1Lecture 9, Slide 1EECS40, Fall 2003 Prof. KingLecture #9ANNOUNCEMENT• Bring your own copy of Lecture #10 notes (posted on the class website) to class on Wednesday! (No hardcopies will be handed out.)OUTLINE• The operational amplifier (“op amp”)• Feedback• Comparator circuits• Ideal op amp• Unity-gain voltage follower circuitReadingChapter 5.1-5.2(with Prof. Neureuther)Lecture 9, Slide 2EECS40, Fall 2003 Prof. KingSolution to Superposition Example• Find Vo:16VV24424=Ω+ΩΩ=′oV–+24 V2 Ω4 Ω4 A4 V+ –+–Find contribution of 24 V source Find contribution of 4 A source Find contribution of 4 V source–+24V2Ω4Ω+Vo′–4Ω2Ω4Ai+Vo′′–V316)4(A34A4422−=Ω−=′′=Ω+ΩΩ=iVio+ –2Ω 4Ω4V+Vo′′′–V38-4V)(424−=Ω+ΩΩ=′′′oVV8=′′′+′′+′=ooooVVVV2Lecture 9, Slide 3EECS40, Fall 2003 Prof. KingFinal Comment on Thévenin Equivalent• If there are no independent sources in a circuit, VTh= 0.– If there are dependent sources in the circuit, we need to apply an external voltage in order to determine RTh.Example: Circuit used in RThCalculation Example #2, Lecture 8:TEST258 VVx=⇒ITEST–+VTEST80 0201640 TESTxxxViVViiV−==−+−−∆∆∆:i of Definition:x node to KCL Applying∆Vx604020TEST ∆−+−=iVVVTESTxΩ==475TESTTESTThIVRLecture 9, Slide 4EECS40, Fall 2003 Prof. KingThe Operational Amplifier• The operational amplifier (“op amp”) is a basic building block used in analog circuits.– Its behavior is modeled using a dependent source.– When combined with resistors, capacitors, and inductors, it can perform various useful functions:• amplification/scaling of an input signal• sign changing (inversion) of an input signal• addition of multiple input signals• subtraction of one input signal from another• integration (over time) of an input signal• differentiation (with respect to time) of an input signalA commonly used op amp is the “741”(You will use these in the EECS40 lab next week.)3Lecture 9, Slide 5EECS40, Fall 2003 Prof. KingOp Amp Circuit Symbol and Terminals+–V +V –non-inverting inputinverting inputpositive power supplynegative power supplyoutputThe output voltage can range from V –to V +The positive and negative power supply voltages do not have to be equal in magnitude.Lecture 9, Slide 6EECS40, Fall 2003 Prof. KingOp Amp Terminal Voltages and Currents+–V +V –• All voltages are referenced to a common node.• Current reference directions are intothe op amp.–Vcc++Vcc–+vn–+vp–common node(external to the op amp)ipinio+vo–ic+ic-4Lecture 9, Slide 7EECS40, Fall 2003 Prof. KingOp Amp Voltage Transfer Characteristic• In the linear region, vo= A (vp– vn)where A is the open-loop gain• Typically, Vcc≤ 20 V and A > 104Æ linear range: -2 mV ≤ vp– vn ≤ 2 mVThus, for an op amp to operate in the linear region, vp≅ vn(i.e. there is a “virtual short” between the input terminals.)vovp–vnThe op amp is adifferentiating amplifier:“linear”“positive saturation”“negative saturation”Vcc-VccRegions of operation:slope = A >>1Lecture 9, Slide 8EECS40, Fall 2003 Prof. KingAchieving a “Virtual Short”• Recall the voltage transfer characteristic of an op amp:Q: How does a circuit maintain a virtual short at the input of an op amp, to ensure operation in the linear region?A: By using negative feedback. A signal is fed back from the output to the inverting input terminal, causing vp-vnto decrease and hence voto decrease … until the op amp operates in its linear region. vovp–vnVcc-Vccslope = A >>1~1 mV~10 Vvovp–vnVcc-Vccslope = A >>1Plotted using different scales for voand vp–vn~10 V~10 VPlotted using similar scales for voand vp–vn5Lecture 9, Slide 9EECS40, Fall 2003 Prof. KingFamiliar examples of negative feedback:• Thermostat controlling room temperature• Driver controlling direction of automobile• Photochromic lenses in eyeglassesFamiliar examples of positive feedback:• Microphone “squawk” in sound system• Mechanical bi-stability in light switches• Thermonuclear reaction in H-bombNegative vs. Positive FeedbackFundamentallypushes towardstabilityFundamentallypushes towardinstability orbi-stabilityLecture 9, Slide 10EECS40, Fall 2003 Prof. KingOp Amp Operation w/o Negative Feedback(Comparator Circuits for Analog-to-Digital Signal Conversion)1. Simple comparator with 1 Volt threshold:• V–is set to 0 Volts (logic “0”)• V+ is set to 2 Volts (logic “1”)• A = 1002. Simple inverter with 1 Volt threshold:• V–is set to 0 Volts (logic “0”)• V+ is set to 2 Volts (logic “1”)• A = 100If VIN> 1.01 V,V0= 2V = Logic “1”If VIN< 0.99 V,V0= 0V = Logic “0”V0VIN12012+−V0VIN+−1VVIN12012V0If VIN> 1.01 V,V0= 0V = Logic “0”If VIN< 0.99 V,V0= 2V = Logic “1”+−V0VIN+−1V6Lecture 9, Slide 11EECS40, Fall 2003 Prof. KingOp Amp Circuits with Negative FeedbackQ: How do we know whether an op amp is operating in the linear region?A: We don’t, a priori.• Assume that the op amp is operating in the linear region and solve for voin the op-amp circuit.– If the calculated value of vois within the range from -Vccto +Vcc,, then the assumption of linear operation is valid.– If the calculated value of vois greater than Vcc, then the assumption of linear operation was invalid, and the op amp output voltage is saturated at Vcc.– If the calculated value of vois less than -Vcc, then the assumption of linear operation was invalid, and the op amp output voltage is saturated at -Vcc.Lecture 9, Slide 12EECS40, Fall 2003 Prof. KingOp Amp Circuit Model (Linear Region)vpvnRi+–RovoA(vp–vn)Riis the equivalent resistance “seen” at the input terminals, typically very large (>1MΩ), so that the input current is usually very small:ip= –in≅ 0Note that significant output current (io) can flow when ipand inare negligible!)(0−+−++−≅=++++ccocconpiiiiiiiiipinio7Lecture 9, Slide 13EECS40, Fall 2003 Prof. KingIdeal Op Amp• Assumptions:– Riis large (≥105Ω)– A is large (≥104)– Rois small (<100 Ω)• Simplified circuit symbol:– power-supply terminals anddc power supplies not shown+–+vn–+vp–ipinio+vo–ip= –in=0vp= vnNote: The resistances used in an op-amp circuit must be much larger than Roand much smaller than Ri in order for the ideal op amp equations to be accurate.Lecture 9, Slide 14EECS40, Fall 2003 Prof. KingUnity-Gain Voltage Follower
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