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CE2004 II‐1 : Operational Amplifiers (Op-Amps)

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CE2004 II‐1 : Operational Amplifiers (Op-Amps) CE2004 II‐1 : Operational Amplifiers (Op-Amps) Weisi Lin Email: [email protected] School of Computer Science and Engineering Nanyang Technological University Singapore CE 2004 – Circuits & Signal Analysis 1 Major Topics of Part 2 • Principles of Op‐Amps • General Signals & Systems • Laplace Transform & frequency‐based system analysis Important Concepts, Logic & Methodology (Principles of Op-Amps) Introduction to Op-Amps (operational amplifiers) Concept of Negative Feedback Two Commonly-used Circuits with Negative Feedback oNon-Inverting Amplifiers oInverting Amplifiers Recap/Summary CE 2004 – Circuits & Signal Analysis 3 We are starting to talk about amplifiers. What is an ideal amplifier? Considerations: Voltage gain Input impedance Output impedance CE 2004 – Circuits & Signal Analysis 4 First op amps built in 1934 Invented by a Bell engineer named Harry Black* Didn’t gain the name operational amplifier until the computer age began a decade or so later Vacuum Tube Op-Amps Vacuum Tube Op-Amps Used in WWII to help to strike military targets - Buffers, summers, differentiators, inverters Took ±300V to ± 100V to power Transistors replaced vacuum tubes in 1950’s Integrated circuits (ICs) invented in the 1960’s, op amps were among the first chips to be designed. *In 1934，Harry Black commuted from his home in New York City to work at Bell Labs in New Jersey by way of a railroad/ferry. The ferry ride relaxed Harry enabling him to do some conceptual thinking… CE 2004 – Circuits & Signal Analysis 5 Introduction to Operational Amplifiers (Op-Amps) Op-amp is a high gain amplifier having (nearly ideal): - Very high voltage gain (104 to 106) - Very high input impedance (typically a few more megohms) explanations in the next - Low output impedance (less than 100 ohm). pages. An op-amp consists of multi-stage transistor amplifier fabricated in an integrated circuit (IC) form. CE 2004 – Circuits & Signal Analysis 6 Internal Circuitry of the Standard 741 Op-Amp Positive DC power supply An IC consisting of transistors resistors capacitors Negative DC power supply CE 2004 – Circuits & Signal Analysis 7 A voltage source followed by an amplifier (very different from Vs) Loading effect if minimization: input impedance of an i.e, amplifier should be much With the same Rs, greater (infinite for an ideal case) than the (similar to V ) CE 2004 – Circuits & Signal Analysis s source impedance. 8 An amplifier followed by another amplifier For amplifier #1: Loading effect minimization: input impedance of Amplif#2 similar analysis as in should be much greater the previous page (infinite for an ideal case) than output impedance of Amplif#1. if Zi2 >>Zo1 CE 2004 – Circuits & Signal Analysis 9 Typical Uses of Op-Amps: Voltage amplifiers, Oscillators, Filter circuits, Instrumentation circuits, and so on. Op-Amp Equivalent Circuit V (see next CC page) As represented in the previous pages V+ ZOUT ZIN Vout V- Zout Vo=AoVin VEE Vin Zin ~ AdVd Vout CE 2004 – Circuits & Signal Analysis 10 Input port: Modeled as a resistance of value ZIN . (Very large, typically 106 ). The input v is known as non-inverting input and v is the inverting input. Output port: Modeled as a dependent voltage source, vo in series with a resistance ZOUT .( is very small, ZOUT typically 100 ). Two DC power supplies: VCC (+ve) and VEE (‐ve). The use of positive and negative voltage allows the output of the op‐amp to swing in both directions. CE 2004 – Circuits & Signal Analysis 11 Input-Output Relationship: Vout Ao (v v ) ‐Ao is the internal voltage gain (open loop voltage gain) of the op‐amp. 4 6 ‐ Typically, Ao will have values 10 to10 (very high) Output Saturation Limits vo can never exceed the op‐amp’s power supply voltages, VCC and (saturation limits of VEE vo ) . VEE Ao(v v) VCC CE 2004 – Circuits & Signal Analysis 12 Voltage transfer characteristics of an op-amp Vout Positive saturation VCC= +15V VCC Linear, i.e., Vo=Ao(Vin) Vin=(V+)–(V-) V V = -15V Negative saturation EE EE Linear region . The slope of linear region is big (Why?) CE 2004 – Circuits & Signal Analysis 13 Op-Amps 1.The saturation limits ofvo are equal to the op-amp supply voltagesVCC andVEE. 2.The gainAo is so high(Ao ) that a very small nonzero value of differential input(v v ) drivesvo to saturation (non linear operation). 3.(v v ) positive vo will saturate at its positive saturation limit VCC . 4.(v v ) negative vo will saturate at its negative saturation limit VEE. VCC V+ ZOUT ZIN Vout V- VEE CE 2004 – Circuits & Signal Analysis 14 5.For linear operation, the differential input voltage (v v ) must be close to zero (very small). 6.The internal input resistance Z IN . Hence the input currents (in +ve and –ve terminals) are assumed to be zero. 7.The internal output resistance ZOUT 0. Hence Vout Vo. Q: What is the main concern in using op-amp as a linear device? A: Saturates for a small Vin. Q: How do we get rid of this problem, and also obtain the desired voltage gain? VCC A: Negative Feedback V+ ZOUT ZIN Vout V- V CE 2004 – Circuits & Signal Analysis EE 15 Harold Stephen Black (April 14, 1898 – December 11, 1983) invented the negative feedback amplifier while he was a passenger on the Lackawanna Ferry (from Hoboken Terminal to Manhattan) on his way to work at Bell Laboratories (located in Manhattan instead of New Jersey in 1927) on August 2, 1927 (US Patent 2,102,671, issued in 1937)— obviously he was thinking while taking ferry. His invention is considered as an important breakthrough of the 20th century in electronics, since it has a wide area of applications. On August 8, 1928, Black submitted his invention to the U. S. Patent Office, which took more than 9 years to issue the patent. The patent office was inundated with fraudulent “perpetual motion” (motion of bodies that continues indefinitely) claims, and dismissed Black’s invention at first sight. Black later wrote: "One reason for the delay was that the concept was so contrary to established beliefs that the Patent Office initially did not believe it would work.” CE 2004 – Circuits & Signal Analysis 16 Concept of Negative Feedback In negative feedback, the output signal (or part of it) is connected back (feedback) to the negative input terminal of an op-amp. Summing Amplifier Node VM VO InputAo Output + - VR output/K (to “‐” terminal) 1/K Vo (VM VR )Ao (VM Vo / K)Ao CE 2004 – Circuits & Signal Analysis 17 Ao K Ao Vo 1 VM Ao Vo VM Ao K K VM Ao Vo K Ao K K Vo VM Ao K Ao K (As Ao K , VM Ao Ao Ao K Ao) Vo=K VM CE 2004 – Circuits & Signal Analysis 18 Negative feedback reduces the closed loop gain to K （this is under the condition that Ao is very high; notice that K is not related to Ao.） Using resistors (as to be illustrated with non-inverting & inverting Op-Amps next) to obtain appropriate value of K such that the output will not reach the saturation limits. Thus, negative feedback ensures linear operation of op- amps, and also yield the required voltage gain. CE 2004 – Circuits & Signal Analysis 19 A question for you to think while we move on… Why are op-amps designed with very high Ao, while the required voltage gain of amplifiers is much lower in practice (so we use negative feedback to reduce the gain and ensure linear operation)? Why not to design op-amps with a lower Ao? Hint: thinking along the flexibility provided to users and benefits to manufacturers. CE 2004 – Circuits & Signal Analysis 20 The Op-amp Golden Rules – with Nagative Feedback Circuits 1.Voltage Rule: Through negative feedback, the output attempts to do whatever is necessary to make the voltage difference between the inputs zero. In a negative feedback op-amp, V+ -V- ≈ 0 (very small). 2. Current Rule: The inputs draw no current, due to the very high input impedance of the op-amp. The input current is so low (0.08 microamps for the standard 741 op-amp). CE 2004 – Circuits & Signal Analysis 21 Linear (not saturated) Op-Amp Circuits V+ 1. Non-Inverting Amplifier VIN + V is applied to the +ve input VOUT IN V terminal of the op-amp. - _ R1 ApartofVO is fed back to the A way to –ve terminal of the op-amp. R2 materialize the negative feedback How does negative feedback concept presented help? previously. If a +ve voltage* is applied to VIN : (V V ) will increase VOU will increase. T *Similar analysis for a -ve voltage case. CE 2004 – Circuits & Signal Analysis 22 •A part ofVOUT is fed back to theV terminal. (Determined by the voltage divider resistors R1 and R2). R2 V VOUT (1) R1 R2 • V increases ( V V ) decreases V OU T decreases. i.e., due to negative feedback,(V V ) is decreased, and thenVOUT is decreased. CE 2004 – Circuits & Signal Analysis 23 •Equilibrium condition V OUT forces ( V V ) to a very small value VOUT will not reach the saturation limits. • Op-Amp golden voltage rule: Input difference voltage is very small Approximated as zero (practically, small non-zero). V V (2) Applying (2) in (1): R2 V VOUT VIN (3) R1 R2 Closed loop-gain, A V: VOUT (R1 R2) R1 Av 1 (4) VIN R2 R2 CE 2004 – Circuits & Signal Analysis 24 Significant Parameters of Non-Inverting Op-Amps ●A V will be always ≥ 1. ●VOUT is always in phase with VIN (i.e., with same polarity, or non-inverting). CE 2004 – Circuits & Signal Analysis 25 Non-Inverting Op-Amps since V+=V- Input impedance: ZIN is very high.
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