Lecture 9 with Prof Neureuther ANNOUNCEMENT 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 circuit Reading Chapter 5 1 5 2 EECS40 Fall 2003 Lecture 9 Slide 1 Prof King Solution to Superposition Example Find Vo 24 V 4V 2 4 Vo Vo Vo Vo 8V 4A Find contribution of 24 V source Vo 2 24V Find contribution of 4 A source 4 Vo 2 Vo 4V i 4 4 24V 16V 2 4 EECS40 Fall 2003 4A 2 4 i 4A A 2 4 3 16 Vo i 4 V 3 Lecture 9 Slide 2 Find contribution of 4 V source 2 4 Vo Vo 4 8 4V V 2 4 3 Prof King 1 Final Comment on Th venin 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 RTh Calculation Example 2 Lecture 8 ITEST Vx VTEST Vx VTEST 40i 20 60 VTEST RTh Applying KCL to node x Vx 40i V V i x TEST 0 16 20 Vx Definition of i i 80 EECS40 Fall 2003 Vx VTEST 75 I TEST 4 8 VTEST 25 Lecture 9 Slide 3 Prof King The 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 signal A commonly used op amp is the 741 You will use these in the EECS40 lab next week EECS40 Fall 2003 Lecture 9 Slide 4 Prof King 2 Op Amp Circuit Symbol and Terminals V non inverting input inverting input positive power supply output V negative power supply The output voltage can range from V to V The positive and negative power supply voltages do not have to be equal in magnitude EECS40 Fall 2003 Lecture 9 Slide 5 Prof King Op Amp Terminal Voltages and Currents All voltages are referenced to a common node Current reference directions are into the op amp V ic ip vp in vn io icV vo Vcc Vcc common node external to the op amp EECS40 Fall 2003 Lecture 9 Slide 6 Prof King 3 Op Amp Voltage Transfer Characteristic vo The op amp is a differentiating amplifier Vcc slope A 1 vp vn Vcc Regions of operation negative saturation positive saturation linear In the linear region vo A vp vn where A is the open loop gain Typically Vcc 20 V and A 104 linear range 2 mV vp vn 2 mV Thus for an op amp to operate in the linear region vp vn i e there is a virtual short between the input terminals EECS40 Fall 2003 Lecture 9 Slide 7 Prof King Achieving a Virtual Short Recall the voltage transfer characteristic of an op amp Plotted using different scales for vo and vp vn Plotted using similar scales for vo and vp vn vo vo Vcc slope A 1 10 V vp vn Vcc Vcc slope A 1 10 V vp vn Vcc 1 mV 10 V 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 vn to decrease and hence vo to decrease until the op amp operates in its linear region EECS40 Fall 2003 Lecture 9 Slide 8 Prof King 4 Negative vs Positive Feedback Familiar examples of negative feedback Thermostat controlling room temperature Driver controlling direction of automobile Photochromic lenses in eyeglasses Fundamentally pushes toward stability Familiar examples of positive feedback Microphone squawk in sound system Mechanical bi stability in light switches Thermonuclear reaction in H bomb EECS40 Fall 2003 Fundamentally pushes toward instability or bi stability Lecture 9 Slide 9 Prof King Op 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 100 VIN V0 V0 2 1 If VIN 1 01 V V0 2V Logic 1 0 1 1V 2 VIN If VIN 0 99 V V0 0V Logic 0 2 Simple inverter with 1 Volt threshold V is set to 0 Volts logic 0 V is set to 2 Volts logic 1 A 100 V0 1V V0 2 1 0 1 If VIN 0 99 V V0 2V Logic 1 2 VIN If VIN 1 01 V V0 0V Logic 0 VIN EECS40 Fall 2003 Lecture 9 Slide 10 Prof King 5 Op Amp Circuits with Negative Feedback Q 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 vo in the op amp circuit If the calculated value of vo is within the range from Vcc to Vcc then the assumption of linear operation is valid If the calculated value of vo is 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 vo is less than Vcc then the assumption of linear operation was invalid and the op amp output voltage is saturated at Vcc EECS40 Fall 2003 Lecture 9 Slide 11 Prof King Op Amp Circuit Model Linear Region vp Ri is the equivalent resistance seen at the input terminals typically very large 1M so that the input current is usually very small ip ip in 0 Ro Ri A v v p n vn in io vo i p in io ic ic 0 io ic ic Note that significant output current io can flow when ip and in are negligible EECS40 Fall 2003 Lecture 9 Slide 12 Prof King 6 Ideal Op Amp Assumptions Ri is large 105 A is large 104 Ro is small 100 ip in 0 vp vn Simplified circuit symbol power supply terminals and dc power supplies not shown Note The resistances used in an op amp circuit must be much larger than Ro and much smaller than Ri in order for the ideal op amp equations to be accurate EECS40 Fall 2003 ip in vp io vo vn Lecture 9 Slide 13 Prof King Unity Gain Voltage Follower Circuit VIN vn vp IIN V0 V V0 vp vn V0 VIN 2 1 1 2 VIN V valid as long as V V0 V Note that the analysis of this simple but important circuit required only one of the ideal 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