Chapter 6 Pulse Processing
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Time Constant of an Rc Circuit
ECGR 2155 Instrumentation and Networks Laboratory UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE Department of Electrical and Computer Engineering EXPERIMENT 10 – TIME CONSTANT OF AN RC CIRCUIT OBJECTIVES The purpose of this experiment is to measure the time constant of an RC circuit experimentally and to verify the results against the values obtained by theoretical calculations. MATERIALS/EQUIPMENT NEEDED Digital Multimeter DC Power Supply Alligator (Clips) Jumper Resistor: 20kΩ Capacitor: 2,200 µF (rating = 50V or more) INTRODUCTION The time constant of RC circuits are used extensively in electronics for timing (setting oscillator frequencies, adjusting delays, blinking lights, etc.). It is necessary to understand how RC circuits behave in order to analyze and design timing circuits. In the circuit of Figure 10-1 with the switch open, the capacitor is initially uncharged, and so has a voltage, Vc, equal to 0 volts. When the single-pole single-throw (SPST) switch is closed, current begins to flow, and the capacitor begins to accumulate stored charge. Since Q=CV, as stored charge (Q) increases the capacitor voltage (Vc) increases. However, the growth of capacitor voltage is not linear; in fact it is an exponential growth. The formula which gives the instantaneous voltage across the capacitor as a function of time is (−t ) VV=1 − eτ cS Figure 10-1 Series RC Circuit EXPERIMENT 10 – TIME CONSTANT OF AN RC CIRCUIT 1 ECGR 2155 Instrumentation and Networks Laboratory This formula describes exponential growth, in which the capacitor is initially 0 volts, and grows to a value of near Vs after a finite amount of time. -
High Frequency Integrated MOS Filters C
N94-71118 2nd NASA SERC Symposium on VLSI Design 1990 5.4.1 High Frequency Integrated MOS Filters C. Peterson International Microelectronic Products San Jose, CA 95134 Abstract- Several techniques exist for implementing integrated MOS filters. These techniques fit into the general categories of sampled and tuned continuous- time niters. Advantages and limitations of each approach are discussed. This paper focuses primarily on the high frequency capabilities of MOS integrated filters. 1 Introduction The use of MOS in the design of analog integrated circuits continues to grow. Competitive pressures drive system designers towards system-level integration. System-level integration typically requires interface to the analog world. Often, this type of integration consists predominantly of digital circuitry, thus the efficiency of the digital in cost and power is key. MOS remains the most efficient integrated circuit technology for mixed-signal integration. The scaling of MOS process feature sizes combined with innovation in circuit design techniques have also opened new high bandwidth opportunities for MOS mixed- signal circuits. There is a trend to replace complex analog signal processing with digital signal pro- cessing (DSP). The use of over-sampled converters minimizes the requirements for pre- and post filtering. In spite of this trend, there are many applications where DSP is im- practical and where signal conditioning in the analog domain is necessary, particularly at high frequencies. Applications for high frequency filters are in data communications and the read channel of tape, disk and optical storage devices where filters bandlimit the data signal and perform amplitude and phase equalization. Other examples include filtering of radio and video signals. -
The Equivalence of Digital and Analog Signal Processing *
Reprinted from I ~ FORMATIO:-; AXDCOXTROL, Volume 8, No. 5, October 1965 Copyright @ by AcademicPress Inc. Printed in U.S.A. INFORMATION A~D CO:";TROL 8, 455- 4G7 (19G5) The Equivalence of Digital and Analog Signal Processing * K . STEIGLITZ Departmentof Electrical Engineering, Princeton University, Princeton, l\rew J er.~e!J A specific isomorphism is constructed via the trallsform domaiIls between the analog signal spaceL2 (- 00, 00) and the digital signal space [2. It is then shown that the class of linear time-invariaIlt realizable filters is illvariallt under this isomorphism, thus demoIl- stratillg that the theories of processingsignals with such filters are identical in the digital and analog cases. This means that optimi - zatioll problems illvolving linear time-illvariant realizable filters and quadratic cost functions are equivalent in the discrete-time and the continuous-time cases, for both deterministic and random signals. FilIally , applicatiolls to the approximation problem for digital filters are discussed. LIST OF SY~IBOLS f (t ), g(t) continuous -time signals F (jCAJ), G(jCAJ) Fourier transforms of continuous -time signals A continuous -time filters , bounded linear transformations of I.J2(- 00, 00) {in}, {gn} discrete -time signals F (z), G (z) z-transforms of discrete -time signals A discrete -time filters , bounded linear transfornlations of ~ JL isomorphic mapping from L 2 ( - 00, 00) to l2 ~L 2 ( - 00, 00) space of Fourier transforms of functions in L 2( - 00,00) 512 space of z-transforms of sequences in l2 An(t ) nth Laguerre function * This work is part of a thesis submitted in partial fulfillment of requirements for the degree of Doctor of Engineering Scienceat New York University , and was supported partly by the National ScienceFoundation and partly by the Air Force Officeof Scientific Researchunder Contract No. -
Lab 5 AC Concepts and Measurements II: Capacitors and RC Time-Constant
Sonoma State University Department of Engineering Science Fall 2017 EE110 Laboratory Introduction to Engineering & Laboratory Experience Lab 5 AC Concepts and Measurements II: Capacitors and RC Time-Constant Capacitors Capacitors are devices that can store electric charge similar to a battery (but with major differences). In its simplest form we can think of a capacitor to consist of two metallic plates separated by air or some other insulating material. The capacitance of a capacitor is referred to by C (in units of Farad, F) and indicates the ratio of electric charge Q accumulated on its plates to the voltage V across it (C = Q/V). The unit of electric charge is Coulomb. Therefore: 1 F = 1 Coulomb/1 Volt). Farad is a huge unit and the capacitance of capacitors is usually described in small fractions of a Farad. The capacitance itself is strictly a function of the geometry of the device and the type of insulating material that fills the gap between its plates. For a parallel plate capacitor, with the plate area of A and plate separation of d, C = (ε A)/d, where ε is the permittivity of the material in the gap. The formula is more complicated for cylindrical and other geometries. However, it is clear that the capacitance is large when the area of the plates are large and they are closely spaced. In order to create a large capacitance, we can increase the surface area of the plates by rolling them into cylindrical layers as shown in the diagram above. Note that if the space between plates is filled with air, then C = (ε0 A)/d, where ε0 is the permittivity of free space. -
Analog Signal Processing Circuits in Organic Transistor Technology a Dissertation Submitted to the Department of Electrical Engi
ANALOG SIGNAL PROCESSING CIRCUITS IN ORGANIC TRANSISTOR TECHNOLOGY A DISSERTATION SUBMITTED TO THE DEPARTMENT OF ELECTRICAL ENGINEERING AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Wei Xiong October 2010 © 2011 by Wei Xiong. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/fk938sr9136 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Boris Murmann, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Zhenan Bao I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Robert Dutton Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii Abstract Low-voltage organic thin-film transistors offer potential for many novel applications. Because organic transistors can be fabricated near room temperature, they allow integrated circuits to be made on flexible plastic substrates. -
(ECE, NDSU) Lab 11 – Experiment Multi-Stage RC Low Pass Filters
ECE-311 (ECE, NDSU) Lab 11 – Experiment Multi-stage RC low pass filters 1. Objective In this lab you will use the single-stage RC circuit filter to build a 3-stage RC low pass filter. The objective of this lab is to show that: As more stages are added, the filter becomes able to better reject high frequency noise When plotted on a Bode plot, the gain approaches two asymptotes: the low frequency gain approaches a constant gain of 0dB while the high-frequency gain drops as 20N dB/decade where N is the number of stages. 2. Background The single stage RC filter is a low pass filter: low frequencies are passed (have a gain of one), while high frequencies are rejected (the gain goes to zero). This is a useful filter to remove noise from a signal. Many types of signals are predominantly low-frequency in nature - meaning they change slowly. This includes measurements of temperature, pressure, volume, position, speed, etc. Noise, however, tends to be at all frequencies, and is seen as the “fuzzy” line on you oscilloscope when you amplify the signal. The trick when designing a low-pass filter is to select the RC time constant so that the gain is one over the frequency range of your signal (so it is passed unchanged) but zero outside this range (to reject the noise). 3. Theoretical response One problem with adding stages to an RC filter is that each new stage loads the previous stage. This loading consumes or “bleeds” some current from the previous stage capacitor, changing the behavior of the previous stage circuit. -
Adaptive Translinear Analog Signal Processing a Prospectus
ADAPTIVE TRANSLINEAR ANALOG SIGNAL PROCESSING A PROSPECTUS Eric J. McDonald, Koji Mensa Odame, and Bradley A. Minch School of Electrical and Computer Engineering Cornell University Ithaca, NY 14853-5401 [email protected] ABSTRACT are directly implementable as networks of MITES. We have devised a systematic method of transforming high- One common implementation of a MITE unit is shown level time-domain descriptions of linear and nonlinear adap- in Fig. 1. In this case, we operate a floating-gate PMOS tive signal-processing algorithms into compact, continuous- transistor in weak-inversion in addition to using a cascode time analog circuitry using basic units called multiple-input transistor to reduce the effects of the gate-to-drain capac- translinear elements (MITES). In this paper, we describe itance and channel-length modulation. The input voltages, the current state of the an and illustrate the method with an VI and V,, capacitively couple into the floating gate through unit-sized capacitors. The drain current of this device is example of an analog phase-locked loop (PLL). given by I = Isew(I’,+1’d/UT, 1. CIRCUIT SYNTHESIS METHODOLOGY where I, is a pre-exponential scaling current, w is the weight- The class of dyiamic translinear circuits [ 1-31 makes possi- ing cwfficient of the inputs (accounting for the body-effect 2.’ _.ble a promising approach to the structured design of analog and the capacitive voltage divider, Cunjt/Ctota,),and UT is ”. .‘ signal and information processing systems [4]. Such cir- the thermal voltage, kT/q. ’ cuits are capable of accurately realizing a wide range of lin- ear and nonlinear systems whose behavior can be described 2. -
Analog Signal Processing Christophe Caloz, Fellow, IEEE, Shulabh Gupta, Member, IEEE, Qingfeng Zhang, Member, IEEE, and Babak Nikfal, Student Member, IEEE
1 Analog Signal Processing Christophe Caloz, Fellow, IEEE, Shulabh Gupta, Member, IEEE, Qingfeng Zhang, Member, IEEE, and Babak Nikfal, Student Member, IEEE Abstract—Analog signal processing (ASP) is presented as a discrimination effects, emphasizing the concept of group delay systematic approach to address future challenges in high speed engineering, and presenting the fundamental concept of real- and high frequency microwave applications. The general concept time Fourier transformation. Next, it addresses the topic of of ASP is explained with the help of examples emphasizing basic ASP effects, such as time spreading and compression, the “phaser”, which is the core of an ASP system; it reviews chirping and frequency discrimination. Phasers, which repre- phaser technologies, explains the characteristics of the most sent the core of ASP systems, are explained to be elements promising microwave phasers, and proposes corresponding exhibiting a frequency-dependent group delay response, and enhancement techniques for higher ASP performance. Based hence a nonlinear phase response versus frequency, and various on ASP requirements, found to be phaser resolution, absolute phaser technologies are discussed and compared. Real-time Fourier transformation (RTFT) is derived as one of the most bandwidth and magnitude balance, it then describes novel fundamental ASP operations. Upon this basis, the specifications synthesis techniques for the design of all-pass transmission of a phaser – resolution, absolute bandwidth and magnitude and reflection phasers -
Current Mode Computational Circuits for Analog Signal Processing
ISSN (Print) : 2320 – 3765 ISSN (Online): 2278 – 8875 International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering (An ISO 3297: 2007 Certified Organization) Vol. 3, Issue 4, April 2014 Current Mode Computational Circuits for Analog Signal Processing Amanpreet Kaur1, Rishikesh Pandey2 PG Student (VLSI), Department of ECE, ThaparUniversity, Patiala,Punjab, India 1 Assistant Professor, Department of ECE, Thapar University, Patiala, Punjab, India2 ABSTRACT: The paper presents current adder and subtractor circuits based on cascode current mirror with improved linearity and wide linear range. The proposed circuits can be used for analog signal processing applications such as amplifiers, operational transconductance amplifiers (OTA), Gm-C filters, etc. In the proposed circuits, cascode current mirror topology is employed to improve current mirroring operation. The proposed circuits have been simulated using TSMC 0.18µm CMOS process technology with a supply voltage of 1.8 V. The proposed circuits operate efficiently within the current range of 0 to 80µA with the permissible error percentage of less than 2.5%. The SPICE simulation results have been presented to demonstrate the effectiveness of the proposed circuits. KEYWORDS: Adaptive biasing, cascode current mirror, current mode circuits, adder, subtractor.. I.INTRODUCTION In low-voltage/ low-power analog systems, current-mode signal processing has been usually considered an attractive strategy due to its potential for high-speed operation and low-voltage compatibility [1]-[4]. The behaviour of electrical circuits is always the result of interplay between voltage and current. In current mode circuits (CMCs), the currents determine the complete circuit response. The voltage signals are irrelevant in determining the circuit performance. -
Time Constant Calculations This Worksheet and All Related Files Are
Time constant calculations This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/, or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA. The terms and conditions of this license allow for free copying, distribution, and/or modification of all licensed works by the general public. Resources and methods for learning about these subjects (list a few here, in preparation for your research): 1 Questions Question 1 Qualitatively determine the voltages across all components as well as the current through all components in this simple RC circuit at three different times: (1) just before the switch closes, (2) at the instant the switch contacts touch, and (3) after the switch has been closed for a long time. Assume that the capacitor begins in a completely discharged state: Before the At the instant of Long after the switch switch closes: switch closure: has closed: C C C R R R Express your answers qualitatively: ”maximum,” ”minimum,” or perhaps ”zero” if you know that to be the case. Before the switch closes: VC = VR = Vswitch = I = At the instant of switch closure: VC = VR = Vswitch = I = Long after the switch has closed: VC = VR = Vswitch = I = Hint: a graph may be a helpful tool for determining the answers! file 01811 2 Question 2 Qualitatively determine the voltages across all components as well as the current through all components in this simple LR circuit at three different times: (1) just before the switch closes, (2) at the instant the switch contacts touch, and (3) after the switch has been closed for a long time. -
Cutoff Frequency, Lightning, RC Time Constant, Schumann Resonance, Spherical Capacitance
International Journal of Theoretical and Mathematical Physics 2019, 9(5): 121-130 DOI: 10.5923/j.ijtmp.20190905.01 Solar System Electrostatic Motor Theory Greg Poole Industrial Tests, Inc., Rocklin, CA, United States Abstract In this paper, the solar system has been visualized as an electrostatic motor for the research of scientific concepts. The Earth and space have all been represented as spherical capacitors to derive time constants from simple RC theory. Using known wave impedance values (R) from antenna theory and celestial capacitance (C) several time constants are derived which collectively represent time itself. Equations from Electro Relativity are verified using known values and constants to confirm wave impedance values are applicable to the earth antenna. Dark energy can be represented as a tremendous capacitor voltage and dark matter as characteristic transmission line impedance. Cosmic energy transfer may be limited to the known wave impedance of 377 Ω. Harvesting of energy wirelessly at the Earth’s surface or from the Sun in space may be feasible by matching the power supply source impedance to a load impedance. Separating the various the three fields allows us to see how high-altitude lightning is produced and the earth maintains its atmospheric voltage. Spacetime, is space and time, defined by the radial size and discharge time of a spherical or toroid capacitor. Keywords Cutoff Frequency, Lightning, RC Time Constant, Schumann Resonance, Spherical Capacitance the nearest thimble, and so put the wheel in motion; that 1. Introduction thimble, in passing by, receives a spark, and thereby being electrified is repelled and so driven forwards; while a second In 1749, Benjamin Franklin first invented the electrical being attracted, approaches the wire, receives a spark, and jack or electrostatic wheel. -
The RC Circuit
The RC Circuit The RC Circuit Pre-lab questions 1. What is the meaning of the time constant, RC? 2. Show that RC has units of time. 3. Why isn’t the time constant defined to be the time it takes the capacitor to become fully charged or discharged? 4. Explain conceptually why the time constant is larger for increased resistance. 5. What does an oscilloscope measure? 6. Why can’t we use a multimeter to measure the voltage in the second half of this lab? 7. Draw and label a graph that shows the voltage across a capacitor that is charging and discharging (as in this experiment). 8. Set up a data table for part one. (V, t (0-300s in 20s intervals, 360, and 420s)) Introduction The goal in this lab is to observe the time-varying voltages in several simple circuits involving a capacitor and resistor. In the first part, you will use very simple tools to measure the voltage as a function of time: a multimeter and a stopwatch. Your lab write-up will deal primarily with data taken in this part. In the second part of the lab, you will use an oscilloscope, a much more sophisticated and powerful laboratory instrument, to observe time behavior of an RC circuit on a much faster timescale. Your observations in this part will be mostly qualitative, although you will be asked to make several rough measurements using the oscilloscope. Part 1. Capacitor Discharging Through a Resistor You will measure the voltage across a capacitor as a function of time as the capacitor discharges through a resistor.