three simplifyingassumptions: Gain is infinite: A = (3) Input resistance is infinite: Ri = (4) Output resistance is zero: Ro= 0 (5)Applying these assumptions to the standard op-amp model results in the ideal op-amp model shownin Figure 3. Because Ri = and the voltage difference Vp – Vn = Vi at the input port is finite, the inputcurrents are zero for an ideal op-amp: in = ip = 0 (6)Hence there is no loading effect at the input port of an ideal op-amp: siVV (7)In addition, because Ro = 0, there is no loading effect at the output port of an ideal op-amp: Vo = A Vi(8)Finally, because A = and Vo must be finite, Vi = Vp – Vn = 0, or Vp = Vn(9)2EECS 43 Spring 2005 Op AmpsNote: Although Equations 3-5 constitute the ideal op-amp assumptions, Equations 6 and 9 are used most often in solving op-amp circuits. VinR2R1Vout+_VpVnI VinVout+_VpVn VinR2R1Vout+_VnVpI Figure 4a: Non-inverting amplifier Figure 5a: Voltage follower Figure 6a: Inverting amplifier VinVoutA>=1 V i nV o u tA = 1 VinVoutA<0 Figure 4b: Voltage transfer curve Figure 5b: Voltage transfer curve Figure 6b: Voltage transfer curve of non-inverting amplifier of voltage follower of inverting amplifier V i nV o u tA > = 1- V p o w e r+ V p o w e r V i nV o u tA = 1- V p o w e r+ V p o w e rVinVoutA<0-Vpower+Vpower Figure 4c: Realistic transfer curve
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