# Ppt on op amp circuits equations

##### Lectures Week 8 The operational amplifier (“op amp”) Feedback

vp = vn ip + – io + vp – in + vo – 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. + vn – EE 42/100 Fall 2005 Week 8, Prof. White Unity-Gain Voltage-Follower Circuit +  VIN vn V0(V) VIN(V) 1 2 IIN vp vp = vn  V0 = VIN/

##### Lecture 3 Circuits and Electronics Chapter 3 and Notes Intro to basic circuits principles Passive, active circuits; circuit laws Filters Op amps (ideal,

discharge equation Electronic circuits - Overview Semiconductors such as Si and Ge Diode: current in one direction Come up with one or two applications of diodes Transistor: amplifies current (current in the collector-emitter path is amplified version of the current in the base) Use of a transistor to amplify audio sound: interface a microphone and a loud speaker Operational amplifier Ideal op amp, Real op amp/

##### PARISUTHAM INSTITUTE OF TECHNOLOGY AND SCIENCE DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING II YEAR/ III SEMESTER LINEAR INTEGRATED CIRCUITS AND.

.A linear system can be described by (a) state transition cavation (b) differential equation (c) dynamic equation (d) none of the above 37.At which of the following frequency, the gain of op-amp will be zero? (a) β cut-off frequency (b) α cut-off frequency/ all of the above 55.Thermal drift of op-amp parameters (a) forced air cooling only (b) careful printed circuit board layout (c) both a and b (d) keep op-amp away from source of heat 56.AC characteristics of op-amp includes (a) Frequency response (b) slew /

##### Stability – 1 TI Precision Labs – Op Amps Developed by Collin Wells, Art Kay, and Ian Williams 1.

Multiple-Choice Quiz 24 What are some possible signs of an unstable op amp circuit? a)oscillations b)large overshoot and ringing c)unpredictable or unexpected response d)all of the above Many common circuits inadvertently cause delay in the feedback network, resulting in stability issues. a/& C LOAD Pole: R O, R ISO, and C LOAD Z1Z1 Z2Z2 Vin Method 1: R ISO – Theory 53 Transfer Function: Zero Equation: Pole Equation: Method 1: R ISO – Theory X A OL (from data sheet)A OL Load Loaded A OL = 54 Method 1: R ISO/

##### EE 174 Spring 2016 Operational Amplifiers. Contents Introduction Brief of History Fundamentals of Op-Amps Basic operation Gain Offset Applications.

Op-Amp Circuits +V 2 : Non-inverting input -V 1 : Inverting input +V s : Positive source PS -V s : Negative source PS V out : Output voltage ON: Offset Null NC: Not Connected Op-Amp Ideal, Equivalent Circuit, Characteristics and Features Ideal Op-Amp Op-Amp Equivalent Circuit Op-Amp Symbol Op-Amp Characteristics 741 Op-Amp/ the dc output voltage is zero when the input signals are zero. (b). The output voltage equation is valid for both ac and dc input signals. The output voltage is given by Thus the /

##### ELECTRIC CIRCUITS EIGHTH EDITION JAMES W. NILSSON & SUSAN A. RIEDEL.

unity-gain low-pass filters. (a) The block diagram (b) The circuit © 2008 Pearson Education 15.4 Higher Order Op Amp Filters   The transfer function of an nth–order Butterworth low-pass filter with a cutoff frequency of 1 rad/s can be determined from the equation: © 2008 Pearson Education 15.4 Higher Order Op Amp Filters By  Finding the roots of the denominator polynomial.  Assigning/

##### Chapter 1 Introduction to Electronics

, and infinite input resistance. These conditions lead to two assumptions useful in analyzing ideal op amp circuits: 1. The voltage difference across the input terminals is zero. 2. The input currents are zero. Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Microelectronic Circuit Design Ideal Op Amp Example Writing a loop equation: From assumption 2, we know that i- = 0. Assumption 1 requires v- = v+ = 0/

##### EC303 – LINEAR INTEGRATED CIRCUITS

Frequency synthesizer FM detector Active Filters Active filters use op-amp(s) and RC components. Advantages over passive filters: op-amp(s) provide gain and overcome circuit losses increase input impedance to minimize circuit loading higher output power sharp cutoff characteristics can be /is 150 mA Dropout voltage is 3 V (i.e. VCC > Vo(max) + 3) LM723 in High-Voltage Configuration Design equations: Choose R1 + R2 = 10 kW, and Cc = 100 pF. External pass transistor and current sensing added. To make Vo /

##### REVIEW. The Equivalent Circuit of the Op-Amp Parameters of Typical Range vs Ideal Values of the Op Amp v d = v 2 - v 1 v o = Av d = A(v 2 – v 1 ) Typical.

d = v 2 - v 1 v o = Av d = A(v 2 – v 1 ) Typical Op- Amp circuits Non-inverting Summing Amp From this frequency response curve we can see that the product of the gain against frequency is constant at any point along the curve. / error of an ideal ADC is half of the step size. Number of bits N: The higher is the number of bits, the more precise is the digital output. ADC EQUATIONS V in = input voltage, V ref+ = ref voltage, V ref- = 0 V, (Note: V ref = V FS ) N = number of bits of precision output_code = V/

##### Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard C. Jaeger Travis N. Blalock Modified by Ming Ouhyoung Microelectronic Circuit.

voltage gain, and infinite input resistance. These conditions lead to two assumptions useful in analyzing ideal op-amp circuits: 1. The voltage difference across the input terminals is zero. 2. The input currents are zero. Microelectronic Circuit Design, 4E McGraw-Hill Chap 1 - 46 Ideal Op Amp Example Writing a loop equation: From assumption 2, we know that i - = 0. Assumption 1 requires v - = v + = 0. Combining/

##### Solving Op Amp Stability Issues Part 3 (For Voltage Feedback Op Amps) Tim Green & Collin Wells Precision Analog Linear Applications 1.

Inverting and Noise Gain Non-Inverting (Output Cload) Original Circuit: Transient Response 59 Noise-Gain Compensation Circuit Configurations Non-Inverting: Inverting: Noise-Gain Circuit Equations 61 1/β Transfer Function: DC 1/β Magnitude: 1/Beta Pole Frequency: 1/Beta Zero Frequency: => Solve for CN The op amp equivalent input capacitance, CI, has been left out of these equations to simplify them. If CI and RF||RI are causing/

##### Solving Op Amp Stability Issues Part 4 (For Voltage Feedback Op Amps) Tim Green & Collin Wells Precision Analog Linear Applications 1.

Inverting and Noise Gain Non-Inverting (Output Cload) Original Circuit: Transient Response 15 Noise-Gain Compensation Circuit Configurations Non-Inverting: Inverting: Noise-Gain Circuit Equations 17 1/β Transfer Function: DC 1/β Magnitude: 1/Beta Pole Frequency: 1/Beta Zero Frequency: => Solve for CN The op amp equivalent input capacitance, CI, has been left out of these equations to simplify them. If CI and RF||RI are causing/

##### Solving Op Amp Stability Issues Part 2

45 degrees phase margin at unity gain Control Loop - Second Order System The traditional second order system control loop block diagram and characteristic equation are shown above. G(s) for us represents our closed loop, 2-pole dominant, op amp circuit. There are well established, documented, and derived behaviors for such a 2-pole dominant system that we can use to help us assess/

##### Solving Op Amp Stability Issues Part 2 (For Voltage Feedback Op Amps) Tim Green & Collin Wells Precision Analog Linear Applications 1.

these designs. The internationally acknowledged authority on electronic amplifiers wrote five very popular books about op amps, the latest being Photodiode Amplifiers: Op Amp Solutions and Optimizing Op Amp Performance. The latter, subtitled "A new approach for maximizing op amp behavior in circuit designs without extensive mathematical analysis," offers design equations and models that reflect real-world op amp behavior and makes analysis of difficult-looking configurations easy. Graemes earlier books are/

##### ACADs (08-006) Covered Keywords Switching power supply, amplifier, logic, digital, circuit, solid state. Description Supporting Material 5.1.12.1.12e5.4.1.15.4.1.2.

Effect Transistor (FET) circuit. 1.1.21 Describe Integrated Circuit (Op Amp) device design and application. 1.1.22 Build/test/analyze integrated (Op Amp) circuits. 1.1.23 Describe Digital Logic symbols and truth tables. 1.1.24 Describe Fiber Optic circuit device design and / By assuming that the two input terminals are at the same potential and using Kirchhoff Current law for a series circuit. 2. We can write the equation for current through Rf and Ra as follows: Vout -Vin / Ra =Vin- 0/Rf We can therefore/

##### ENGR-43_Lec-04_Op-Amps.ppt 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE Licensed Electrical.

Amps.ppt 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Engineering 43 Chp 4 Op Amp Circuits BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 2 Bruce Mayer, PE Engineering-43: Engineering Circuit/BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 38 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Required Draw The Linear Equivalent Circuit Write The Loop Equations 1.Locate Nodes + - o/

##### OPERATIONAL AMPLIFIERS. OPERATIONAL AMPLIFIERS (OP-AMP) The standard operational amplifier (op-amp) symbol is shown in Figure 12-1(a). It has two terminals,

Differential Amplifier A basic differential amplifier circuit and its symbol are shown in Figure 12-4. The diff-amp stages that make up part of the op-amp provide high voltage gain and common-mode rejection. Notice that the differential amplifier has two outputs where an op-amp has only one output. Modes/0 to 50 A. The interbase resistance RBB is the resistance of the device between terminals B1 and B2 when IE is 0. In equation form; R BB = (R B1 + R B2 ) IE = 0 (RBB is typically within the range of 4 to 10 /

##### Licensed Electrical & Mechanical Engineer

shown explicitly But they MUST physically be there to actually Power the Operational Amplifier OpAmp Circuit Model DRIVING CIRCUIT LOAD OP-AMP vi→vo Transfer Characteristics Linear Region vo/vi = Const Saturation The OUTPUT Voltage Level /Circuit Using Linear Model For Op-Amp Example Required Draw The Linear Equivalent Circuit Locate Nodes Write The Loop Equations + - o v R i O Locate Nodes Place the nodes in linear circuit model Example cont Add Remaining Components to Complete Linear Model Examine Circuit/

##### ELEC 2005 ELEC-2005 Electronics in High Energy Physics Spring term: Integrated circuits and VLSI technology for physics Basic Analog Design Giovanni Anelli.

CONFIGURATION INVERTING CONFIGURATION BUFFER The above equations are valid only if the gain A 0 of the op amp is very high! ELEC 2005Giovanni Anelli - CERN22 Single-stage Op Amp V DD I SS T1T1 T2T2 /SMALL PMLARGE PM ELEC 2005Giovanni Anelli - CERN33 Frequency Compensation Single-pole op-amps would always be stable (the phase does not go below - 90  ). But a typical op-amp circuit always contains several poles (and zeros!). These op- amps can easily be unstable, and they need therefore to be compensated./

##### Overview of ENGR 220 Circuits 1 Fall 2005 Harding University Jonathan White.

computers Basis for analog computers OP Amp Questions What is V o equal to in the circuit below? What is V o equal to in the circuit below? AC Circuits Introduction Sine waves, frequency, period Sine waves, frequency, period RMS values of voltage RMS values of voltage Angular measurement of sine waves Angular measurement of sine waves Equation for sine waves Equation for sine waves Non sinusoidal/

##### Inverting Amplifier. Introduction An inverting amplifier is a type of electrical circuit that reverses the flow of current passing through it. This reversal.

A infinity then, V + - V  0 V + = V  I + = I  = 0 Seems strange, but the input terminals to an op-amp act as a short and open at the same time Summary of op-amp behavior To analyze an op-amp circuit for linear operation Write node equations at + and - terminals (I i =I + = I - = 0) Set V + = V - Solve for V o Inverting amplifier gain One of/

##### Higher Physics – Unit 2 2.4Analogue Electronics. Op-Amp An op-amp has two inputs and one output. The symbol for an op-amp is: inverting input non-inverting.

Q2 (a) + (c), Q3 (b) + (d), Q4 Differential Mode When the op-amp is in differential mode, both inputs are used. Circuit + - R1R1 VoVo V1V1 RfRf 0 V R2R2 R3R3 V2V2 Resistor R 3 is usually chosen/op-amp connected to a Wheatstone bridge circuit is shown. 3000 Ω Calculate the output voltage of the op-amp. Transistor Output TURD – temperature up, resistance of thermistor goes down. Voltage across thermistor goes down.  V 1 goes down. V1V1 0 V +V S V2V2 + - 230 V motor for cooling fan M VoVo Consider the equation/

##### 1 ENGG 1203 Tutorial Op Amps 8 Mar Learning Objectives  Analyze circuits with ideal operational amplifiers News  HW2 (18 Mar 23:55)  Mid term (22 Mar.

R so that V o = 2 (V 1 − V 2 ). 8 No current in +ve or -ve inputs : Ideal op-amp: 9 Op Amp Configurations (II) Fill in the values of R1 and R2 required to satisfy the equations in the left column of the following table. The values must be non-negative (i.e., in the range [0,∞]) 10 R1R1/ (a number) for R 2. If R 3 = R 4 then the right motor input is 5V. If α i = α o then the gain of the left op-amp circuit must be 5 so that the motor voltage is 0. The gain is R 1 + R 2 /R 1, so R 2 must be 4000Ω. 27 5 55 1 0/

##### EE70 Review.

is present. Assume that the differential input voltage and the input current of the op amp are forced to zero. (This is the summing-point constraint.) Apply standard circuit-analysis principles, such as Kirchhoff’s laws and Ohm’s law, to solve for/ resistor: Charging a Capacitance from a DC Source through a Resistance Rearranging: This is a linear first-order differential equation with contant coefficients. Charging a Capacitance from a DC Source through a Resistance The boundary conditions are given by the/

##### REFERENCE CIRCUITS A reference circuit is an independent voltage or current source which has a high degree of precision and stability. Output voltage/current.

practice, the fabricated value of K (which depends on emitter area ratio, current ratio, and resistance ratio) may not satisfy the given equation. This will lead to Vref value at testing temp to differ from the therretically given value. A resistance value (typically R3) can be/in Vref, so that Vref temp co matches R4 temp co. CMOS version in subthreshold With a good op amp, ID1=ID2 Characterization of a bandgap circuit Assuming an ideal op amp with an infinite gain, we have V A = V B and I 1 = I 2. /

##### EENG 2610: Circuits Analysis Class 7: Operational Amplifiers (Op-Amp), 2/2 Oluwayomi Adamo Department of Electrical Engineering College of Engineering,

Engineering College of Engineering, University of North Texas Op-Amp Circuit Analysis General rule for op-amp circuit analysis  Use the ideal op-amp model conditions  Write nodal equations at the op-amp input terminals Example 4.5: Determine v o Example 4.6: Determine v o This is a precision differential voltage gain device 1 2 Comparator Comparator is a variant of op-amp  Ideal comparator and its transfer curve Comparator is/

##### ECE 342 – Jose Schutt-Aine 1 ECE 342 Solid-State Devices & Circuits 17. Differential Amplifiers Jose E. Schutt-Aine Electrical & Computer Engineering University.

Jose Schutt-Aine 31 Example - II (d) The incremental differential voltage gain of the circuit is defined as: Calculate r e and  ECE 342 – Jose Schutt-Aine 32 Example - II Applying the gain equation and assuming r out >> 1.6 k  gives (e) The voltage at the /3 0.40.6 r o (k  ) 222 111 ECE 342 – Jose Schutt-Aine 74 2-Stage Op Amp – Frequency Response Incremental Circuit ECE 342 – Jose Schutt-Aine 75 2-Stage Op Amp – Frequency Response ECE 342 – Jose Schutt-Aine 76 Transmission zero at s = s Z with Two poles/

##### AMPLIFIERS, DIODES,RECTIFIERS,WAVESHAPPING CIRCUITS

also be expressed in logarithmic terms EXAMPLE Calculate the CMRR for the circuit measurements Inverting Op-Amp Non-inverting Op-Amp Summation Difference If all resistors are equal: Differentiating Op-Amp Integrating Op-Amp Differentiating Op-Amp (where Vin and Vout are functions of time) SEMICONDUCTOR Si/ and zener tunneling. PN Junction Diode V-A Characteristic PN Junction Diode V-A Characteristic Current Equations • The forward bias current is closely approximated by where VT =kT/q is the thermal /

##### 1 Chapter 7 First-Order Circuits 電路學 ( 一 ). 2 First-Order Circuits Chapter 7 7.1The Source-Free RC Circuit 7.2The Source-Free RL Circuit 7.3Singularity.

function, which may be a voltage or a current source. 30 7.4 The Step-Response of a RC Circuit (2) Integrating both sides and considering the initial conditions, the solution of the equation is: Final value at t -> ∞ Initial value at t = 0 Source-free Response Complete Response = / t > 0. Calculate i for t = 2 s and t = 5 s. 7.5 The Step-Response of a RL Circuit (6) 40 7.6 First-Order Op Amp Circuits (1) Example 21 For the op amp circuit, find v o for t > 0, given that that v (0) = 3 V. Let R f = 80 k,/

##### EENG 2610: Circuit Analysis Class 11: Capacitor and Inductor Combinations RC Operational Amplifier Circuits Oluwayomi Adamo Department of Electrical Engineering.

equivalent capacitance at terminals A-B. Series Inductors Parallel Inductors RC Operational Amplifier Circuits - Differentiator General rules for op-amp circuit analysis  Use the ideal op-amp model conditions:  Write nodal equations at the op-amp input terminals RC Operational Amplifier Circuits - Integrator General rules for op-amp circuit analysis  Use the ideal op-amp model conditions:  Write nodal equations at the op-amp input terminals Example 6.17:The waveform below is applied to the input of/

##### 1 13. Pulsed waveforms and Timing Circuit Design 13.1Op. Amp. Pulse GeneratorsOp. Amp. Pulse Generators 13.2555 timer IC Oscillator555 timer IC Oscillator.

Generators Study example 14.7-page786 for this pulse generator with diode EE3601-13 Electronics Circuit Design 3 Summary of Design Equations Op. Amp. Pulse Generators EE3601-13 Electronics Circuit Design 4 Example: Given the Op. Amp. Pulse Generator circuit below, (a) calculate and sketch the output waveform (b) frequency output and (c) duty cycle of the output waveform if C = 0.1  F, R = 20k , R 1/

##### F REQUENCY R ESPONSE & R ESONANT C IRCUITS Filters, frequency response, time domain connection, bode plots, resonant circuits.

C IRCUITS Filters, frequency response, time domain connection, bode plots, resonant circuits. O UTLINE AND TOPICS Low-pass filters High-pass filters Other filters Resonance (Ch 20) Ideal op-amps and active filters Decibels & log scales Linear systems and transfer functions Bode plots/ scale referenced to 1 mW, 600Ω and a 3 V rms voltage scale. L INEAR SYSTEMS RLC circuits, op-amps are linear circuit elements i.e. a differential equation can describe them. You can add solutions at a given ω i.e. if exp(jωt) /

##### Objective of Lecture Discuss analog computing and the application of 1 st order operational amplifier circuits. Derive the equations that relate the output.

Lecture Discuss analog computing and the application of 1 st order operational amplifier circuits. Derive the equations that relate the output voltage to the input voltage for a differentiator and /and Subtractors Summing and difference amplifiers Differentiators Integrators 1 st order op amp circuits Capacitors Differentiator Ideal Op Amp Model Virtual ground Op Amp Model Virtual ground Analysis Since current is not allowed to enter the input terminals of an ideal op amp. Example #1 Suppose v S (t) = 3V u/

##### Integrator Op Amp Amplifier M.S.P.V.L. Polytechnic College, Department of ECE & EEE, Pavoorchatram.

College, Department of ECE & EEE, Pavoorchatram. Introduction An integrator op amp (operational amplifier) is one type of op amp circuit. The Integrator operational amplifier circuit performs the mathematical operation of Integration. The magnitude of its output is/capacitor C is given as: Assuming that the input impedance of the op-amp is infinite (ideal op-amp), no current flows into the op-amp terminal. Therefore, the nodal equation at the inverting input terminal is given as: From which we have/

##### Solving Op Amp Stability Issues Part 3 (For Voltage Feedback Op Amps) Tim Green & Collin Wells Precision Analog Linear Applications 1.

2) Compensate with 1/Beta Pole (CF) 37 3) 1/Beta Pole/Zero Equations 38 1/Beta Transfer Function: DC 1/Beta: 1/Beta Pole Frequency: 1/Beta Zero Frequency: => Solve for CF CI is the equivalent input capacitance of the op amp. (See Appendix #7) 3) Select CF to Compensate Circuit Calculate CF(min) from fp3 < *fcl : Calculate CF(max) from fz1 < f/

##### FILTERS. DEFINITION Filters - electronic circuits which perform signal processing functions, specifically to remove unwanted frequency components from.

> ƒc, Just like the low pass filter, the operation of a high pass active filter can be verified from the frequency gain equation above as: Frequency response curve Cut-off frequency of High-pass filter: Second-order (Sallen-Key) High-pass filter - A first-/ Band Pass Filter is to connect the basic passive high and low pass filters we look at previously to an amplifying op- amp circuit as shown. Active Band Pass Filter - this cascading together of the individual low and high pass passive filters produces a/

##### CHAPTER 10 Op-Amp Limitations. OBJECTIVES Describe and Analyze: Input bias currents Input offset current Input offset voltage Frequency response Slew.

gain bandwidth” (UGB) or the “gain-bandwidth product” (GBW) Bandwidth: A CL & A OL The closed-loop gain (A CL ) of an op-amp circuit is typically much less than the open-loop gain (A OL ). On a Bode plot, A CL is a horizontal line. At some frequency, call /output. The equation says we can use higher frequencies if we keep the amplitude low, or we can have higher amplitudes if we keep the frequency low. Troubleshooting As always, check to see if DC voltages are within the correct range. If an op-amp needs to /

##### ECE201 Lect-131 Loop Analysis (7.8) Circuits with Op-Amps (3.3) Dr. Holbert October 9, 2001.

Solve Equations I 1 = 239.9 + j0.23  A I 2 = -12.36 + j5.98  A I 3 = -12.54 + j3.46  A ECE201 Lect-1312 Solve for V out ECE201 Lect-1313 |V out | as a function of  ECE201 Lect-1314 Class Example Learning Extension E7.14(a) ECE201 Lect-1315 Op Amps Op Amp is / the input(s). ECE201 Lect-1328 Where is the Feedback? – + V in + – V out R1R1 R2R2 +–+– ECE201 Lect-1329 Review To solve an op-amp circuit, we usually apply KCL at one or both of the inputs. We then invoke the consequences of the ideal model. –The/

##### A Differentiator Circuit.  All of the diagrams use a uA741 op amp. ◦ You are to construct your circuits using an LM 356 op amp.  There is a statement.

frequency components will be amplified significantly over the signal of interest (look at the equation for the output voltage after you have taken the derivative of the input voltage). ◦ The circuit may become unstable – and certainly the shape of the output signal will not / pass filter. If the difference in the voltage between the negative input terminal on the op amp and Vo is relatively constant, C1 acts like an open circuit and all of the current through R2 and C1 will flow through R1. If the difference/

##### 6. RLC CIRCUITS CIRCUITS by Ulaby & Maharbiz. Overview.

  Natural solution  Forced solution (steady state)  Unknowns from initial conditions Example 6-13: Op-Amp Circuit Substitute v out into KCL expression, rearrange for diff. equation in terms of i L Example 6-13: Op-Amp Circuit (cont.) Cont. Example 6-13: Op-Amp Circuit (cont.) Cont. Example 6-13: Op-Amp Circuit (cont.) Multisim Example of RLC Circuit RFID Circuit Tech Brief 12: Micromechanical Sensors and Actuators Tech Brief 13: Touchscreens and Active Digitizers/

##### Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Chapter #8: Differential and Multistage Amplifiers.

active mode and entering saturation.  Equations (8.66) and (8.67) define the minimum and maximum common-mode input voltages. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Summary  The differential-pair or differential-amplifier configuration is most widely used building block in analog IC designs. The input stage of every op-amp is a differential amplifier.  There/

##### Introduction  Filters are circuits that are capable of passing signals within a band of frequencies while rejecting or blocking signals of frequencies.

”.  Filter can be passive or active filter. Passive filters Passive filters: The circuits built using RC, RL, or RLC circuits. Active filters Active filters : The circuits that employ one or more op-amps in the design an addition to resistors and capacitors Advantages of Active Filters over Passive/ it a high Q.  The Q is set by the feedback resistors R 5 and R 6 according to the following equations :  The configuration is similar to the band-pass version BUT R 3 has been moved and R 4 has been added/

#####  The differentiator or differentiating amplifier is as shown in figure.  This circuit will perform the mathematical operation of differentiation.

.  It can operate as an integrator over a short frequency.  Op-amp parameters affect the output.  Gain reduces with increase in frequency.  In a triangular wave or ramp generators.  In the ADC.  In the integral type controllers in a closed loop control system.  In analog computers to solve differential equation.  As a low pass filter.  In the communication circuits for recovering the modulating signal.

##### Filters and Tuned Amplifiers

transfer function of Eq. (16.68) is realized by feeding the input signal through appropriate components to the inputs of the three op amps. This circuit can realize all special second-order functions. The design equations are given in Table 16.2. Microelectronic Circuits, Sixth Edition Sedra/Smith Copyright © 2010 by Oxford University Press, Inc. Figure 16.27 (a) Feedback loop obtained by placing a/

##### Interfacing Analog and Digital Circuits

, values R and 2R. R-2R Ladder DAC R-2R DAC Equation b3, b2, b1, and b0 are binary values either ‘1’ or ‘0’. MC1408 Integrated Circuit DAC Popular, inexpensive 8-bit multiplying DAC. Also designated DAC0808. Output is proportional to the reference voltage. Operation of the MC1408 Requires an external op-amp to increase the output voltage and current. Can be wired to/

##### CP2 Circuit Theory Dr Todd Huffman Aims of this course: Understand basic circuit.

theory: complex notation, phasor diagrams, RC, RL, LCR circuits, resonance, bridges… Op amps: ideal operational amplifier circuitsOp-amps are now on the exam syllabus Stored energy, RC and RL transient circuits Reading List Electronics: Circuits, Amplifiers and Gates, D V Bugg, Taylor and Francis Chapters/R 1 =3kΩ R 2 =2kΩ R 3 =6kΩ VXVX 0V USE PASSIVE SIGN CONVENTION!!! - - + - Only one equation, Mesh analysis would give two. All currents leave all labeled nodes And apply V/R to each current. 2V 9V + + /

##### Characteristics of Op-Amp & Applications. OPERATIONAL AMPLIFIER An operational amplifier is a direct coupled high gain amplifier consisting of one or.

the highest quality voltage regulation  3-pin types make regulator circuit design simple Multipin IC Voltage Regulator LM 723C Schematic  The LM723 has an equivalent circuit that contains most of the parts of the op-amp voltage regulator discussed earlier.  It has an internal voltage reference/ (i.e. V CC > V o(max) + 3) LM723 in High-Voltage Configuration External pass transistor and current sensing added. Design equations: Choose R 1 + R 2 = 10 k , and C c = 100 pF. To make V o variable, replace R 1 /

##### REFERENCE CIRCUITS A reference circuit is an independent voltage or current source which has a high degree of precision and stability. Output voltage/current.

= 87.13 o Cc=1 pF, Phase Margin = 56.99 o Lower bandwidth BG Simulation for different diode current id=13uA Characterization of a bandgap circuit Assuming an ideal op amp with an infinite gain, we have V A = V B and I 1 = I 2. Schematic of the current-mode bandgap/,pVB,pVC,pVD,pID1,pID2); pVCpVos= -(Vt+ID1*R1)*(ID2*R0+Vt+ID2*R2) /(-Vt*R2*ID2+ID1*R0*R1*ID2+ID1*Vt*R1) Schematic and Nodal Equations Derivative wrpt to 1/A: VC*(1/A)=VA-VB eq1=(pVA-pVC)/R1+pID1=0; eq2=(pVB-pVC)/R2+pID2=0; eq3=VC+pVC/A=pVA-pVB; /

##### 1 九十七學年度第二學期 電路學（二）授課綱要 課本： Fundamentals of Electric Circuits, 3rd edition. by Charles K. Alexander and Matthew N. O. Sadiku 計分方式： 平時： 40 % （出席： 20% ，小考、演習課：

-order op amp circuit. Example 14 (p.344) In the op amp circuit, f ind v o (t) for t > 0 when v s = 10u(t) mV. Let R 1 = R 2 = 10 k , C 1 = 20 μF, and C 2 = 100 μF 35 8.8 Duality (1) Two circuits are said to be duals of one another if they are described by the same charactering equations with/

##### Op-Amps Microprocessor Interface. Operational Amplifier (Op-Amp)  Very high differential gain  High input impedance  Low output impedance  Provide.

: (1)The voltage between V + and V  is zero V + = V  (2)The current into both V + and V  termainals is zero For ideal Op-Amp circuit: (1)Write the kirchhoff node equation at the noninverting terminal V + (2)Write the kirchhoff node eqaution at the inverting terminal V  (3)Set V + = V  and solve for the desired closed-loop gain Noninverting Amplifier (/