DOCSLIB.ORG

On the Modified Barkhausen Criterion

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
On the Modified Barkhausen Criterion On the Modified Barkhausen Criterion Erik Lindberg, Lifemember IEEE, K. Murali Reader Emeritus at The Technical University of Denmark, Department of Physics, Anna University, Kongens Lyngby, DK2800, Denmark, Chennai-600 025, India e-mail: [email protected] e-mail: [email protected] Abstract—Oscillators are normally designed according to the TABLE I Modified Barkhausen Criterion i.e. the complex pole pair is moved out in RHP so that the linear circuit becomes unstable. (A) R2 = 10e + 3 1 1 By means of the Mancini Phaseshift Oscillator it is demonstrated ideal op.amps A1 = A3 = Sigma (real) Omega (imag) Q that the distortion of the oscillator may be minimized by 1 introducing a nonlinear ”Hewlett Resistor” so that the complex +0.00000e-01 -1.00000e+04 +0.00000e-01 +1.00000e+04 1 pole-pair is in the RHP for small signals and in the LHP for -1.00000e+04 +0.00000e-01 +0.50 large signals i.e. the complex pole pair of the instant linearized (B) R = 10e + 3 small signal model is moving around the imaginary axis in the 2 perfect op.amps A1 = 100e + 3 A3 = 100e + 3 complex frequency plane. Sigma (real) Omega (imag) Q -9.99990e-2 -9.99990e+03 +50.0e+03 I. INTRODUCTION -9.99990e-2 +9.99990e+03 +50.0e+03 In order to design electrical and electronic circuits we -1.00000e+4 +0.00000e-01 +0.50 (C) R2 = 10:1e + 3 assume that the wave length of the highest frequency is much perfect op.amps R2A = 10:1e + 3 R2B = 1 larger than the circuit so lumped elements could be used - Sigma (real) Omega (imag) Q quasi stationary circuits. +2.46521e+01 -9.97496e+03 -202.314 Since the 1930’ies the Barkhausen Criterion [1] has been +2.46521e+01 +9.97496e+03 -202.314 -9.95049e+03 +0.00000e-01 +0.50 used as a starting point for the design of oscillators. The (D) R2 = 8248 basic assumption is that the oscillator topology is a loop of a perfect op.amps R2A = 10:1e + 3 R2B = 45e + 3 linear inverting amplifier and a linear frequency determining Sigma (real) Omega (imag) Q feedback circuit. The loop is opened and the transfer-function -5.28186e+2 -9.97496e+3 +9.9 -5.28186e+2 +9.97496e+3 +9.9 of the open loop circuit - the loop gain - is designed to be -1.10670e+4 +0.00000e-1 +0.50 equal to 16 0. The loop is then closed and we have a linear Very little is reported about how far out in RHP the complex pole pair should be placed. In order to obtain a steady state oscillation with constant amplitude nonlinear components are introduced for clipping of the amplitude. A steady state oscillator is a nonlinear circuit [2], [3]. The clipping introduce distortion so also filtering must be introduced to obtain clean sinusoidal oscillation. II. MANCINI’S PHASESHIFT OSCILLATOR Figure 1 shows the Mancini Phaseshift Oscillator [4]. The circuit is a loop of three integrator circuits, two active and one passive RC integrator. The idea of this quadrature oscillator is to use the fact that the double integral of a sine wave is a negative sine wave of the same frequency and phase, in other words, the original sine wave 180 deg phase shifted. The phase Fig. 1. Mancini’s Phaseshift Oscillator. of the second integrator is then inverted and applied as positive feedback to induce oscillation. Both outputs V (3) and V (6) oscillator with a complex pole-pair on the imaginary axis of have relatively high distortion, that can be reduced with a gain- the complex frequency plane. In order to secure oscillations stabilizing circuit. With reference to fig. 1 - which is taken the complex pole-pair is moved to the right half of the complex from figure 20, page 19 of [4] - node 1 is connected to an frequency-plane RHP so the linear circuit becomes unstable. ideal 2.5V power source in the derivation of the following This approach is called the Modified Barkhausen Criterion. equations. It is assumed that the amplifiers are ideal op-amps Fig. 3. Hewletts Wien Bridge Oscillator. Fig. 4. ”Hewlett Resistor” to be used instead of an incandescent lamp R3. The quality-factor Q of a complex pole is defined as: p Q = Sigma2 + Omega2=(−2 × Sigma) (3) It is a measure for the distance of the pole from the imaginary axis. It is seen that Q becomes 1 for poles on the imaginary Fig. 2. Amplitude control section of Hewlett’s oscillator patent axis. Q is negative for poles in the right-half-plane RHP and positive for poles in the left-half-plane LHP . i.e. V (1) = V (2) and V (4) = V (5) and V (1) = 0. The order Table I case (A) shows that the solution of the characteristic of the circuit is 3 i.e. the characteristic polynomial is a third polynomial for R1 = R2 = R3 = R = 10kΩ and C1 = C2 = order polynomial. The roots of the polynomial are a real root and a complex pole pair. The node equations for the nodes 2, 4 and 5 may be derived by means of Kirchhoffs current law. From the node equations the following equation is derived: [ ] G1G2(G3 + sC3) + sC1(G2 + sC2)sC3 V3 = 0 (1) (G2 + sC2)sC3 where Gn = 1=Rn. If we observe that V (3) =6 0 the numerator in equation (1) must be zero and the characteristic polynomial of the linear circuit becomes: G G G G G G s3 + s2 2 + s 1 2 + 1 2 3 = 0 (2) C2 C1C2 C1C2C3 It is difficult to find expressions for the roots of this polynomial Fig. 5. FFT spectrum of Sine output V3 of Mancini’s Phaseshift Oscillator so numerical calculations are used. fig. 1. R2A and R2B refer to fig. 4. C3 = C = 10nF is a complex pole-pair on the imaginary axis and real pole in LHP . The frequency becomes ! = 2πf = 1=RC i.e. f = !=(2π) = 1:591549431kHz Fig. 7. Power source currents I(VR10);I(VP );I(VN) The cases (B), (C) and (D) of TABLE I are calculated by means of the ANP3 program [5]. Case (B) shows that A = V =(V − V ) A = V =(V − V ) Fig. 6. Static gains 1 3 1 2 and 3 6 4 5 the complex pole pair is very close to the imaginary axis if the amplifiers are assumed to be perfect with infinite III. DISTORTION MINIMIZATION input impedance, zero output impedance and constant gain Figure 2 shows the comments on the amplitude control in A = vout=vin = 100e + 3, Q = 50k. Case (C) shows that Hewlett’s oscillator patent [7], [8], [9]. He assumes that the the complex pole pair is in RHP when R2 = 10:100e + 3, − circuit is linear so it is necessary to introduce a nonlinear (Q = 200). Q becomes greater for smaller values of R2 e.g. ) − ) negative feedback resistor R3 which vary with the amplitude R2 = 10:010e + 3 Q = 2k and R2 = 10:001e + 3 of the signals. He also claim that this approach could be used Q = −33k. in other types of oscillation generators. He mention nothing Now the ”Hewlett resistor” is introduced and case (D) shows about the poles of the instant small signal model. that the complex pole pair is in LHP for large signals R2 = Figure 3 shows fig.1 of Hewletts Wien Bridge Oscillator 8:248e + 3,(Q = +10) i.e. it is not necessary to have a patent. Please note the resistor R3 a tungsten lamp. symmetric placement of the complex pole pairs. In [10] it is shown that the distortion for a negative resis- Figure 5 shows the ”fft” spectrum of the Sine output V3 tance oscillator may be minimized by introducing a nonlinear for the cases (B), (C) and (D) calculated by means of PSpice feed-back resistor ”Hewlett resistor” so that the complex pole- [6], with the following options: ”.tran 0 1000e-3 100e-3 1e-4 pair of the time-varying small-signal model move symmetri- ; uic” and ”+ RELTOL = 1e-6”. Distortion is increased when cally around the j! axis. In the following it is shown that it the complex pole pair is moved to RHP , case (C). Distortion is possible to reduce the distortion of the Mancini Phaseshift is minimized when the ”Hewlett resistor” is introduced, case Oscillator by introducing resistor R2 as a nonlinear ”Hewlett (D). resistor”, fig. 4. Figure 6 shows the static gains of the op-amps A1 = V3=(V1 − V2) and A3 = V6=(V4 − V5) in the three cases. It is obvious that the distortion is minimized when the ”Hewlett Resistor” is introduced, case (D). Figure 7 shows the power source currents. It is seen how the currents I(VP ) and I(VN) become almost constant in case (D). IV. CONCLUSION The starting point for the design of an oscillator is the Barkhausen Criterion which result in a linear circuit with a complex pole-pair on the imaginary axis. In order to guarantee oscillations the complex pole pair is moved to the right half of the complex frequency plane RHP so that the linear circuit becomes unstable, the Modified Barkhausen Criterion. The amplitudes of signals will go to infinity, 1. When the oscil- lator is built the amplifiers used are nonlinear. The amplitudes of the steady state signals will be limited and distortion is observed. In his Wien Bridge oscillator William Hewlett used a tube amplifier operating in the linear range so he introduced a nonlinear resistor, a tungsten lamp, as the necessary nonlin- earity for steady state oscillations.
Load more

Recommended publications
  • TRANSIENT STABILITY of the WIEN BRIDGE OSCILLATOR I
    TRANSIENT STABILITY OF THE WIEN BRIDGE OSCILLATOR i TRANSIENT STABILITY OF THE WIEN BRIDGE OSCILLATOR by RICHARD PRESCOTT SKILLEN, B. Eng. A Thesis Submitted ··to the Faculty of Graduate Studies in Partial Fulfilment of the Requirements for the Degree Master of Engineering McMaster University May 1964 ii MASTER OF ENGINEERING McMASTER UNIVERSITY (Electrical Engineering) Hamilton, Ontario TITLE: Transient Stability of the Wien Bridge Oscillator AUTHOR: Richard Prescott Skillen, B. Eng., (McMaster University) NUMBER OF PAGES: 105 SCOPE AND CONTENTS: In many Resistance-Capacitance Oscillators the oscillation amplitude is controlled by the use of a temperature-dependent resistor incorporated in the negative feedback loop. The use of thermistors and tungsten lamps is discussed and an approximate analysis is presented for the behaviour of the tungsten lamp. The result is applied in an analysis of the familiar Wien Bridge Oscillator both for the presence of a linear circuit and a cubic nonlinearity. The linear analysis leads to a highly unstable transient response which is uncommon to most oscillators. The inclusion of the slight cubic nonlinearity, however, leads to a result which is in close agreement to the observed response. ACKNOWLEDGEMENTS: The author wishes to express his appreciation to his supervisor, Dr. A.S. Gladwin, Chairman of the Department of Electrical Engineering for his time and assistance during the research work and preparation of the thesis. The author would also like to thank Dr. Gladwin and all his other undergraduate professors for encouragement and instruction in the field of circuit theor.y. Acknowledgement is also made for the generous financial support of the thesis project by the Defence Research Board·under grant No.
    [Show full text]
  • Oscillator Circuits
    Oscillator Circuits 1 II. Oscillator Operation For self-sustaining oscillations: • the feedback signal must positive • the overall gain must be equal to one (unity gain) 2 If the feedback signal is not positive or the gain is less than one, then the oscillations will dampen out. If the overall gain is greater than one, then the oscillator will eventually saturate. 3 Types of Oscillator Circuits A. Phase-Shift Oscillator B. Wien Bridge Oscillator C. Tuned Oscillator Circuits D. Crystal Oscillators E. Unijunction Oscillator 4 A. Phase-Shift Oscillator 1 Frequency of the oscillator: f0 = (the frequency where the phase shift is 180º) 2πRC 6 Feedback gain β = 1/[1 – 5α2 –j (6α – α3) ] where α = 1/(2πfRC) Feedback gain at the frequency of the oscillator β = 1 / 29 The amplifier must supply enough gain to compensate for losses. The overall gain must be unity. Thus the gain of the amplifier stage must be greater than 1/β, i.e. A > 29 The RC networks provide the necessary phase shift for a positive feedback. They also determine the frequency of oscillation. 5 Example of a Phase-Shift Oscillator FET Phase-Shift Oscillator 6 Example 1 7 BJT Phase-Shift Oscillator R′ = R − hie RC R h fe > 23 + 29 + 4 R RC 8 Phase-shift oscillator using op-amp 9 B. Wien Bridge Oscillator Vi Vd −Vb Z2 R4 1 1 β = = = − = − R3 R1 C2 V V Z + Z R + R Z R β = 0 ⇒ = + o a 1 2 3 4 1 + 1 3 + 1 R4 R2 C1 Z2 R4 Z2 Z1 , i.e., should have zero phase at the oscillation frequency When R1 = R2 = R and C1 = C2 = C then Z + Z Z 1 2 2 1 R 1 f = , and 3 ≥ 2 So frequency of oscillation is f = 0 0 2πRC R4 2π ()R1C1R2C2 10 Example 2 Calculate the resonant frequency of the Wien bridge oscillator shown above 1 1 f0 = = = 3120.7 Hz 2πRC 2 π(51×103 )(1×10−9 ) 11 C.
    [Show full text]
  • 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.
    [Show full text]
  • Van Der Pol Approximation Applied to Wien Oscillators João Casaleiroa,B,∗, Luís B
    Available online at www.sciencedirect.com ScienceDirect Procedia Technology 17 ( 2014 ) 335 – 342 Conference on Electronics, Telecommunications and Computers – CETC 2013 Van der Pol Approximation Applied to Wien Oscillators João Casaleiroa,b,∗, Luís B. Oliveirab, António C. Pintoa aDep. of Electronics, Telecommunications and Computers Engineering, Instituto Superior de Engenharia de Lisboa - ISEL, Lisboa, Portugal bDepartment of Electrical Engineering, FCT, CTS-Uninova, Caparica, Portugal Abstract This paper presents a nonlinear analysis of the Wien type oscillators based on the Van der Pol approximation. The steady-state equations for the key parameters, frequency and amplitude, are derived and their sensitivities to ambient temperature are discussed. The added value of this work is to present an analytical method to obtain the fundamental characteristics of the Wien type oscillators and to relate these characteristics with the circuit parameters in a simpler manner. The simulation results confirm the amplitude and frequency equations, and confirm that the amplitude is controlled by the limiter circuit. ©c 20142014 TheThe Authors. Authors. Published Published byby Elsevier Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license (Selectionhttp://creativecommons.org/licenses/by-nc-nd/3.0/ and peer-review under responsibility of ISEL). – Instituto Superior de Engenharia de Lisboa. Peer-review under responsibility of ISEL – Instituto Superior de Engenharia de Lisboa, Lisbon, PORTUGAL. Keywords: Oscillator, Wien oscillator, quasi-sinusoidal, Van der Pol, amplitude stabilization. 1. Introduction The oscillators of the Wien type are well known, second order, quasi-sinusoidal oscillators, suited for low frequencies and low distortion applications [1]. The low-distortion feature of this type of oscillator justifies its use for the characterization of analog-to-digital converters (ADC)[2], instrumentation circuits and a wide variety of measurement circuits.
    [Show full text]
  • Loop Stability Compensation Technique for Continuous-Time Common-Mode Feedback Circuits
    Loop Stability Compensation Technique for Continuous-Time Common-Mode Feedback Circuits Young-Kyun Cho and Bong Hyuk Park Mobile RF Research Section, Advanced Mobile Communications Research Department Electronics and Telecommunications Research Institute (ETRI) Daejeon, Korea Email: [email protected] Abstract—A loop stability compensation technique for continuous-time common-mode feedback (CMFB) circuits is presented. A Miller capacitor and nulling resistor in the compensation network provide a reliable and stable operation of the fully-differential operational amplifier without any performance degradation. The amplifier is designed in a 130 nm CMOS technology, achieves simulated performance of 57 dB open loop DC gain, 1.3-GHz unity-gain frequency and 65° phase margin. Also, the loop gain, bandwidth and phase margin of the CMFB are 51 dB, 27 MHz, and 76°, respectively. Keywords-common-mode feedback, loop stability compensation, continuous-time system, Miller compensation. Fig. 1. Loop stability compensation technique for CMFB circuit. I. INTRODUCTION common-mode signal to the opamp. In Fig. 1, two poles are The differential output amplifiers usually contain common- newly generated from the CMFB loop. A dominant pole is mode feedback (CMFB) circuitry [1, 2]. A CMFB circuit is a introduced at the opamp output and the second pole is located network sensing the common-mode voltage, comparing it with at the VCMFB node. Typically, the location of these poles are a proper reference, and feeding back the correct common-mode very close which deteriorates the loop phase margin (PM) and signal with the purpose to cancel the output common-mode makes the closed loop system unstable.
    [Show full text]
  • PH-218 Lec-16: Oscillator
    Analog & Digital Electronics Course No: PH-218 Lec-16: Oscillator Course Instructors: Dr. A. P. VAJPEYI Department of Physics, Indian Institute of Technology Guwahati, India 1 Positive Feedback When input and feedback signal both are in same phase, It is called a positive feedback. Positive feedback is used in analog and digital systems. A primary use of +ve feedback is in the production of oscillators. + Vi Vs Σ A( f) Vo + Vf SelectiveNetwork β(f) V A o = V = AV = A(V +V ) and V f = βVo o i s f Vs 1− Aβ Barkhausen Criterion: for oscillator βA=1 and +ve feedback 2 Oscillator Circuit Oscillator is an electronic circuit which converts dc signal into ac signal. Oscillator is basically a positive feedback amplifier with unity loop gain. For an inverting amplifier- feedback network provides a phase shift of 180 °°° while for non-inverting amplifier- feedback network provides a phase shift of 0°°° to get positive feedback . Vo A = If βA=1 then V o = ∞ ; Very high output with zero input. Vs 1− Aβ Use positive feedback through frequency-selective feedback network to ensure sustained oscillation at ω0 Use of Oscillator Circuits Clock input for CPU, DSP chips … Local oscillator for radio receivers, mobile receivers, etc As a signal generators in the lab Clock input for analog-digital and digital-analog converters 3 Oscillators If the feedback signal is not positive and gain is less than unity, oscillations dampen out. If the gain is higher than unity then oscillation saturates. Type of Oscillators Oscillators can be categorized according to the types of feedback network used: RC Oscillators: Phase shift and Wien Bridge Oscillators LC Oscillators: Colpitt and Hartley Oscillators Crystal Oscillators 4 RC Oscillators R −1 X C Vo = ( )Vin and φ = tan ( ) R − jX c R o o Φ =0 if Xc=0 and Φ =90 if R=0 However adjusting R to zero is impractical because it would lead to no voltage across R, thus in a RC circuit, phase shift is always ≤ 90 o and it is a function of frequency.
    [Show full text]
  • Stability Via the Nyquist Diagram Range of Gain for Stability Problem
    Stability via the Nyquist diagram Range of gain for stability Problem: For the unity feedback system be- low, where K G(s)= , s(s + 3)(s + 5) find the range of gain, K, for stability, insta- bility and the value of K for marginal stability. For marginal stability, also find the frequency of oscillation. Use the Nyquist criterion. Figure above; Closed-loop unity feedback sys- tem. 1 Solution: K G(jω)= s jω s(s + 3)(s + 5)| → 8Kω j K(15 ω2) = − − · − 64ω3 + ω(15 ω2)2 − When K = 1, 8ω j (15 ω2) G(jω)= − − · − 64ω3 + ω(15 ω2)2 − Important points: Starting point: ω = 0, G(jω)= 0.0356 j − − ∞ Ending point: ω = , G(jω) = 0 270 ∞ 6 − ◦ Real axis crossing: found by setting the imag- inary part of G(jω) as zero, K ω = √15, , j0 {−120 } 2 When K = 1, P = 0, from the Nyquist plot, N is zero, so the system is stable. The real axis crossing K does not encircle [ 1, j0)] −120 − until K = 120. At that point, the system is marginally stable, and the frequency of oscilla- tion is ω = √15 rad/s. Nyquist Diagram Nyquist Diagram 0.05 2 0.04 0.03 1.5 0.02 System: G 1 Real: −0.00824 0.01 Imag: 1e−005 Frequency (rad/sec): −3.91 0.5 0 0 Imaginary Axis −0.01 Imaginary Axis −0.5 −0.02 −1 −0.03 −0.04 −1.5 −0.05 −2 −0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 −3 −2.5 −2 −1.5 −1 −0.5 0 Real Axis Real Axis (a) (b) Figure above; Nyquist plots of ( )= K ; G s s(s+3)(s+5) (a) K = 1; (b)K = 120.
    [Show full text]
  • Considerations for Measuring Loop Gain in Power Supplies
    Power Supply Design Seminar Considerations for Measuring Loop Gain in Power Supplies Reproduced from 2018 Texas Instruments Power Supply Design Seminar SEM2300, Topic 6 TI Literature Number: SLUP386 © 2018 Texas Instruments Incorporated Power Supply Design Seminar resources are available at: www.ti.com/psds Considerations for Measuring Loop Gain in Power Supplies Manjing Xie ABSTRACT Loop gain measurements show how stable a power supply is and provide insight to improve output transient response. This presentation discusses the theory of open-loop transfer functions and empirical loop gain measurement methods. The presentation then demonstrates how to configure the frequency analyzer and prepare the power supply under test for accurate loop gain measurements. Examples are provided to illustrate proper loop gain measurement techniques. I. INTRODUCTION Figure 2 includes a power stage, the output feedback resistor divider, pulse width modulation Loop gain is the product of all gains around a (PWM) comparator and error amplifier with feedback loop. Figure 1 shows a simple system compensation network. The power stage contains with negative feedback. the power devices, magnetics and capacitors, which V VIN + OUT G(s) transfer energy from the input source to the output. - The output is sensed by the feedback resistor divider. The error amplifier with the compensation network T(s) forms the compensator which amplifies the error between the output feedback (FB) and the reference H(s) voltage, VREF. The output of the compensator, COMP, is modulated by the PWM comparator Figure 1 – Block diagram of a feedback system. which converts COMP, a continuous signal, into a discrete driving signal. When the driving signal is The loop gain of this system is defined as: high, the buck converter low-side MOSFET is T(s)=G(s)⋅ H(s) (1) turned off and high-side MOSFET is turned on.
    [Show full text]
  • " Impedance-Based Stability Analysis for Interconnected Converter
    " Impedance-Based Stability Analysis for Interconnected Converter Systems with Open-Loop RHP Poles " Yicheng Liao and Xiongfei Wang This is a preprint of the paper submitted to the IEEE Transaction on Power Electronics. Copyright 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. This is a preprint version. The preprint has been submitted to the IEEE Transactions on Power Electronics. Impedance-Based Stability Analysis for Interconnected Converter Systems with Open-Loop RHP Poles Yicheng Liao, Student Member, IEEE, Xiongfei Wang, Senior Member, IEEE (Corresponding author: Xiongfei Wang) Abstract – Small-signal instability issues of interconnected converter systems can be addressed by the impedance-based stability analysis method, where the impedance ratio at the point of common connection of different subsystems can be regarded as the open-loop gain, and thus the stability of the system can be predicted by the Nyquist stability criterion. However, the right-half plan (RHP) poles may be present in the impedance ratio, which then prevents the direct use of Nyquist curves for defining stability margins or forbidden regions. To tackle this challenge, this paper proposes a general rule of impedance-based stability analysis with the aid of Bode plots. The method serves as a sufficient and necessary stability condition, and it can be readily used to formulate the impedance specifications graphically for various interconnected converter systems.
    [Show full text]
  • Wien-Bridge Oscillator with Low Harmonic Distortion
    WIRELESS WORLD MAY 1981 51 Wien-bridge oscillator with low harmonic distortion New way of using Wien network to give 0.001 % t.h.d. by J. L. Linsley Hood, Robins (Electronics) The Wien-bridge network can be 1kHz of some 0.003%, which tended to connected in a different way in an increase with frequency above this point, R oscillator circuit to give a sine wave as the effectiveness of the common-mode with very low total harmonic isolation deteriorated. distortion. An I.e.d/photocell However, it is not implicit, in the use of a Wien network as the frequency-control amplitude control is external to the Output circuit. method, that the configuration shown in Fig. 1, in which the output of the network is taken to the non-inverting input of the R The Wien-bridge network remains the amplifier and the amplitude controlling most popular method of construction of negative-feedback signal is taken to the variable-frequency sine-wave oscillators, other, is the only circuit configuration since the basic circuit can be very simple in which can be employed. In particular, con­ ov form. It is a fairly straightforward matter sideration of the phase and transmission to design oscillators of this type in which characteristics of such a network, shown in Table 1 and Fig. 2 for equal values of C the harmonic distortion is only of the order Fig. 1. Basic Wien-bridge oscillator circuit of 0.01-0.02%, and which allow frequency control by means of a simple 2-gang poten­ Fig.
    [Show full text]
  • Notes on Gain-Error in Op-Amp Amplifiers This Article Is About the Errors You Can Make in Calculating the Gain of an Op-Amp Amplifier Circuit
    Notes On Gain-Error In Op-Amp Amplifiers This article is about the errors you can make in calculating the gain of an op-amp amplifier circuit. I'm assuming here that you are familiar with op-amp amplifier circuits. But let's do a quick review anyway. As you know, the key idea in op-amp circuits is that you start with a very high gain, and then trade off that gain in exchange for increased bandwidth and improved characteristics. What characteristics? You remember; things like input impedance (it gets bigger), output impedance (it gets smaller), distortion (it becomes less), and so forth. Op-amps have enormous open-loop gain . Open-loop gain is the gain of the op-amp chip itself with no feedback. That gain is too big to be used, so you lower it with negative feedback. The gain with feedback is the closed-loop gain . Below are schematics for the two basic feedback circuits: the inverting amplifier and the non-inverting amplifier. The gain equation for each circuit is included. Notice that the gain equations do not include frequency as a variable. Before we get to the punch-line of this article, there's a short story to tell. So, please be patient. Many books either say or imply that the closed-loop gain doesn't change with frequency until the line for ACL meets the line for AOL on the amplifier's Bode plot. What's a Bode plot? C'mon, you remember! It's a graph that shows how the gain of an amplifier "rolls off" as signal frequency increases.
    [Show full text]
  • The Barkhausen Criterion (Observation ?)
    View metadata,Downloaded citation and from similar orbit.dtu.dk papers on:at core.ac.uk Dec 17, 2017 brought to you by CORE provided by Online Research Database In Technology The Barkhausen Criterion (Observation ?) Lindberg, Erik Published in: Proceedings of NDES 2010 Publication date: 2010 Document Version Publisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Lindberg, E. (2010). The Barkhausen Criterion (Observation ?). In Proceedings of NDES 2010 (pp. 15-18). Dresden, Germany. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems (NDES2010) The Barkhausen Criterion (Observation ?) Erik Lindberg, IEEE Life member Faculty of Electrical Eng. & Electronics, 348 Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark Email: [email protected] Abstract—A discussion of the Barkhausen Criterion which is a necessary but NOT sufficient criterion for steady state oscillations of an electronic circuit.
    [Show full text]