6.061 Class Notes, Chapter 1: Review of Network Theory
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Chapter 6 Two-Port Network Model
Chapter 6 Two-Port Network Model 6.1 Introduction In this chapter a two-port network model of an actuator will be briefly described. In Chapter 5, it was shown that an automated test setup using an active system can re- create various load impedances over a limited range of frequencies. This test set-up can therefore be used to automatically reproduce any load impedance condition (related to a possible application) and apply it to a test or sample actuator. It is then possible to collect characteristic data from the test actuator such as force, velocity, current and voltage. Those characteristics can then be used to help to determine whether the tested actuator is appropriate or not for the case simulated. However versatile and easy to use this test set-up may be, because of its limitations, there is some characteristic data it will not be able to provide. For this reason and the fact that it can save a lot of measurements, having a good linear actuator model can be of great use. Developed for transduction theory [29], the linear model presented in this chapter is 77 called a Two-Port Network model. The automated test set-up remains an essential complement for this model, as it will allow the development and verification of accuracy. This chapter will focus on the two-port network model of the 1_3 tube array actuator provided by MSI (Cf: Figure 5.5). 6.2 Theory of the Two–Port Network Model As a transducer converts energy from electrical to mechanical forms, and vice- versa, it can be modelled as a Two-Port Network that relates the electrical properties at one port to the mechanical properties at the other port. -
Analysis of Microwave Networks
! a b L • ! t • h ! 9/ a 9 ! a b • í { # $ C& $'' • L C& $') # * • L 9/ a 9 + ! a b • C& $' D * $' ! # * Open ended microstrip line V + , I + S Transmission line or waveguide V − , I − Port 1 Port Substrate Ground (a) (b) 9/ a 9 - ! a b • L b • Ç • ! +* C& $' C& $' C& $ ' # +* & 9/ a 9 ! a b • C& $' ! +* $' ù* # $ ' ò* # 9/ a 9 1 ! a b • C ) • L # ) # 9/ a 9 2 ! a b • { # b 9/ a 9 3 ! a b a w • L # 4!./57 #) 8 + 8 9/ a 9 9 ! a b • C& $' ! * $' # 9/ a 9 : ! a b • b L+) . 8 5 # • Ç + V = A V + BI V 1 2 2 V 1 1 I 2 = 0 V 2 = 0 V 2 I 1 = CV 2 + DI 2 I 2 9/ a 9 ; ! a b • !./5 $' C& $' { $' { $ ' [ 9/ a 9 ! a b • { • { 9/ a 9 + ! a b • [ 9/ a 9 - ! a b • C ) • #{ • L ) 9/ a 9 ! a b • í !./5 # 9/ a 9 1 ! a b • C& { +* 9/ a 9 2 ! a b • I • L 9/ a 9 3 ! a b # $ • t # ? • 5 @ 9a ? • L • ! # ) 9/ a 9 9 ! a b • { # ) 8 -
Brief Study of Two Port Network and Its Parameters
© 2014 IJIRT | Volume 1 Issue 6 | ISSN : 2349-6002 Brief study of two port network and its parameters Rishabh Verma, Satya Prakash, Sneha Nivedita Abstract- this paper proposes the study of the various ports (of a two port network. in this case) types of parameters of two port network and different respectively. type of interconnections of two port networks. This The Z-parameter matrix for the two-port network is paper explains the parameters that are Z-, Y-, T-, T’-, probably the most common. In this case the h- and g-parameters and different types of relationship between the port currents, port voltages interconnections of two port networks. We will also discuss about their applications. and the Z-parameter matrix is given by: Index Terms- two port network, parameters, interconnections. where I. INTRODUCTION A two-port network (a kind of four-terminal network or quadripole) is an electrical network (circuit) or device with two pairs of terminals to connect to external circuits. Two For the general case of an N-port network, terminals constitute a port if the currents applied to them satisfy the essential requirement known as the port condition: the electric current entering one terminal must equal the current emerging from the The input impedance of a two-port network is given other terminal on the same port. The ports constitute by: interfaces where the network connects to other networks, the points where signals are applied or outputs are taken. In a two-port network, often port 1 where ZL is the impedance of the load connected to is considered the input port and port 2 is considered port two. -
Automated Problem and Solution Generation Software for Computer-Aided Instruction in Elementary Linear Circuit Analysis
AC 2012-4437: AUTOMATED PROBLEM AND SOLUTION GENERATION SOFTWARE FOR COMPUTER-AIDED INSTRUCTION IN ELEMENTARY LINEAR CIRCUIT ANALYSIS Mr. Charles David Whitlatch, Arizona State University Mr. Qiao Wang, Arizona State University Dr. Brian J. Skromme, Arizona State University Brian Skromme obtained a B.S. degree in electrical engineering with high honors from the University of Wisconsin, Madison and M.S. and Ph.D. degrees in electrical engineering from the University of Illinois, Urbana-Champaign. He was a member of technical staff at Bellcore from 1985-1989 when he joined Ari- zona State University. He is currently professor in the School of Electrical, Computer, and Energy Engi- neering and Assistant Dean in Academic and Student Affairs. He has more than 120 refereed publications in solid state electronics and is active in freshman retention, computer-aided instruction, curriculum, and academic integrity activities, as well as teaching and research. c American Society for Engineering Education, 2012 Automated Problem and Solution Generation Software for Computer-Aided Instruction in Elementary Linear Circuit Analysis Abstract Initial progress is described on the development of a software engine capable of generating and solving textbook-like problems of randomly selected topologies and element values that are suitable for use in courses on elementary linear circuit analysis. The circuit generation algorithms are discussed in detail, including the criteria that define an “acceptable” circuit of the type typically used for this purpose. The operation of the working prototype is illustrated, showing automated problem generation, node and mesh analysis, and combination of series and parallel elements. Various graphical features are available to support student understanding, and an interactive exercise in identifying series and parallel elements is provided. -
9 Op-Amps and Transistors
Notes for course EE1.1 Circuit Analysis 2004-05 TOPIC 9 – OPERATIONAL AMPLIFIER AND TRANSISTOR CIRCUITS . Op-amp basic concepts and sub-circuits . Practical aspects of op-amps; feedback and stability . Nodal analysis of op-amp circuits . Transistor models . Frequency response of op-amp and transistor circuits 1 THE OPERATIONAL AMPLIFIER: BASIC CONCEPTS AND SUB-CIRCUITS 1.1 General The operational amplifier is a universal active element It is cheap and small and easier to use than transistors It usually takes the form of an integrated circuit containing about 50 – 100 transistors; the circuit is designed to approximate an ideal controlled source; for many situations, its characteristics can be considered as ideal It is common practice to shorten the term "operational amplifier" to op-amp The term operational arose because, before the era of digital computers, such amplifiers were used in analog computers to perform the operations of scalar multiplication, sign inversion, summation, integration and differentiation for the solution of differential equations Nowadays, they are considered to be general active elements for analogue circuit design and have many different applications 1.2 Op-amp Definition We may define the op-amp to be a grounded VCVS with a voltage gain (µ) that is infinite The circuit symbol for the op-amp is as follows: An equivalent circuit, in the form of a VCVS is as follows: The three terminal voltages v+, v–, and vo are all node voltages relative to ground When we analyze a circuit containing op-amps, we cannot use the -
Circuit Elements Basic Circuit Elements
CHAPTER 2: Circuit Elements Basic circuit elements • Voltage sources, • Current sources, • Resistors, • Inductors, • Capacitors We will postpone introducing inductors and capacitors until Chapter 6, because their use requires that you solve integral and differential equations. 2.1 Voltage and Current Sources • An electrical source is a device that is capable of converting nonelectric energy to electric energy and vice versa. – A discharging battery converts chemical energy to electric energy, whereas a battery being charged converts electric energy to chemical energy. – A dynamo is a machine that converts mechanical energy to electric energy and vice versa. • If operating in the mechanical-to-electric mode, it is called a generator. • If transforming from electric to mechanical energy, it is referred to as a motor. • The important thing to remember about these sources is that they can either deliver or absorb electric power, generally maintaining either voltage or current. 2.1 Voltage and Current Sources • An ideal voltage source is a circuit element that maintains a prescribed voltage across its terminals regardless of the current flowing in those terminals. • Similarly, an ideal current source is a circuit element that maintains a prescribed current through its terminals regardless of the voltage across those terminals. • These circuit elements do not exist as practical devices—they are idealized models of actual voltage and current sources. 2.1 Voltage and Current Sources • Ideal voltage and current sources can be further described as either independent sources or dependent sources. An independent source establishes a voltage or current in a circuit without relying on voltages or currents elsewhere in the circuit. -
Introduction to Transmission Lines
INTRODUCTION TO TRANSMISSION LINES DR. FARID FARAHMAND FALL 2012 http://www.empowermentresources.com/stop_cointelpro/electromagnetic_warfare.htm RF Design ¨ In RF circuits RF energy has to be transported ¤ Transmission lines ¤ Connectors ¨ As we transport energy energy gets lost ¤ Resistance of the wire à lossy cable ¤ Radiation (the energy radiates out of the wire à the wire is acting as an antenna We look at transmission lines and their characteristics Transmission Lines A transmission line connects a generator to a load – a two port network Transmission lines include (physical construction): • Two parallel wires • Coaxial cable • Microstrip line • Optical fiber • Waveguide (very high frequencies, very low loss, expensive) • etc. Types of Transmission Modes TEM (Transverse Electromagnetic): Electric and magnetic fields are orthogonal to one another, and both are orthogonal to direction of propagation Example of TEM Mode Electric Field E is radial Magnetic Field H is azimuthal Propagation is into the page Examples of Connectors Connectors include (physical construction): BNC UHF Type N Etc. Connectors and TLs must match! Transmission Line Effects Delayed by l/c At t = 0, and for f = 1 kHz , if: (1) l = 5 cm: (2) But if l = 20 km: Properties of Materials (constructive parameters) Remember: Homogenous medium is medium with constant properties ¨ Electric Permittivity ε (F/m) ¤ The higher it is, less E is induced, lower polarization ¤ For air: 8.85xE-12 F/m; ε = εo * εr ¨ Magnetic Permeability µ (H/m) Relative permittivity and permeability -
WAVEGUIDE ATTENUATORS : in Order to Control Power Levels in a Microwave System by Partially Absorbing the Transmitted Microwave Signal, Attenuators Are Employed
UNIT II MICROWAVE COMPONENTS Waveguide Attenuators- Resistive card, Rotary Vane types. Waveguide Phase Shifters : Dielectric, Rotary Vane types. Waveguide Multi port Junctions- E plane and H plane Tees, Magic Tee, Hybrid Ring. Directional Couplers- 2 hole, Bethe hole types. Ferrites-Composition and characteristics, Faraday Rotation. Ferrite components: Gyrator, Isolator, Circulator. S-matrix calculations for 2 port junction, E & H plane Tees, Magic Tee, Directional Coupler, Circulator and Isolator WAVEGUIDE ATTENUATORS : In order to control power levels in a microwave system by partially absorbing the transmitted microwave signal, attenuators are employed. Resistive films (dielectric glass slab coated with aquadag) are used in the design of both fixed and variable attenuators. A co-axial fixed attenuator uses the dielectric lossy material inside the centre conductor of the co-axial line to absorb some of the centre conductor microwave power propagating through it dielectric rod decides the amount of attenuation introduced. The microwave power absorbed by the lossy material is dissipated as heat. 1 In waveguides, the dielectric slab coated with aquadag is placed at the centre of the waveguide parallel to the maximum E-field for dominant TEIO mode. Induced current on the lossy material due to incoming microwave signal, results in power dissipation, leading to attenuation of the signal. The dielectric slab is tapered at both ends upto a length of more than half wavelength to reduce reflections as shown in figure 5.7. The dielectric slab may be made movable along the breadth of the waveguide by supporting it with two dielectric rods separated by an odd multiple of quarter guide wavelength and perpendicular to electric field. -
A Unified State-Space Approach to Rlct Two-Port
A UNIFIED STATE-SPACE APPROACH TO RLCT TWO-PORT TRANSFER FUNCTION SYNTHESIS By EDDIE RANDOLPH FOWLER Bachelor of Science Kan,sas State University Manhattan, Kansas 1957 Master of Science Kansas State University Manhattan, Kansas 1965 Submitted to the Faculty of the Graduate Col.lege of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY May, 1969 OKLAHOMA STATE UNIVERSITY LIBRARY SEP 2l1 l969 ~ A UNIFIED STATE-SPACE APPROACH TO RLCT TWO-PORT TRANSFER FUNCTION SYNTHESIS Thesis Approved: Dean of the Graduate College ii AC!!..NOWLEDGEMENTS Only those that have had children in school all during their graduate studies know the effort and sacrifice that my wife, Pat, has endured during my graduate career. I appreciate her accepting this role without complainL Also I am deeply grateful that she was willing to take on the horrendous task of typing this thesis. My heartfelt thanks to Dr. Rao Yarlagadda, my thesis advisor, who was always available for $Uidance and help during the research and writing of this thesis. I appreciate the assistance and encouragement of the other members of my graduate comruitteei, Dr. Kenneth A. McCollom, Dr. Charles M. Bacon ar1d Dr~ K.ar 1 N.... ·Re id., I acknowledge Paul Howell, a fellow Electrical Engineering grad uate student, whose Christian Stewardship has eased the burden during these last months of thesis preparation~ Also Dwayne Wilson, Adminis trative Assistant, has n1y gratitude for assisting with the financial and personal problems of the Electrical Engineering graduate students. My thanks to Dr. Arthur M. Breipohl for making available the assistant ship that was necessary before it was financially possible to initiate my doctoral studies. -
Transmission Line and Lumped Element Quadrature Couplers
High Frequency Design From November 2009 High Frequency Electronics Copyright © 2009 Summit Technical Media, LLC QUADRATURE COUPLERS Transmission Line and Lumped Element Quadrature Couplers By Gary Breed Editorial Director uadrature cou- This month’s tutorial article plers are used for reviews the basic design Qpower division and operation of power and combining in circuits divider/combiners with where the 90º phase shift ports that have a 90- between the two coupled degree phase difference ports will result in a desirable performance characteristic. Common uses of quadrature couplers include: Antenna feed systems—The combination of power division/combining and 90º phase shift can simplify the feed network of phased array antenna systems, compared to alternative net- Figure 1 · The branch line quadrature works using delay lines, other types of com- hybrid, implemented using λ/4 transmission biners and impedance matching networks. It line sections. is especially useful for feeding circularly polarized arrays. Test and measurement systems—The phase each module has active devices in push-pull shift performance performance may be suffi- (180º combined), both even- and odd-order ciently accurate for phase comparisons over a harmonics can be reduced, which simplifies substantial fraction of an octave. A less critical output filtering. use is to resolve phase ambiguity in test cir- In an earlier tutorial [1], I introduced a cuits. A number of measurement techniques range of 90º coupler types without much anal- have a discontinuity at 180º—as this value is ysis. In this article, we focus on the two main approached, a 90º phase “rotation” moves the coupler types—the branch-line and coupled- system away from that point. -
1. Characteristics and Parameters of Operational Amplifiers
1. CHARACTERISTICS AND PARAMETERS OF OPERATIONAL AMPLIFIERS The characteristics of an ideal operational amplifier are described first, and the characteristics and performance limitations of a practical operational amplifier are described next. There is a section on classification of operational amplifiers and some notes on how to select an operational amplifier for an application. 1.1 IDEAL OPERATIONAL AMPLIFIER 1.1.1 Properties of An Ideal Operational Amplifier The characteristics or the properties of an ideal operational amplifier are: i. Infinite Open Loop Gain, ii. Infinite Input Impedance, iii. Zero Output Impedance, iv. Infinite Bandwidth, v. Zero Output Offset, and vi. Zero Noise Contribution. The opamp, an abbreviation for the operational amplifier, is the most important linear IC. The circuit symbol of an opamp shown in Fig. 1.1. The three terminals are: the non-inverting input terminal, the inverting input terminal and the output terminal. The details of power supply are not shown in a circuit symbol. 1.1.2 Infinite Open Loop Gain From Fig.1.1, it is found that vo = - Ao × vi, where `Ao' is known as the open-loop 5 gain of the opamp. Let vo be -10 Volts, and Ao be 10 . Then vi is 100 :V. Here 1 the input voltage is very small compared to the output voltage. If Ao is very large, vi is negligibly small for a finite vo. For the ideal opamp, Ao is taken to be infinite in value. That means, for an ideal opamp vi = 0 for a finite vo. Typical values of Ao range from 20,000 in low-grade consumer audio-range opamps to more than 2,000,000 in premium grade opamps ( typically 200,000 to 300,000). -
Implementing Voltage Controlled Current Source in Electromagnetic Full-Wave Simulation Using the FDTD Method Khaled Elmahgoub and Atef Z
Implementing Voltage Controlled Current Source in Electromagnetic Full-Wave Simulation using the FDTD Method Khaled ElMahgoub and Atef Z. Elsherbeni Center of Applied Electromagnetic System Research (CAESR), Department of Electrical Engineering, The University of Mississippi, University, Mississippi, USA. [email protected] and [email protected] Abstract — The implementation of a voltage controlled FDTD is introduced with efficient use of both memory and current source (VCCS) in full-wave electromagnetic simulation computational time. This new approach can be used to analyze using finite-difference time-domain (FDTD) is introduced. The VCCS is used to model a metal oxide semiconductor field effect circuits including VCCS or circuits include devices such as transistor (MOSFET) commonly used in microwave circuits. This MOSFETs and BJTs using their equivalent circuit models. To new approach is verified with several numerical examples the best of the authors’ knowledge, the implementation of including circuits with VCCS and MOSFET. Good agreement is dependent sources using FDTD has not been adequately obtained when the results are compared with those based on addressed before. In addition, in most of the previous work the analytical solution and PSpice. implementation of nonlinear devices such as transistors has Index Terms — Finite-difference time-domain, dependent been handled using FDTD-SPICE models or by importing the sources, voltage controlled current source, MOSFET. S-parameters from another technique to the FDTD simulation [2]-[7]. In this work the implementation of the VCCS in I. INTRODUCTION FDTD will be used to simulate a MOSFET with its equivalent The finite-difference time-domain (FDTD) method has gained model without the use of external tools, the entire simulation great popularity as a tool used for electromagnetic can be done using the FDTD.