Stability and Frequency Compensation
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Op Amp Stability and Input Capacitance
Amplifiers: Op Amps Texas Instruments Incorporated Op amp stability and input capacitance By Ron Mancini (Email: [email protected]) Staff Scientist, Advanced Analog Products Introduction Figure 1. Equation 1 can be written from the op Op amp instability is compensated out with the addition of amp schematic by opening the feedback loop an external RC network to the circuit. There are thousands and calculating gain of different op amps, but all of them fall into two categories: uncompensated and internally compensated. Uncompen- sated op amps always require external compensation ZG ZF components to achieve stability; while internally compen- VIN1 sated op amps are stable, under limited conditions, with no additional external components. – ZG VOUT Internally compensated op amps can be made unstable VIN2 + in several ways: by driving capacitive loads, by adding capacitance to the inverting input lead, and by adding in ZF phase feedback with external components. Adding in phase feedback is a popular method of making an oscillator that is beyond the scope of this article. Input capacitance is hard to avoid because the op amp leads have stray capaci- tance and the printed circuit board contributes some stray Figure 2. Open-loop-gain/phase curves are capacitance, so many internally compensated op amp critical stability-analysis tools circuits require external compensation to restore stability. Output capacitance comes in the form of some kind of load—a cable, converter-input capacitance, or filter 80 240 VDD = 1.8 V & 2.7 V (dB) 70 210 capacitance—and reduces stability in buffer configurations. RL= 2 kΩ VD 60 180 CL = 10 pF 150 Stability theory review 50 TA = 25˚C 40 120 Phase The theory for the op amp circuit shown in Figure 1 is 90 β 30 taken from Reference 1, Chapter 6. -
EE C128 Chapter 10
Lecture abstract EE C128 / ME C134 – Feedback Control Systems Topics covered in this presentation Lecture – Chapter 10 – Frequency Response Techniques I Advantages of FR techniques over RL I Define FR Alexandre Bayen I Define Bode & Nyquist plots I Relation between poles & zeros to Bode plots (slope, etc.) Department of Electrical Engineering & Computer Science st nd University of California Berkeley I Features of 1 -&2 -order system Bode plots I Define Nyquist criterion I Method of dealing with OL poles & zeros on imaginary axis I Simple method of dealing with OL stable & unstable systems I Determining gain & phase margins from Bode & Nyquist plots I Define static error constants September 10, 2013 I Determining static error constants from Bode & Nyquist plots I Determining TF from experimental FR data Bayen (EECS, UCB) Feedback Control Systems September 10, 2013 1 / 64 Bayen (EECS, UCB) Feedback Control Systems September 10, 2013 2 / 64 10 FR techniques 10.1 Intro Chapter outline 1 10 Frequency response techniques 1 10 Frequency response techniques 10.1 Introduction 10.1 Introduction 10.2 Asymptotic approximations: Bode plots 10.2 Asymptotic approximations: Bode plots 10.3 Introduction to Nyquist criterion 10.3 Introduction to Nyquist criterion 10.4 Sketching the Nyquist diagram 10.4 Sketching the Nyquist diagram 10.5 Stability via the Nyquist diagram 10.5 Stability via the Nyquist diagram 10.6 Gain margin and phase margin via the Nyquist diagram 10.6 Gain margin and phase margin via the Nyquist diagram 10.7 Stability, gain margin, and -
Indirect Compensation Techniques for Three- Stage Fully-Differential Op-Amps
1 Indirect Compensation Techniques for Three- Stage Fully-Differential Op-amps Vishal Saxena, Student Member, IEEE and R. Jacob Baker, Senior Member, IEEE op-amps. A novel cascaded fully-differential, three-stage op- Abstract— As CMOS technology continues to evolve, the amp topology is presented with simulation results, which is supply voltages are decreasing while at the same time the tolerant to device mismatches and exhibits superior transistor threshold voltages are remaining relatively constant. performance. Making matters worse, the inherent gain available from the nano-CMOS transistors is dropping. Traditional techniques for achieving high-gain by cascoding become less useful in nano-scale II. INDIRECT FEEDBACK COMPENSATION CMOS processes. Horizontal cascading (multi-stage) must be Indirect Feedback Compensation is a lucrative method to used in order to realize high-gain op-amps in low supply voltage compensate op-amps for higher speed operation [1]. In this processes. This paper discusses indirect compensation techniques for op-amps using split-length devices. A reversed-nested indirect method, the compensation capacitor is connected to an internal compensated (RNIC) topology, employing double pole-zero low impedance node in the first gain stage, which allows cancellation, is illustrated for the design of three-stage op-amps. indirect feedback of the compensation current from the output The RNIC topology is then extended to the design of three-stage node to the internal high-impedance node. Further, in nano- fully-differential op-amps. Novel three-stage fully-differential CMOS processes low-voltage, high-speed op-amps can be gain-stage cascade structures are presented with efficient designed by employing a split-length composite transistor for common mode feedback (CMFB) stabilization. -
Switch-Mode Power Converter Compensation Made Easy
Switch-mode power converter compensation made easy Robert Sheehan Systems Manager, Power Design Services Member Group Technical Staff Louis Diana Field Application, America Sales and Marketing Senior Member Technical Staff Texas Instruments Using this paper as a quick look-up reference can help designers compensate the most popular switch-mode power converter topologies. Engineers have been designing switch-mode power converters for some time now. If you’re new to the design field or you don’t compensate converters all the time, compensation requires some research to do correctly. This paper will break the procedure down into a step-by-step process that you can follow to compensate a power converter. We will explain the theory of compensation and why it is necessary, examine various power stages, and show how to determine where to place the poles and zeros of the compensation network to compensate a power converter. We will examine typical error amplifiers as well as transconductance amplifiers to see how each affects the control loop and work through a number of topologies/examples so that power engineers have a quick reference when they need to compensate a power converter. Introduction Many SMPS designers would appreciate a how- A switch-mode power supply (SMPS) regulates to reference paper that they can use to look up the output voltage against any changes in compensation solutions to various topologies with output loading or input line voltage. An SMPS various feedback modes. We are striving to provide accomplishes this regulation with a feedback loop, this in a single paper. which requires compensation if it has an error Control-loop and compensation amplifier with linear feedback. -
OA-25 Stability Analysis of Current Feedback Amplifiers
OBSOLETE Application Report SNOA371C–May 1995–Revised April 2013 OA-25 Stability Analysis of Current Feedback Amplifiers ..................................................................................................................................................... ABSTRACT High frequency current-feedback amplifiers (CFA) are finding a wide acceptance in more complicated applications from dc to high bandwidths. Often the applications involve amplifying signals in simple resistive networks for which the device-specific data sheets provide adequate information to complete the task. Too often the CFA application involves amplifying signals that have a complex load or parasitic components at the external nodes that creates stability problems. Contents 1 Introduction .................................................................................................................. 2 2 Stability Review ............................................................................................................. 2 3 Review of Bode Analysis ................................................................................................... 2 4 A Better Model .............................................................................................................. 3 5 Mathematical Justification .................................................................................................. 3 6 Open Loop Transimpedance Plot ......................................................................................... 4 7 Including Z(s) ............................................................................................................... -
Chapter 6 Amplifiers with Feedback
ELECTRONICS-1. ZOLTAI CHAPTER 6 AMPLIFIERS WITH FEEDBACK Purpose of feedback: changing the parameters of the amplifier according to needs. Principle of feedback: (S is the symbol for Signal: in the reality either voltage or current.) So = AS1 S1 = Si - Sf = Si - ßSo Si S1 So = A(Si - S ) So ß o + A from where: - Sf=ßSo * So A A ß A = Si 1 A 1 H where: H = Aß Denominations: loop-gain H = Aß open-loop gain A = So/S1 * closed-loop gain A = So/Si Qualitatively different cases of feedback: oscillation with const. amplitude oscillation with narrower growing amplitude pos. f.b. H -1 0 positive feedback negative feedback Why do we use almost always negative feedback? * The total change of the A as a function of A and ß: 1(1 A) A A 2 A* = A (1 A) 2 (1 A) 2 Introducing the relative errors: A * 1 A A A * 1 A A 1 A According to this, the relative error of the open loop gain will be decreased by (1+Aß), and the error of the feedback circuit goes 1:1 into the relative error of the closed loop gain. This is the Elec1-fb.doc 52 ELECTRONICS-1. ZOLTAI reason for using almost always the negative feedback. (We can not take advantage of the negative sign, because the sign of the relative errors is random.) Speaking of negative or positive feedback is only justified if A and ß are real quantities. Generally they are complex quantities, and the type of the feedback is a function of the frequency: E.g. -
MT-033: Voltage Feedback Op Amp Gain and Bandwidth
MT-033 TUTORIAL Voltage Feedback Op Amp Gain and Bandwidth INTRODUCTION This tutorial examines the common ways to specify op amp gain and bandwidth. It should be noted that this discussion applies to voltage feedback (VFB) op amps—current feedback (CFB) op amps are discussed in a later tutorial (MT-034). OPEN-LOOP GAIN Unlike the ideal op amp, a practical op amp has a finite gain. The open-loop dc gain (usually referred to as AVOL) is the gain of the amplifier without the feedback loop being closed, hence the name “open-loop.” For a precision op amp this gain can be vary high, on the order of 160 dB (100 million) or more. This gain is flat from dc to what is referred to as the dominant pole corner frequency. From there the gain falls off at 6 dB/octave (20 dB/decade). An octave is a doubling in frequency and a decade is ×10 in frequency). If the op amp has a single pole, the open-loop gain will continue to fall at this rate as shown in Figure 1A. A practical op amp will have more than one pole as shown in Figure 1B. The second pole will double the rate at which the open- loop gain falls to 12 dB/octave (40 dB/decade). If the open-loop gain has dropped below 0 dB (unity gain) before it reaches the frequency of the second pole, the op amp will be unconditionally stable at any gain. This will be typically referred to as unity gain stable on the data sheet. -
Operational Amplifiers: Part 3 Non-Ideal Behavior of Feedback
Operational Amplifiers: Part 3 Non-ideal Behavior of Feedback Amplifiers AC Errors and Stability by Tim J. Sobering Analog Design Engineer & Op Amp Addict Copyright 2014 Tim J. Sobering Finite Open-Loop Gain and Small-signal analysis Define VA as the voltage between the Op Amp input terminals Use KCL 0 V_OUT = Av x Va + + Va OUT V_OUT - Note the - Av “Loop Gain” – Avβ β V_IN Rg Rf Copyright 2014 Tim J. Sobering Liberally apply algebra… 0 0 1 1 1 1 1 1 1 1 Copyright 2014 Tim J. Sobering Get lost in the algebra… 1 1 1 1 1 1 1 Copyright 2014 Tim J. Sobering More algebra… Recall β is the Feedback Factor and define α 1 1 1 1 1 Copyright 2014 Tim J. Sobering You can apply the exact same analysis to the Non-inverting amplifier Lots of steps and algebra and hand waving yields… 1 This is very similar to the Inverting amplifier configuration 1 Note that if Av → ∞, converges to 1/β and –α /β –Rf /Rg If we can apply a little more algebra we can make this converge on a single, more informative, solution Copyright 2014 Tim J. Sobering You can apply the exact same analysis to the Non-inverting amplifier Non-inverting configuration Inverting Configuration 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Copyright 2014 Tim J. Sobering Inverting and Non-Inverting Amplifiers “seem” to act the same way Magically, we again obtain the ideal gain times an error term If Av → ∞ we obtain the ideal gain 1 1 1 Avβ is called the Loop Gain and determines stability If Avβ –1 1180° the error term goes to infinity and you have an oscillator – this is the “Nyquist Criterion” for oscillation Gain error is obtained from the loop gain 1 For < 1% gain error, 40 dB 1 (2 decades in bandwidth!) 1 Copyright 2014 Tim J. -
How to Measure the Loop Transfer Function of Power Supplies (Rev. A)
Application Report SNVA364A–October 2008–Revised April 2013 AN-1889 How to Measure the Loop Transfer Function of Power Supplies ..................................................................................................................................................... ABSTRACT This application report shows how to measure the critical points of a bode plot with only an audio generator (or simple signal generator) and an oscilloscope. The method is explained in an easy to follow step-by-step manner so that a power supply designer can start performing these measurements in a short amount of time. Contents 1 Introduction .................................................................................................................. 2 2 Step 1: Setting up the Circuit .............................................................................................. 2 3 Step 2: The Injection Transformer ........................................................................................ 4 4 Step 3: Preparing the Signal Generator .................................................................................. 4 5 Step 4: Hooking up the Oscilloscope ..................................................................................... 4 6 Step 5: Preparing the Power Supply ..................................................................................... 4 7 Step 6: Taking the Measurement ......................................................................................... 5 8 Step 7: Analyzing a Bode Plot ........................................................................................... -
The TL431 in the Control of Switching Power Supplies Agenda
The TL431 in the Control of Switching Power Supplies Agenda Feedback generalities The TL431 in a compensator Small-signal analysis of the return chain A type 1 implementation with the TL431 A type 2 implementation with the TL431 A type 3 implementation with the TL431 Design examples Conclusion Agenda Feedback generalities The TL431 in a compensator Small-signal analysis of the return chain A type 1 implementation with the TL431 A type 2 implementation with the TL431 A type 3 implementation with the TL431 Design examples Conclusion What is a Regulated Power Supply? Vout is permanently compared to a reference voltage Vref. The reference voltage Vref is precise and stable over temperature. The error,ε =−VVrefα out, is amplified and sent to the control input. The power stage reacts to reduce ε as much as it can. Power stage - H Vout Control d variable Error amplifier - G Rupper + - Vin - - α + + Vp Modulator - G V PWM ref Rlower How is Regulation Performed? Text books only describe op amps in compensators… Vout Verr The market reality is different: the TL431 rules! V I’m the out law! Verr TL431 optocoupler How do we Stabilize a Converter? We need a high gain at dc for a low static error We want a sufficiently high crossover frequency for response speed ¾ Shape the compensator G(s) to build phase and gain margins! Ts( ) fc = 6.5 kHz 0° -0 dB ∠Ts( ) -88° GM = 67 dB ϕm = 92° -180° Ts( ) =−67 dB 10 100 1k 10k 100k 1Meg How Much Phase Margin to Chose? a Q factor of 0.5 (critical response) implies a ϕm of 76° a 45° ϕm corresponds -
Differential AC Boosting Compensation for Power-Efficient
Copyright © 2019 American Scientific Publishers Journal of All rights reserved Low Power Electronics Printed in the United States of America Vol. 15, 379–387, 2019 Differential AC Boosting Compensation for Power-Efficient Multistage Amplifiers Tayebeh Asiyabi1 and Jafar Torfifard2 ∗ 1Department of Electrical Engineering, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran 2Department of Electrical Engineering, Izeh Branch, Islamic Azad University, Izeh, Iran (Received: 26 February 2019; Accepted: 22 July 2019) In this paper, a new architecture of four-stage CMOS operational transconductance amplifier (OTA) based on an alternative differential AC boosting compensation called DACBC is proposed. The pre- sented structure removes feedforward and boosts feedback paths of compensation network simul- taneously. Moreover, the presented circuit uses a fairly small compensation capacitor in the order of 1 pF, which makes the circuit very compact regarding enhanced several small-signal and large- signal characteristics. The proposed circuit along with several state-of-the-art schemes from the literature have been extensively analysed and compared together. The simulation results show with the same capacitive load and power dissipation the unity-gain frequency (UGF) can be improved over 60 times than conventional nested Miller compensation. The results of the presented OTA with 15 pF capacitive load demonstrated 65 phase margin, 18.88 MHz as UGF and DC gain of 115 dB with power dissipation of 462 Wfrom1.8V. Keywords: Differential AC Boosting, Frequency Compensation, CMOS Operational IP: 192.168.39.210 On: Sun, 03 Oct 2021 15:57:22 TransconductanceCopyright: Amplifier American (OTA), Scientific Low Power, Publishers Low Voltage. Delivered by Ingenta 1. INTRODUCTION is compulsory for high-precision purposes. -
Design of a TL431-Based Controller for a Flyback Converter
Design of a TL431-Based Controller for a Flyback Converter Dr. John Schönberger Plexim GmbH Technoparkstrasse 1 8005 Zürich 1 Introduction The TL431 is a reference voltage source that is commonly used in the control circuit of isolated power supplies. Typically used to provide a precision reference voltage, the TL431 can also be configured as an analog controller by exploiting its on-board error amplifier. In this report, the design of a TL431-based voltage controller for a flyback converter is presented. The example circuit is shown in Fig. 1. 0 ) ( %& -./ ' *+, !""# $#"" Fig. 1: Schematic of current-controlled flyback converter with a TL431 configured as a type 2 voltage controller. The flyback converter comprises two control loops. The inner current control loop, based on peak current mode control, is realized using a UCC38C4x current-controlled PWM modulator. The outer voltage control loop is a type 2 controller, which is commonly used in power supply voltage control loops. The voltage control circuit regulates the output voltage of the 5 V winding and includes an optocoupler to maintain isolation between the input and output stages. The voltage controller must regulate the measured 5 V output voltage over a range of loading conditions on the 12 V windings, which induce voltage deviations on the 5 V winding. The load resistances on the ± 12 V windings vary between 15 and 7.5 Ω. The starting point for the voltage controller design is the ± calculation of the converter’s open-loop transfer function, Vo(s) , which is depicted as a Bode plot. The type Vc(s) 2 controller is then designed in the frequency domain to ensure that it provides a sufficiently fast and stable closed-loop transient response.