EE 174 Fall 2019 Operational Amplifiers Table of

EE 174 Fall 2019 Operational Amplifiers

Table of Contents • Introduction to Operational Amplifier (Op-Amp) • • Brief of History Op-Amp Internal Circuit Op-Amp: Practical, Ideal, symbol and Characteristics Table Op-Amp: CMRR, Golden Rules Op-Amp: Negative and Positive Feedback Gain and Bandwidth (GBP) Op-Amp: The Four Amplifier Types Common Mode Rejection Ratio (CMRR) • Fundamentals of Op-Amps • • Basic operation Gain Offset CMRR • Applications

Introduction to Op-Amp • Operational Amplifier (Op-Amp for short) which name comes from the early days of amplifier design, when the op amp was used in analog computers to perform various mathematical operations. • Op-Amp is an active circuit element consisting of transistors, resistors, diodes and capacitor. • Op-Amp is two-port networks in which the output voltage or current is directly proportional to either input voltage or current. Four different type of amplifiers exits: • Voltage amplifier (VCVS): Av = Vo / Vi • Current amplifier (ICIS): Ai = Io / Ii • Transconductance amplifier (VCIS): Gm = Io / Vi (Siemens) • Transresistance amplifier (ICVS): Rm = Vo / Ii • Op-Amp is ideal device which takes a relatively weak signal (sensor) as an input and produce a much stronger signal as an output without affecting its other properties. • Op-Amps are commonly used for both linear and nonlinear applications: Inverting/Non-inverting Amplifiers, Variable Gains Amplifiers, Summers, Integrators/Differentiators, Filters and Schmitt trigger, Comparators, A/D converters.

Brief History of Op-Amp Monolithic IC Op-Amp Vacuum Tube Op-Amps (1930’s-1940’s) Solid State Discrete Op-Amps Dual-supply voltage of +300/-300 V (1960’s) Output swing +/- 50 volts Open-loop voltage gain of 15, 000 to 20, 000, Slew rate of +/- 12 volts/µsecond Maximum output current of 1 m. A George Philbrick Dual-supply voltage of +15/-15 V Output swing +/- 11 volts Open-loop voltage gain of 40, 000, Slew rate of +/- 1. 5 volts/µsecond Maximum output current of 2. 2 m. A • First created in 1963 μA 702 by Fairchild Semiconductor • μA 741 created in 1968, became widely used due to its ease of use 8 pin, dual in -line package (DIP) • Further advancements include use of field effects transistors (FET), greater precision, faster response, and smaller packaging

Op-Amp Internal Circuit Compensation Cap Op-Amp 3 -stages: • Differential Amplifier (Blue) • Gain Stage (Magneta) • Output Stage (Cyan) • Current Mirrors/Sources (Red) • Voltage Level Shifter (Green)

Op-Amp: Practical, Ideal, Symbol and Characteristics Table Non-Inverting Input Ouput Inverting Input Parameter Practical Op-Amp Ideal Op-Amp Differential/Open Loop Gain (Aol) 105 - 109 � Common Mode Gain (Acm) 10– 5 0 > 60 d. B � Input Impedance (Ri) (Bipolar-FET) 106 - 1012 � Output Impedance (Ro) 100 -1 kΩ 0 Bandwidth 1 -20 MHz � Slew rate (SR) A few V/µs � Offset Voltage < 10 m. V 0 Offset Current < 50 n. A 0 Common Mode Rejection Ratio (CMRR)

Op-Amp: Common Mode Rejection Ratio (CMRR)

Op-Amp: Voltage Offset

Op-Amp: Current Offset In order to cancel the effects of the bias current in an inverting op-amp configuration, a simple bias compensation resistor, R 3, (R 3=R 1||R 2) can be used to introduce a voltage drop in the non-inverting input to match and thus compensate the drop in the parallel combination of R 1 and R 2 in the inverting input. This minimizes additional offset voltage error. VO = R 2 (IB– – IB+) = R 2 IOS = 0, If IB+ = IB– (well-matched) Neglecting VOS

Op-Amp Offset Example Fig #1 Fig #2

Op-Amp: Gain and Bandwidth Example: For closed loop gain 70 d. B. What is closed-loop BW? Gain: 20 log(Acl)= 70 d. B log (Acl)= 70/20 = 3. 5 or Acl = 103. 5 = 3162 Closed-loop BW: fcl = f. T /Acl = 1 MHz / 3162 = 316. 3 Hz. Vi + V V+ + Open loop gain: Gain is measured when no feedback is applied to the op amp. Open-loop gain (Aol) is very high. Loop gain: The difference between the open-loop gain and the closed-loop gain. This is useful information because it gives you the amount of negative feedback that can apply to the amplifier system. Gain versus Bandwidth: Applying feedback will reduce the gain but increase the bandwidth. Gain-bandwidth (GBW) product is defined as the op-amp gain A multiplied by the bandwidth (BW). The product of the gain and bandwidth are constant. Acl fcl = Aol fol The GBW product is also equal to the unity gain frequency f. T = Acl fcl = f. T /Acl where f. T is the unity-gain bandwidth. V 0 A = 105, BW = 10 Hz, GBW = 105 x 10 Hz = 1 MHz A = 1, BW = 1 MHz, V 0 GBW = 1 x 1 MHz = 1 MHz

Op-Amp Slew Rate SR = 0. 63 V/ µs. Fig. 1 Fig. 2

Op-Amp: The Four Amplifier Types Description Gain Symbol Transfer Function Voltage Amplifier or Voltage Controlled Voltage Source (VCVS) Av Vout/Vin Current Amplifier or Current Controlled Current Source (ICIS) Ai Iout/Iin Transconductance Amplifier or Voltage Controlled Current Source (VCIS) gm (siemens) Iout/Vin Transresistance Amplifier or Current Controlled Voltage Source (ICVS) rm (ohms) Vout/Iin

Op-Amp: Four Amplifier Types

Op-Amp: Golden Rules vd = v+ – v– vo = Avd = A (v+ – v–) + Vd – 1. i+ = i – = 0 (Since Ri = �. This is always true for any feedback configuration). 2. v+ = v– (In negative feedback, the output of the op amp will try to adjust its output so that the voltage difference between the + and − inputs is zero V+ = V−). Rule 2. is not applied if VO in saturation. 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.

Op-Amp: Negative and Positive Feedback Negative feedback: Vout = A(V+ – V–) = A(Vin – Vout) If Vout > Vin Vout ↓ goes down toward Vin If Vout < Vin Vout ↑ goes up toward Vin This drives Vout = Vin or V+ = V Negative feedback Op-Amp can produce any voltage in the supply power range. Negative feedback: Positive feedback: Vout = A(V+ – V–) = A(Vout – Vin) If Vout > Vin Vout ↑ goes way up to + saturation If Vout < Vin Vout ↓ goes way down to – saturation This drives Vout to either directions: + / – saturation Positive feedback Op-Amp can only produce maximum and minimum voltages of the range. Positive feedback:

Op-Amp: Non-inverting Negative Feedback

Op-Amp: Inverting Negative Feedback Virtual Ground

Op-Amp: Saturation The op-amp output voltage is limited by the supply voltages. In practice the limits are about 1. 5 to 2 V below the value of the supply voltages. The op amp has three distinct regions of operation: • Linear region: −VEE < Vo < VCC Vo/Vi = A = constant • Positive saturation: Vo > VCC Vo = VCC • Negative saturation: Vo < −VEE Vo = –VEE Note that the saturation voltage, in general, is not symmetric. For an amplifier with a given gain, A, the above range of Vo translate into a certain range for Vi − VEE < Vo < VCC or − VEE < A Vi < VCC − VEE / A < Vi < VCC / A Any amplifier will enter its saturation region if Vi is raised above certain limit. The figure shows how the amplifier output clips when amplifier is not in the linear region. Example: For A = 105, –VDD = – 12 V, VCC = +15 V, find range of input Vi to prevent saturation. Solution: – 12 V / 105 < Vi < 15 V / 105 or – 0. 12 m. V < Vi < 0. 15 m. V

Op-Amp: Two Basic Op-Amp Configurations Negative feedback is when the occurence of an event causes something to happen that counteracts the original event. In negative-feedback configuration, op-amp always “wants” both inputs (inverting and non-inverting) to be the same value. The Non-Inverting Op Amp The Inverting Op Amp When Rf = 0 and R 1 = ∞, the non-inverting amplifier becomes a voltage follower or unity gain buffer (gain Acl = 1). This configuration offers very high input impedance and its very low output impedance. Vi V+ V– Vo

Op-Amp: Top Op-Amp Application Configurations Differential Amplifier Converter current – voltage Non-inverting Summing Amplifier Negative resistance Inverting Summing Amplifier Intrumentation two op-amps to buffer the input signals and a third to cancel out the commonmode noise.

Op-Amp: Op-Amp Circuits The Howland Current Pump Circuit IR = Vi/2 R IO = IS + IR Ballanced Differential Amplifier #1 #2 VL (V) Vo (V) I 1 (m. A) I 2 (m. A) IL (m. A) 2 4 0 -2 2 1 2 -1 -1 2 0 0 -2 0 2 -1 -2 -3 -1 2 -2 -4 -4 -2 2

Op-Amp: Top Op-Amp Application Configurations Example: (a) For LPF with gain, find suitable components to achieve a − 3 -d. B frequency of 1 k. Hz with a dc gain of 20 d. B and an input resistance of at least 10 kΩ (b) At what frequency does gain drop to 0 d. B?

Op-Amp: Op-Amp Circuits (a) Find i, if and vo. i=0 A (b) For the ideal op amp shown below, what should be the value of resistor Rf to obtain a gain of 5? V+

Op-Amp: Op-Amp Circuits (a) Given an op-amp circuit below. If the power supplies for the op-amp are ± VCC = ± 12 V. Determine: a. Overall gain A = VOUT / VIN, VOUT and IOUT. b. If op-amp in saturation, what is voltages at V+ and V-.

Op-Amp: Op-Amp Circuits (a) Given gain A 1 = RF/RS = 100, 741 Op-Amp GBW product = A 0 ω0 = K = 2π × 106. Determine the overall 3 -d. B bandwidth of the cascade amplifier below: (b) Voltage follower application: Solutions: Given Rs = 1 kΩ, RL = 100Ω For source and load connected directly: VL = 0. 1 Vin Huge attenuation of the signal source. For source and load connected via voltage follower (buffer amplifier): VL = Vp = Vin

(1) Find Vx , Vo Op-Amp: Op-Amp Circuits (3) Find Vy , Vo Vx = 3. 2 V Vo = -11. 2 V (2) Find Vx , Vo Vy = 3/2 Vo Vo = -11. 4 V (4) Find Vo Vx = 0. 5 Vo Vo = 0. 8 Vi v+= v-= 6 V

Basic Comparators • An ideal comparator compares two input voltages (inverting and noninverting input) and produces an output indicating the relationship between them. If V+ > V– Vout is HIGH If V+ < V– Vout is LOW • The inputs can be two signals (V 1, V 2) or an input signal (Vin) and a fixed dc reference voltage (Vref). The output that usually swings from rail to rail. • A typical comparator has low offset, high gain, and high common-mode rejection. • Comparators are designed to work as open-loop systems, to drive logic circuits, and to work at high speed, even when overdriven. • The voltage at which a comparator changes from one level to another is called the crossover (or threshold) voltage. • The output logic voltages can be symmetrical or asymmetrical depends on the digital logic requirements. Symmetrical Assymmetrica

Basic Comparators Non-Inverting zero-crossing (Vref = 0 V) comparator Non-Inverting non-zero reference (Vref ≠ 0 V) comparator Inverting zero-crossing (Vref = 0 V) comparator Inverting non-zero reference (Vref ≠ 0 V) comparator

Basic Schmitt Comparator Schmitt trigger uses positive feedback: • When op-amp output VO rises then (V+ − V−) will increase. This causes output to positive saturation VO = +Vsat. • If VO = +Vsat = +15 V, then Vf = 5 V. For any Vi < 5 V, then (V+ − V−) > 0 output stays at +Vsat VO = +15 V. • If Vi > 5 V, then (V+ − V−) < 0 output switch to its minimum value or negative saturation VO = −Vsat = − 15 V. • If VO = −Vsat = − 15 V, then Vf = − 5 V output will only switch back to VO = +Vsat = +15 V when Vi < − 5 V. Notes: • Negative feedback stabilizes the output to make V+ ≃ V−. • Positive feedback adjusts the output to maximize |V+ − V−|. Output will switch between its maximum and minimum values, e. g. ±Vsat. • Switching will happen when V+ = V−.

The Comparators w/o and w/Hysteresis – Single power supply Noise or signal variation at the comparison threshold will cause multiple transitions. Hysteresis sets an upper and lower threshold to eliminate the multiple transitions caused by noise.

Design of Hysteresis Comparator Equations (1) and (2) can be used to select the resistors needed to set the hysteresis threshold voltages V H and VL. Rh VL = Rx V H – VL (1) Ry VL Rx = VCC – VH (2) Example: The design requirements are as follows: • Supply Voltage: +5 V • Input: 0 V to 5 V • VL (Lower Threshold) = 2. 3 V • VH (Upper Threshold) = 2. 7 V • VH – VL = 0. 4 V • Vth ± 0. 2 V = 2. 5 V ± 0. 2 V • Equations (1) and (2) can be used to select the resistors needed to set the hysteresis threshold voltages VH and VL. • One value (RX) must be arbitrarily selected. In this example, Rx was set to 100 kΩ to minimize current draw. • Rh was calculated to be 575 kΩ, so the closest standard value 576 kΩ was used

When To Use Op-amp Comparator Circuit? ? ? Although op amps are not designed to be used as comparators, there are, nevertheless, many applications where the use of an op amp as a comparator is a proper engineering decision. WHY USE AN OP AMP AS A COMPARATOR? • Convenience • Economy (e. g. use spare op-amps in quad package and cheaper than comparator) • Low bias current (IB) • Low offset voltage (VOS) Note: This is not a good design practice. WHY NOT USE AN OP AMP AS A COMPARATOR? • Speed • Inconvenient input structures (Comparator is designed for large differential input voltages) • Inconvenient logic structures (Compartor TTL, CMOS) • Stability/hysteresis (stability)

References: • https: //www. analog. com/media/en/training-seminars/tutorials/MT-038. pdf • http: //www. ume. gatech. edu/mechatronics_course/Op. Amp_F 08. ppt • http: //www. allaboutcircuits. com/textbook/semiconductors/chpt-8/operational-amplifier-models/ • http: //www. ti. com/lit/an/slaa 068 a. pdf • http: //www. radio-electronics. com/info/circuits/opamp_basics/operational-amplifier-slew-rate. php • http: //www. planetanalog. com/author. asp? section_id=483&doc_id=562347 • http: //www-ferp. ucsd. edu/najmabadi/CLASS/ECE 60 L/02 -S/NOTES/opamp. pdf • http: //www-inst. eecs. berkeley. edu/~ee 105/fa 14/lectures/Lecture 06 -Non-ideal%20 Op%20 Amps%20(Offset. Slew%20 rate). pdf • http: //nptel. ac. in/courses/117107094//lecturers/lecture_6/lecture 6_page 1. htm • http: //www. ti. com/ww/en/bobpease/assets/AN-31. pdf • http: //www. cs. tut. fi/kurssit/TLT-8016/Chapter 2. pdf • http: //www. electronics-tutorials. ws/opamp/op-amp-comparator. html • http: //hyperphysics. phy-astr. gsu. edu/hbase/electronic/schmitt. html • http: //lpsa. swarthmore. edu/Bode. Examples. html

References: http: //www. allaboutcircuits. com/worksheets/inverting-and-noninverting-opamp-voltage-amplifier-circuits/ Fundamentals of Electrical Engineering, Giorgio Rizzoni, Mc. Graw-Hill Higher Education http: //chrisgammell. com/how-does-an-op-amp-work-part-1/ http: //electronicdesign. com/analog/whats-all-noise-gain-stuff-anyhow http: //howtomechatronics. com/how-it-works/electrical-engineering/schmitt-trigger/ http: //www. analog. com/media/en/training-seminars/design-handbooks/Basic-Linear-Design/Chapter 1. pdf http: //www. ti. com/lit/an/sloa 011. pdf http: //www. analog. com/media/en/technical-documentation/application-notes/AN-849. pdf http: //www. ti. com/lit/ug/tidu 020 a. pdf https: //en. wikipedia. org/wiki/Instrumentation_amplifier https: //www. tubecad. com/2012/07/blog 0238. htm https: //www. allaboutcircuits. com/technical-articles/the-howland-current-pump/

Top Fundamental Op Amp Circuits Inverting Amplifier Differential Amplifier Voltage Follower / Unity Gain Buffer Non-inverting Amplifier Non-inverting Summing Amplifier Inverting Summing Amplifie Vo Vo https: //www. arrow. com/en/research-and-events/articles/fundamentals-of-op-amp-circuits