Beam Current Monitors

Size: px
Start display at page:

Download "Beam Current Monitors"

Transcription

1 Beam Current Monitors Accelerator Beam Diagnos4cs W. Blokland (ORNL) USPAS and University of New Mexico Albuquerque NM, June 23 26, 2009 USPAS09 at UNM Accelerator and Beam Diagnos4cs 1

2 Beam Current Monitors Why use Beam Current Monitors? How to couple to the beam Transformer Resis4ve Wall Current monitor Faraday Cups Limita4ons: Noise, bandwidth Lab USPAS09 at UNM Accelerator and Beam Diagnos4cs 2

3 Par4cle Accelerators One measure of performance: Power The amount of particles delivered at a certain energy. SNS Power on target SNS Energy delivered to target USPAS09 at UNM Accelerator and Beam Diagnos4cs 3

4 Par4cle Accelerators How well do you accelerate beam? What percent of the particles make it to the end Effectiveness of acceleration process. E.g. stripping losses 3-5% of beam What percent of time are you operational? Damage to accelerator What is the quality of your beam? Emittance (collider) Density profile (target) Position stability Radio-activation USPAS09 at UNM Accelerator and Beam Diagnos4cs 4

5 Charged Beam What is the beam current? I beam = qen t = qen l βc In an accelerator the current is formed by N par4cles of charge state q per unit of 4me t or unit of length l and velocity β = v/c. The beam is nearly an ideal current source with a very high source impedance We can measure the beam through the electric and magnetic fields created by the beam. USPAS09 at UNM Accelerator and Beam Diagnos4cs 5

6 Beam Current Structure SNS Beam Structure USPAS09 at UNM Accelerator and Beam Diagnos4cs 6

7 Beam Image currents [5] [5] Moving charge Fast moving charge Fast moving par4cles (moving E field) create an H field. The H field moves the E field induced image charges. At high veloci4es the wall current spectrum is an image (opposite sign) of the beam spectrum: at at a speed of 0.5c, approx RMS length is 90ps or 1.8GHz USPAS09 at UNM Accelerator and Beam Diagnos4cs 7

8 Beam Image currents If the wall current mirrors the beam current then the magne4c field outside the beam pipe is cancelled: Ampere's Law : H dl = I and with I beam = - I image then H dl = I beam + I image = 0 H = 0 Is it completely cancelled? Skin depth: the length in which the fields are reduced by a factor of e ( 8.7 db). At 10Mhz, a typical 0.794mm stainless pipe aeenuates 53dB. δ = π ρ f with ρ the resistivity and f the frequency From [2] Webber. USPAS09 at UNM Accelerator and Beam Diagnos4cs 8

9 Beam Pipe Break No field outside of beam pipe. Either: install detector inside beam pipe or Inside beam pipe means installa4on in vacuum use a ceramic break Ceramic break forces image current to find another path and it will do so! Z gap USPAS09 at UNM Accelerator and Beam Diagnos4cs 9

10 You beeer define your gap impedance. Something will always be present, such as a path to ground and capacitance. Z gap is combina4on of the gap capacitance and all external parallel elements Gap voltage Gap Impedance Courtesy of Jim Crisp & Mike can be generated up to beam voltage Z gap USPAS09 at UNM Accelerator and Beam Diagnos4cs 10

11 Current transformer Measure the beam current through the magne4c field of the beam. Assume the beam is long enough to be regarded as a line current. E.g. SNS Ring: 250 meters for 1usec Line current field : B = µ I beam 2πr a ϕ [1] Β Torus to guide the magnetic field I beam R v out USPAS09 at UNM Accelerator and Beam Diagnos4cs 11

12 V p I p Primary winding N p turns H N turns Current transformer toroid material permeability = µ 0 µ r cross section = A Mean radius = r I s I p R s R s Secondary winding N s turns Integration path dl v s V s Ampere s Law: H dl = N p I p + N s I s = I p + N s I s with N p =1 H = (I p + N s I s ) /2πr (1) Φ = Flux: (thin toroid approxima4on) ds= µha = µa(i p + N s I s ) /2πr with A as area (2) B S Faraday s Law: V s = N s dφ dt = I s R s (3) Combine (2) and (3): I s R s = N s µa 2πr d(i + N I ) p s s dt Differen4al equa4on: di s dt + R s I s = 1 di p L s N s dt Laplace rewrite: I s (iω) I p (iω) = 1 N s iω (iω + R s /L s ) with L s = N 2 sµa 2πr USPAS09 at UNM Accelerator and Beam Diagnos4cs 12 (4)

13 Current transformer Great, we got our transfer function and now we can figure out what the behavior is of our current transformer: I s (iω) I p (iω) = 1 N s iω (iω + R s /L s ) When Power: iω >> R s /L s P s = I 2 s R s = I 2 p N R 2 s s I s = I p N s (transferred from beam) USPAS09 at UNM Accelerator and Beam Diagnos4cs 13

14 Current transformer The inductance plays an important role in the design of transformer. Note that in the calculation for inductance, the geometry of the setup plays and important role as well as the µ and windings. Inductance of a torus with a square cross section: Φ = B ds= S µhds = S µi 2πr ldr = µi 2π lln r out r out with L = NΦ then I L = µn 2 l 2π ln r out and µ = µ 0 µ r r in r in r in µ r can be > ι ds r in µ r r out L s = N s 2 L p USPAS09 at UNM Accelerator and Beam Diagnos4cs 14

15 Current transformer Too bad there is also a capacitance: we get an LCR circuit: [1] 1 Z = 1 R + 1 iωl + iωc iωl Z = 1+ iωl /R (ωl /R) (ωrc) USPAS09 at UNM Accelerator and Beam Diagnos4cs 15

16 LRC Proper4es What are proper4es of an LRC circuit? iωl Z = 1+ iωl /R (ωl /R) (ωrc) For low frequency : ω << R /L Z = iωl For high frequency : ω >>1/RC Z =1/iωC For mid frequency : R /L << ω <<1/RC Z R It s a band pass with a: droop 4me t droop rise 4me t rise log [5] R/L 1/RC ω USPAS09 at UNM Accelerator and Beam Diagnos4cs 16

17 Bandpass effects on pulse shape USPAS09 at UNM Accelerator and Beam Diagnos4cs 17

18 Rise 4me and droop 4me Rise 4me t rise : defined as the 4me it takes the amplitude to go from 10% to 90%. Rise 4me constant τ rise : and τ A (1 e t /τ rise ) rise corresponds to the 4me for an increase by e 1 = 37 %. t rise = ln0.9 ln0.1 ω high = ω high = πf high ω high =1/RC t rise 2RC 1 3 f high or t rise 2τ rise with τ rise = RC Droop 4me t droop = ω low = R /L ln0.9 ln0.1 ω low = ω low = πf low 1 3 f low t low 2L /R or t low 2τ low with τ low = L /R USPAS09 at UNM Accelerator and Beam Diagnos4cs 18

19 Current Transformer Add (long) cable to current transformer: add cable resistance, capacitance and inductance: τ rise = L s C s τ droop = L /(R +R L ) [1] Ac4ve Transformer: use a trans impedance circuit to lower the load impedance. τ droop = L /(R f / A +R L ) = L /R L [1] USPAS09 at UNM Accelerator and Beam Diagnos4cs 19

20 Design of Current Transformer How to design a current transformer: High sensi4vity > low number of turns, low N s High droop 4me > high L > high µ, high N s τ droop = L s /R s V s = I s R s = I b N s R s L s = l 2π ln r out 2 µ N s Fast rise 4me > low stray capacitance r in τ rise = L s C s with cable τ rise = RC without cable USPAS09 at UNM Accelerator and Beam Diagnos4cs 20

21 Design of Current Transformer Passive transformer Ac4ve transformer USPAS09 at UNM Accelerator and Beam Diagnos4cs 21

22 DC Current Transformer How to measure the DC current? The current transformer discussed sees only changes in the flux. The DC Current Transformer (DCCT): look at the magne4c satura4on of the torus. Modula4on of the primary windings forces the torus into satura4on twice per cycle. Secondary windings sense modula4on signal and cancel each other. But with the I beam, the satura4on is shiued and I sense is not zero Adjust compensa4on current un4l I sense is zero once again. DC Transformer Opera4on, see [1] USPAS09 at UNM Accelerator and Beam Diagnos4cs 22

23 DC Current Transformer Example bandwidth: DC to 20kHz, resolu4on 2µA [1] Modula4on of the primary windings forces the torus into satura4on twice per cycle. Secondary windings sense modula4on signal and cancel each other. But with the I beam, the satura4on is shiued and I sense is not zero Adjust compensa4on current un4l I sense is zero once again. USPAS09 at UNM Accelerator and Beam Diagnos4cs 23

24 Current Monitor Limita4ons Limita4on to transformers: The permeability of a core can be saturated: specs of max B field or max current 4me product I*t, Thermal noise: V n 4k b Tf high R -> µa range lower limit Weiss domains lead to Barkhausen noise if termina4ng with high impedance (limit for DC type) Avoid external magne4c fields Torus material has dependency of µ r on temperature or on mechanical stress (micro phonic pickup) Avoid secondary electrons from being measured USPAS09 at UNM Accelerator and Beam Diagnos4cs 24

25 BCM Tes4ng Fixture Image by M. Kesselman USPAS09 at UNM Accelerator and Beam Diagnos4cs 25

26 SNS Current Transformer Image by M. Kesselman. USPAS09 at UNM Accelerator and Beam Diagnos4cs 26

27 LHC Fast Current Transformer U. Raich CAS Frasca Beam Diagnos4cs USPAS09 at UNM Accelerator and Beam Diagnos4cs 27

28 COMPONENTS INSIDE HEBT BCM ASSEMBLY Design by BNL for SNS USPAS09 at UNM Accelerator and Beam Diagnos4cs 28

29 Wall Current Monitor Put a resistor over the gap and measure its voltage. V gap = R gap I beam V out R No DC in image current USPAS09 at UNM Accelerator and Beam Diagnos4cs 29

30 Wall Current Monitor U. Raich USPAS09 at UNM Accelerator and Beam Diagnos4cs 30

31 Wall Current Monitor Now for the details: Ceramic gap to avoid working in vacuum Distributed resistors (30 to 100) for beam posi4on independency Ferrite rings for low frequency response Shield for ground currents and noise protec4on Schema4cs of a wall current monitor and its equivalent circuit [1] USPAS09 at UNM Accelerator and Beam Diagnos4cs 31

32 Wait, there is more I in /n Broadband Model [4] 2ζ= (R L / R L + R s )((R s C/L e + (1/ R L ) L e /C) ω o = 1/(R L / R L + R s ) L e C I in /n Even a resistor is not a resistor: Low to Midband Model [4] USPAS09 at UNM Accelerator and Beam Diagnos4cs 32

33 Faraday Cups The Faraday Cup destruc4vely intercepts the beam DC coupled! (With just a resistor the signal is V out = I beam *R) Low current measurements possible e.g., 10pA Problem with secondary electrons: - Use long cup or voltage suppression or magne4c field If not properly terminated > very high voltage (beam poten4al) Must process beam power (SNS full power 1.4MW) [1] USPAS09 at UNM Accelerator and Beam Diagnos4cs 33

34 Faraday Cups Low power Faraday Cup [1] High power (1MW) Faraday Cup [1] USPAS09 at UNM Accelerator and Beam Diagnos4cs 34

35 Noise Issues Noise can be a problem! There are many powerful noise sources in Accelerators: - Switching power supplies - Accelera4ng RF - Source RF Case in point: - SNS DTL BCM > single ended and inside a cavity (due to space limita4ons) USPAS09 at UNM Accelerator and Beam Diagnos4cs 35

36 Noise Issues Noise from switching power supplies Grounded [8] USPAS09 at UNM Noise from RF Beam Noise of DTL current transformer (inside cavity, single ended) Accelerator and Beam Diagnos4cs 36

37 Noise Issues Beam SCL Beam Current Monitor (single ended) USPAS09 at UNM [8] Accelerator and Beam Diagnos4cs 37

38 Noise Issues Beeer: CCL BCM outside of cavity but s4ll single ended. Beam CCL Beam Current Monitor (single ended) USPAS09 at UNM Accelerator and Beam Diagnos4cs 38

39 Noise Issues: Common Mode If noise is coupled into both wires, we can reject it! > common mode noise rejec4on by taking the difference. You will do this as a lab experiment. 20mV 2mV 20mV Differen4al noise on long twinax with far end shield grounded. Leu: top and boeom, noise on either center conductor into 50 ohms (each 20mV/div); center, difference (2mV/div); (most of residual signal due to digital scope subtrac4on). Right: same signals faster 4me scale (each 20mV/div and 1uS/div). From [2] Webber. USPAS09 at UNM Accelerator and Beam Diagnos4cs 39

40 References [1] Forck P., Lecture Notes on Beam Instrumenta4on and Diagnos4cs, Joint University Accelerator School, [2] Webber R.C., Tutorial on Beam Current Monitoring, BIW 2000, pp [3] Webber R.C., Charged Par4cle Beam Current Monitoring Tutorial, BIW1994, pp 3 23 [4] Webber R.C., Longitudinal Emieance: An Introduc4on to the Concept and Survey of Measurement Techniques, Including Design of a Wall Current Monitor BIW 1993 [5] Denard, J.C. CERN Accelerator School on Beam Diagnos4cs, 28 May 6 June 2008, Dourdan. [6] Hammond P., Electromagne4sm for Engineers, Pergamon Press. [7] Waters C., Current Transformers provide accurate, isolated Measurements, Power Conversion& Intelligent Mo4on, Issue December 1986 [8] Plum M., LANL Current Monitor Pickup Final Design Review, March [9] Edminister J., Schaum's Outline of Electromagne4cs BCM Lunch4me Seminar 40

Application Note. So You Need to Measure Some Inductors?

Application Note. So You Need to Measure Some Inductors? So You Need to Measure Some nductors? Take a look at the 1910 nductance Analyzer. Although specifically designed for production testing of inductors and coils, in addition to measuring inductance (L),

More information

Current Probes. User Manual

Current Probes. User Manual Current Probes User Manual ETS-Lindgren L.P. reserves the right to make changes to any product described herein in order to improve function, design, or for any other reason. Nothing contained herein shall

More information

Edmund Li. Where is defined as the mutual inductance between and and has the SI units of Henries (H).

Edmund Li. Where is defined as the mutual inductance between and and has the SI units of Henries (H). INDUCTANCE MUTUAL INDUCTANCE If we consider two neighbouring closed loops and with bounding surfaces respectively then a current through will create a magnetic field which will link with as the flux passes

More information

Pulsed Power Engineering Diagnostics

Pulsed Power Engineering Diagnostics Pulsed Power Engineering Diagnostics January 12-16, 2009 Craig Burkhart, PhD Power Conversion Department SLAC National Accelerator Laboratory Diagnostic Techniques and Considerations in Pulsed Power Systems

More information

Current Probes, More Useful Than You Think

Current Probes, More Useful Than You Think Current Probes, More Useful Than You Think Training and design help in most areas of Electrical Engineering Copyright 1998 Institute of Electrical and Electronics Engineers. Reprinted from the IEEE 1998

More information

An equivalent circuit of a loop antenna.

An equivalent circuit of a loop antenna. 3.2.1. Circuit Modeling: Loop Impedance A loop antenna can be represented by a lumped circuit when its dimension is small with respect to a wavelength. In this representation, the circuit parameters (generally

More information

Grounding Demystified

Grounding Demystified Grounding Demystified 3-1 Importance Of Grounding Techniques 45 40 35 30 25 20 15 10 5 0 Grounding 42% Case 22% Cable 18% Percent Used Filter 12% PCB 6% Grounding 42% Case Shield 22% Cable Shielding 18%

More information

Lecture 24. Inductance and Switching Power Supplies (how your solar charger voltage converter works)

Lecture 24. Inductance and Switching Power Supplies (how your solar charger voltage converter works) Lecture 24 Inductance and Switching Power Supplies (how your solar charger voltage converter works) Copyright 2014 by Mark Horowitz 1 Roadmap: How Does This Work? 2 Processor Board 3 More Detailed Roadmap

More information

Last time : energy storage elements capacitor.

Last time : energy storage elements capacitor. Last time : energy storage elements capacitor. Charge on plates Energy stored in the form of electric field Passive sign convention Vlt Voltage drop across real capacitor can not change abruptly because

More information

A wave lab inside a coaxial cable

A wave lab inside a coaxial cable INSTITUTE OF PHYSICS PUBLISHING Eur. J. Phys. 25 (2004) 581 591 EUROPEAN JOURNAL OF PHYSICS PII: S0143-0807(04)76273-X A wave lab inside a coaxial cable JoãoMSerra,MiguelCBrito,JMaiaAlves and A M Vallera

More information

Estimates of mutual inductance

Estimates of mutual inductance Estimates of mutual inductance Biot-avarts law: B I 2r B is the magnetic flux density at a distance r from a (long) conductor carrying a current I. B increases with increasing I B decreases with increasing

More information

Impedance Matching and Matching Networks. Valentin Todorow, December, 2009

Impedance Matching and Matching Networks. Valentin Todorow, December, 2009 Impedance Matching and Matching Networks Valentin Todorow, December, 2009 RF for Plasma Processing - Definition of RF What is RF? The IEEE Standard Dictionary of Electrical and Electronics Terms defines

More information

Output Ripple and Noise Measurement Methods for Ericsson Power Modules

Output Ripple and Noise Measurement Methods for Ericsson Power Modules Output Ripple and Noise Measurement Methods for Ericsson Power Modules Design Note 022 Ericsson Power Modules Ripple and Noise Abstract There is no industry-wide standard for measuring output ripple and

More information

Iron Powder Cores for Switchmode Power Supply Inductors. by: Jim Cox

Iron Powder Cores for Switchmode Power Supply Inductors. by: Jim Cox HOME APPLICATION NOTES Iron Powder Cores for Switchmode Power Supply Inductors by: Jim Cox Purpose: The purpose of this application note is to cover the properties of iron powder as a magnetic core material

More information

Subject: Glenair MIL-PRF 24758 Conduit Surface Transfer Impedance Test

Subject: Glenair MIL-PRF 24758 Conduit Surface Transfer Impedance Test Lothar O. Hoeft, Ph.D. Consultant, Electromagnetic Effects 5012 San Pedro Ct., NE Albuquerque, New Mexico 87109-2515 Phone: (505)-889-9705 E-mail: bud.hoeft@ieee.org 1 February 24, 2006 Subject: Glenair

More information

PHY114 S11 Term Exam 3

PHY114 S11 Term Exam 3 PHY4 S Term Exam S. G. Rajeev Mar 2 20 2:0 pm to :45 pm PLEASE write your workshop number and your workshop leader s name at the top of your book, so that you can collect your graded exams at the workshop.

More information

Standex-Meder Electronics. Custom Engineered Solutions for Tomorrow

Standex-Meder Electronics. Custom Engineered Solutions for Tomorrow Standex-Meder Electronics Custom Engineered Solutions for Tomorrow RF Reed Relays Part II Product Training Copyright 2013 Standex-Meder Electronics. All rights reserved. Introduction Purpose Designing

More information

Application Note AN:005. FPA Printed Circuit Board Layout Guidelines. Introduction Contents. The Importance of Board Layout

Application Note AN:005. FPA Printed Circuit Board Layout Guidelines. Introduction Contents. The Importance of Board Layout FPA Printed Circuit Board Layout Guidelines By Paul Yeaman Principal Product Line Engineer V I Chip Strategic Accounts Introduction Contents Page Introduction 1 The Importance of 1 Board Layout Low DC

More information

ES250: Electrical Science. HW7: Energy Storage Elements

ES250: Electrical Science. HW7: Energy Storage Elements ES250: Electrical Science HW7: Energy Storage Elements Introduction This chapter introduces two more circuit elements, the capacitor and the inductor whose elements laws involve integration or differentiation;

More information

ILB, ILBB Ferrite Beads

ILB, ILBB Ferrite Beads ILB, ILBB Ferrite Beads Electro-Magnetic Interference and Electro-Magnetic Compatibility (EMI/EMC) avid B. Fancher Inductive Products ivision INTROUCTION Manufacturers of electrical and electronic equipment

More information

Slide 1 / 26. Inductance. 2011 by Bryan Pflueger

Slide 1 / 26. Inductance. 2011 by Bryan Pflueger Slide 1 / 26 Inductance 2011 by Bryan Pflueger Slide 2 / 26 Mutual Inductance If two coils of wire are placed near each other and have a current passing through them, they will each induce an emf on one

More information

Inductor and Magnetic Product Terminology

Inductor and Magnetic Product Terminology INTRODUCTION IFC LPT ILB IHSM IM IMC LPE TJ LPC IRF IHB The scope of this application note is to define the terminology associated with inductors and their applications. Some of these terms are listed

More information

MEASUREMENT SET-UP FOR TRAPS

MEASUREMENT SET-UP FOR TRAPS Completed on 26th of June, 2012 MEASUREMENT SET-UP FOR TRAPS AUTHOR: IW2FND Attolini Lucio Via XXV Aprile, 52/B 26037 San Giovanni in Croce (CR) - Italy iw2fnd@gmail.com Trappole_01_EN 1 1 DESCRIPTION...3

More information

Ferroxcube. For more information on Product Status Definitions, see page 3. 2008 Sep 01 275 CBW625

Ferroxcube. For more information on Product Status Definitions, see page 3. 2008 Sep 01 275 CBW625 CBW625 For more information on Product Status Definitions, see page 3. 2008 Sep 01 275 INTRODUCTION Ferrites are used not only in the known consumer and professional electronics applications, but also

More information

AMPLIFIED HIGH SPEED FIBER PHOTODETECTOR USER S GUIDE

AMPLIFIED HIGH SPEED FIBER PHOTODETECTOR USER S GUIDE AMPLIFIED HIGH SPEED FIBER PHOTODETECTOR USER S GUIDE Thank you for purchasing your Amplified High Speed Fiber Photodetector. This user s guide will help answer any questions you may have regarding the

More information

NZQA registered unit standard 20431 version 2 Page 1 of 7. Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians

NZQA registered unit standard 20431 version 2 Page 1 of 7. Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians NZQA registered unit standard 0431 version Page 1 of 7 Title Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians Level 3 Credits 7 Purpose This unit standard covers

More information

April 1. Physics 272. Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html. Prof. Philip von Doetinchem philipvd@hawaii.

April 1. Physics 272. Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html. Prof. Philip von Doetinchem philipvd@hawaii. Physics 272 April 1 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272 - Spring 14 - von Doetinchem - 164 Summary Gauss's

More information

AVX EMI SOLUTIONS Ron Demcko, Fellow of AVX Corporation Chris Mello, Principal Engineer, AVX Corporation Brian Ward, Business Manager, AVX Corporation

AVX EMI SOLUTIONS Ron Demcko, Fellow of AVX Corporation Chris Mello, Principal Engineer, AVX Corporation Brian Ward, Business Manager, AVX Corporation AVX EMI SOLUTIONS Ron Demcko, Fellow of AVX Corporation Chris Mello, Principal Engineer, AVX Corporation Brian Ward, Business Manager, AVX Corporation Abstract EMC compatibility is becoming a key design

More information

Coupling Impedance of SIS18 and SIS100 beampipe CERN-GSI-Webmeeting

Coupling Impedance of SIS18 and SIS100 beampipe CERN-GSI-Webmeeting Coupling Impedance of SIS18 and SIS100 beampipe CERN-GSI-Webmeeting 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 1 Contents Motivation / Overview

More information

Homework #11 203-1-1721 Physics 2 for Students of Mechanical Engineering

Homework #11 203-1-1721 Physics 2 for Students of Mechanical Engineering Homework #11 203-1-1721 Physics 2 for Students of Mechanical Engineering 2. A circular coil has a 10.3 cm radius and consists of 34 closely wound turns of wire. An externally produced magnetic field of

More information

Brookhaven National Laboratoy, Upton, NY 11973, USA

Brookhaven National Laboratoy, Upton, NY 11973, USA 10th Beam Instrumentation Workshop BNL, Upton, NY, May 6-9,2002 BNL-69259 BPM System for the SNS Ring and Transfer Lines1 W. C. Dawson, P. Cameron, P. Cerniglia, J. Cupolo, C. Degen, A. DellaPenna, A.

More information

RX-AM4SF Receiver. Pin-out. Connections

RX-AM4SF Receiver. Pin-out. Connections RX-AM4SF Receiver The super-heterodyne receiver RX-AM4SF can provide a RSSI output indicating the amplitude of the received signal: this output can be used to create a field-strength meter capable to indicate

More information

Crosstalk effects of shielded twisted pairs

Crosstalk effects of shielded twisted pairs This article deals with the modeling and simulation of shielded twisted pairs with CST CABLE STUDIO. The quality of braided shields is investigated with respect to perfect solid shields. Crosstalk effects

More information

Chapter 14: Inductor design

Chapter 14: Inductor design Chapter 14 Inductor Design 14.1 Filter inductor design constraints 14.2 A step-by-step design procedure 14.3 Multiple-winding magnetics design using the K g method 14.4 Examples 14.5 Summary of key points

More information

RLC Resonant Circuits

RLC Resonant Circuits C esonant Circuits Andrew McHutchon April 20, 203 Capacitors and Inductors There is a lot of inconsistency when it comes to dealing with reactances of complex components. The format followed in this document

More information

DDX 7000 & 8003. Digital Partial Discharge Detectors FEATURES APPLICATIONS

DDX 7000 & 8003. Digital Partial Discharge Detectors FEATURES APPLICATIONS DDX 7000 & 8003 Digital Partial Discharge Detectors The HAEFELY HIPOTRONICS DDX Digital Partial Discharge Detector offers the high accuracy and flexibility of digital technology, plus the real-time display

More information

G019.A (4/99) UNDERSTANDING COMMON MODE NOISE

G019.A (4/99) UNDERSTANDING COMMON MODE NOISE UNDERSTANDING COMMON MODE NOISE PAGE 2 OF 7 TABLE OF CONTENTS 1 INTRODUCTION 2 DIFFERENTIAL MODE AND COMMON MODE SIGNALS 2.1 Differential Mode signals 2.2 Common Mode signals 3 DIFFERENTIAL AND COMMON

More information

Chapter 15: Transformer design

Chapter 15: Transformer design Chapter 15 Transformer Design Some more advanced design issues, not considered in previous chapter: : n Inclusion of core loss + + Selection of operating flux i 1 density to optimize total loss v 1 v Multiple

More information

Power Supplies. 1.0 Power Supply Basics. www.learnabout-electronics.org. Module

Power Supplies. 1.0 Power Supply Basics. www.learnabout-electronics.org. Module Module 1 www.learnabout-electronics.org Power Supplies 1.0 Power Supply Basics What you ll learn in Module 1 Section 1.0 Power Supply Basics. Basic functions of a power supply. Safety aspects of working

More information

UNDERSTANDING AND CONTROLLING COMMON-MODE EMISSIONS IN HIGH-POWER ELECTRONICS

UNDERSTANDING AND CONTROLLING COMMON-MODE EMISSIONS IN HIGH-POWER ELECTRONICS Page 1 UNDERSTANDING AND CONTROLLING COMMON-MODE EMISSIONS IN HIGH-POWER ELECTRONICS By Henry Ott Consultants Livingston, NJ 07039 (973) 992-1793 www.hottconsultants.com hott@ieee.org Page 2 THE BASIC

More information

Toroids. Toroids. Design Considerations

Toroids. Toroids. Design Considerations Ferrite toroids provide an often convenient and very effective shape for many wide band, pulse and power transformers and inductors. The continuous magnetic path yields the highest effective permeability

More information

Measuring Telecommunication Transformers

Measuring Telecommunication Transformers Measuring Telecommunication Transformers Rapid expansion of the Internet and Mobile Communications has driven the need to transmit digital information at high frequencies. This need has put new requirements

More information

Understanding Power Impedance Supply for Optimum Decoupling

Understanding Power Impedance Supply for Optimum Decoupling Introduction Noise in power supplies is not only caused by the power supply itself, but also the load s interaction with the power supply (i.e. dynamic loads, switching, etc.). To lower load induced noise,

More information

Wireless Power Transfer System Design. Julius Saitz ANSYS

Wireless Power Transfer System Design. Julius Saitz ANSYS Wireless Power Transfer System Design Julius Saitz ANSYS 1 WPT System 2 Wireless Power Transfer (WPT) Near-Field (Inductive coupling, resonant) Do not rely on propagating EM waves Operate at distances

More information

EE301 Lesson 14 Reading: 10.1-10.4, 10.11-10.12, 11.1-11.4 and 11.11-11.13

EE301 Lesson 14 Reading: 10.1-10.4, 10.11-10.12, 11.1-11.4 and 11.11-11.13 CAPACITORS AND INDUCTORS Learning Objectives EE301 Lesson 14 a. Define capacitance and state its symbol and unit of measurement. b. Predict the capacitance of a parallel plate capacitor. c. Analyze how

More information

Chapter 11. Inductors ISU EE. C.Y. Lee

Chapter 11. Inductors ISU EE. C.Y. Lee Chapter 11 Inductors Objectives Describe the basic structure and characteristics of an inductor Discuss various types of inductors Analyze series inductors Analyze parallel inductors Analyze inductive

More information

Chapter 30 Inductance

Chapter 30 Inductance Chapter 30 Inductance - Mutual Inductance - Self-Inductance and Inductors - Magnetic-Field Energy - The R- Circuit - The -C Circuit - The -R-C Series Circuit . Mutual Inductance - A changing current in

More information

Common Mode Choke Filtering Improves CMRR in Ethernet Transformer Applications. Application Note. June 2011

Common Mode Choke Filtering Improves CMRR in Ethernet Transformer Applications. Application Note. June 2011 Common Mode Choke Filtering Improves CMRR in Ethernet Transformer Applications June 2011 Application Note Common mode chokes provide an effective EMI filtering solution for Ethernet transformer applications.

More information

Solution Derivations for Capa #11

Solution Derivations for Capa #11 Solution Derivations for Capa #11 Caution: The symbol E is used interchangeably for energy and EMF. 1) DATA: V b = 5.0 V, = 155 Ω, L = 8.400 10 2 H. In the diagram above, what is the voltage across the

More information

Digital Systems Ribbon Cables I CMPE 650. Ribbon Cables A ribbon cable is any cable having multiple conductors bound together in a flat, wide strip.

Digital Systems Ribbon Cables I CMPE 650. Ribbon Cables A ribbon cable is any cable having multiple conductors bound together in a flat, wide strip. Ribbon Cables A ribbon cable is any cable having multiple conductors bound together in a flat, wide strip. Each dielectric configuration has different high-frequency characteristics. All configurations

More information

Reading: HH Sections 4.11 4.13, 4.19 4.20 (pgs. 189-212, 222 224)

Reading: HH Sections 4.11 4.13, 4.19 4.20 (pgs. 189-212, 222 224) 6 OP AMPS II 6 Op Amps II In the previous lab, you explored several applications of op amps. In this exercise, you will look at some of their limitations. You will also examine the op amp integrator and

More information

Using ferrites for interference suppression

Using ferrites for interference suppression Using ferrites for interference suppression 1. Introduction Tim Williams, Elmac Services 2. The effect of magnetic material on a conductor 3. Common and differential mode cable currents 4. The effect of

More information

Making Accurate Voltage Noise and Current Noise Measurements on Operational Amplifiers Down to 0.1Hz

Making Accurate Voltage Noise and Current Noise Measurements on Operational Amplifiers Down to 0.1Hz Author: Don LaFontaine Making Accurate Voltage Noise and Current Noise Measurements on Operational Amplifiers Down to 0.1Hz Abstract Making accurate voltage and current noise measurements on op amps in

More information

Outline. Systems and Signals 214 / 244 & Energy Systems 244 / 344. Ideal Inductor. Ideal Inductor (cont... )

Outline. Systems and Signals 214 / 244 & Energy Systems 244 / 344. Ideal Inductor. Ideal Inductor (cont... ) Outline Systems and Signals 214 / 244 & Energy Systems 244 / 344 Inductance, Leakage Inductance, Mutual Inductance & Transformers 1 Inductor revision Ideal Inductor Non-Ideal Inductor Dr. P.J. Randewijk

More information

Solar Inverters. Ferrites in Renewable Energies: Solar Inverters. customer requirements. Support and flexibility to design custom product to fulfill

Solar Inverters. Ferrites in Renewable Energies: Solar Inverters. customer requirements. Support and flexibility to design custom product to fulfill Support and flexibility to design custom product to fulfill customer requirements Optimum ferrite material selection for magnetic applications in the design for cost saving, and performance improvement

More information

Common Mode and Differential Mode Noise Filtering

Common Mode and Differential Mode Noise Filtering Summary Introduction This application note gives a practical explanation of differential mode and common mode noise along with the traditional filtering approaches. In addition, an alternative method of

More information

a leap ahead in analog

a leap ahead in analog EMV Contactless Payment Systems based on AS3911 Overview and System Simulations Giuliano Manzi, PhD Mannheim, May 23 25, 2012 CST EUROPEAN USER CONFERENCE 2012 a leap ahead in analog OUTLINE AS3911 OVERVIEW

More information

Category 8 Cable Transmission Measurements Comparative Study between 4-port single wire measurements and 2-port balun measurements

Category 8 Cable Transmission Measurements Comparative Study between 4-port single wire measurements and 2-port balun measurements Category 8 Cable Transmission Measurements Comparative Study between 4-port single wire measurements and 2-port balun measurements Stefan Estevanovich Rafael Herrera, Nadim Kafati Hitachi Cable USA NDC

More information

Since any real component also has loss due to the resistive component, the average power dissipated is 2 2R

Since any real component also has loss due to the resistive component, the average power dissipated is 2 2R Quality factor, Q Reactive components such as capacitors and inductors are often described with a figure of merit called Q. While it can be defined in many ways, it s most fundamental description is: Q

More information

MA4AGSW8-2. SP8T AlGaAs PIN Diode Switch Rev. V2 CHIP LAYOUT FEATURES DESCRIPTION. Absolute Maximum Ratings T AMB = +25 C (Unless Otherwise Noted) 1

MA4AGSW8-2. SP8T AlGaAs PIN Diode Switch Rev. V2 CHIP LAYOUT FEATURES DESCRIPTION. Absolute Maximum Ratings T AMB = +25 C (Unless Otherwise Noted) 1 FEATURES Specified Performance : 50 MHz to 40 GHz Operational Performance: 50 MHz to 50 GHz 2.0 db Typical Insertion Loss at 40 GHz 30 db Typical Isolation at 40 GHz thru 3 Diodes 22 db Typical Isolation

More information

Lab #4 Capacitors and Inductors. Capacitor and Inductor Transient Response

Lab #4 Capacitors and Inductors. Capacitor and Inductor Transient Response Capacitor and Inductor Transient Response Capacitor Theory Like resistors, capacitors are also basic circuit elements. Capacitors come in a seemingly endless variety of shapes and sizes, and they can all

More information

NUCLEAR MAGNETIC RESONANCE. Advanced Laboratory, Physics 407, University of Wisconsin Madison, Wisconsin 53706

NUCLEAR MAGNETIC RESONANCE. Advanced Laboratory, Physics 407, University of Wisconsin Madison, Wisconsin 53706 (revised 4/21/03) NUCLEAR MAGNETIC RESONANCE Advanced Laboratory, Physics 407, University of Wisconsin Madison, Wisconsin 53706 Abstract This experiment studies the Nuclear Magnetic Resonance of protons

More information

RF SYSTEM FOR VEPP-5 DAMPING RING

RF SYSTEM FOR VEPP-5 DAMPING RING Ó³ Ÿ. 2006.. 3, º 7(136).. 60Ä64 Š 621.384.634.14 RF SYSTEM FOR VEPP-5 DAMPING RING Ye. Gusev, N. Kot, S. Krutikhin, I. Kuptsov, G. Kurkin, I. Makarov, N. Matyash, L. Mironenko, S. Motygin, V. Osipov,

More information

Coupling Magnetic Signals to a SQUID Amplifier

Coupling Magnetic Signals to a SQUID Amplifier SQUID Application Note 105-0 Coupling Magnetic Signals to a SQUID Amplifier Matching the effective inductances of the Pickup Coil and the Input Coil to detect and couple magnetic flux maximizes the sensitivity

More information

TRANSISTOR AMPLIFIERS AET 8. First Transistor developed at Bell Labs on December 16, 1947

TRANSISTOR AMPLIFIERS AET 8. First Transistor developed at Bell Labs on December 16, 1947 AET 8 First Transistor developed at Bell Labs on December 16, 1947 Objective 1a Identify Bipolar Transistor Amplifier Operating Principles Overview (1) Dynamic Operation (2) Configurations (3) Common Emitter

More information

Basics of Ferrite and Noise Countermeasures

Basics of Ferrite and Noise Countermeasures TDK EMC Technology Basic Section Basics of Ferrite and Noise Countermeasures TDK Corporation Magnetics Business Group Shinichiro Ito 1 What is Ferrite? Ferrite was invented by Dr. Kato and Dr. Takei in

More information

Balanced vs. Unbalanced Audio Interconnections

Balanced vs. Unbalanced Audio Interconnections Revised 7/2/08 Balanced vs. Unbalanced Audio Interconnections In discussing the characteristics and performance of various interconnect systems; two points should be kept in mind. Balance is defined in

More information

1) Magnetic field lines come out of the south pole of a magnet and enter at the north pole.

1) Magnetic field lines come out of the south pole of a magnet and enter at the north pole. Exam Name 1) Magnetic field lines come out of the south pole of a magnet and enter at the north pole. 2) Which of the following statements is correct? A) Earth's north pole is magnetic north. B) The north

More information

Title: Low EMI Spread Spectrum Clock Oscillators

Title: Low EMI Spread Spectrum Clock Oscillators Title: Low EMI oscillators Date: March 3, 24 TN No.: TN-2 Page 1 of 1 Background Title: Low EMI Spread Spectrum Clock Oscillators Traditional ways of dealing with EMI (Electronic Magnetic Interference)

More information

Constructing a precision SWR meter and antenna analyzer. Mike Brink HNF, Design Technologist.

Constructing a precision SWR meter and antenna analyzer. Mike Brink HNF, Design Technologist. Constructing a precision SWR meter and antenna analyzer. Mike Brink HNF, Design Technologist. Abstract. I have been asked to put together a detailed article on a SWR meter. In this article I will deal

More information

PHYS 222 Spring 2012 Final Exam. Closed books, notes, etc. No electronic device except a calculator.

PHYS 222 Spring 2012 Final Exam. Closed books, notes, etc. No electronic device except a calculator. PHYS 222 Spring 2012 Final Exam Closed books, notes, etc. No electronic device except a calculator. NAME: (all questions with equal weight) 1. If the distance between two point charges is tripled, the

More information

Tamura Closed Loop Hall Effect Current Sensors

Tamura Closed Loop Hall Effect Current Sensors Tamura Closed Loop Hall Effect Current Sensors AC, DC, & Complex Currents Galvanic Isolation Fast Response Wide Frequency Bandwidth Quality & Reliability RoHs Compliance Closed Loop Hall Effect Sensors

More information

APPLICATION NOTE - 016

APPLICATION NOTE - 016 APPLICATION NOTE - 016 Testing RFI Line Filters Frequency Response Analysis Testing RFI line filters Radio frequency interference (RFI) is unwanted electromagnetic noise within a radio communications frequency

More information

EEE1001/PHY1002. Magnetic Circuits. The circuit is of length l=2πr. B andφ circulate

EEE1001/PHY1002. Magnetic Circuits. The circuit is of length l=2πr. B andφ circulate 1 Magnetic Circuits Just as we view electric circuits as related to the flow of charge, we can also view magnetic flux flowing around a magnetic circuit. The sum of fluxes entering a point must sum to

More information

Amplifier for Small Magnetic and Electric Wideband Receiving Antennas (model AAA-1B)

Amplifier for Small Magnetic and Electric Wideband Receiving Antennas (model AAA-1B) Amplifier for Small Magnetic and Electric Wideband Receiving Antennas (model AAA-1B) 1. Description and Specifications Contents 1.1 Description 1.2 1.2 Specifications 1.3 1.3 Tested parameters in production

More information

A Low Frequency Adapter for your Vector Network Analyzer (VNA)

A Low Frequency Adapter for your Vector Network Analyzer (VNA) Jacques Audet, VE2AZX 7525 Madrid St, Brossard, QC, Canada J4Y G3: jacaudet@videotron.ca A Low Frequency Adapter for your Vector Network Analyzer (VNA) This compact and versatile unit extends low frequency

More information

Doc. CC-0007 FOR MOSFET OR IGBT CONTROL, SCR TRIGGERING, DC/DC CONVERSION POWER LINE COMMUNICATION COUPLING TRANSFORMERS

Doc. CC-0007 FOR MOSFET OR IGBT CONTROL, SCR TRIGGERING, DC/DC CONVERSION POWER LINE COMMUNICATION COUPLING TRANSFORMERS PRODUCT INDEX FLYBACK TRANSFORMERS RANGE TRANSFORMERS/CONTROL CIRCUITS CROSS REFERENCE LIST 1 TO 9 W EE 16 74090 74091 74092 74093 74094 74095 1 TO 6 W EE 16 74000 74001 74002 74003 6 TO 12 W EE 16 74010

More information

INTEGRATED CIRCUITS DATA SHEET. TDA8340 TDA8341 Television IF amplifier and demodulator. Product specification File under Integrated Circuits, IC02

INTEGRATED CIRCUITS DATA SHEET. TDA8340 TDA8341 Television IF amplifier and demodulator. Product specification File under Integrated Circuits, IC02 INTEGRATED CIRCUITS DATA SHEET Television IF amplifier and demodulator File under Integrated Circuits, IC02 November 1987 DESCRIPTION The ;Q and ;Q are integrated IF amplifier and demodulator circuits

More information

SIGNAL GENERATORS and OSCILLOSCOPE CALIBRATION

SIGNAL GENERATORS and OSCILLOSCOPE CALIBRATION 1 SIGNAL GENERATORS and OSCILLOSCOPE CALIBRATION By Lannes S. Purnell FLUKE CORPORATION 2 This paper shows how standard signal generators can be used as leveled sine wave sources for calibrating oscilloscopes.

More information

Module 11: Conducted Emissions

Module 11: Conducted Emissions Module 11: Conducted Emissions 11.1 Overview The term conducted emissions refers to the mechanism that enables electromagnetic energy to be created in an electronic device and coupled to its AC power cord.

More information

Induced voltages and Inductance Faraday s Law

Induced voltages and Inductance Faraday s Law Induced voltages and Inductance Faraday s Law concept #1, 4, 5, 8, 13 Problem # 1, 3, 4, 5, 6, 9, 10, 13, 15, 24, 23, 25, 31, 32a, 34, 37, 41, 43, 51, 61 Last chapter we saw that a current produces a magnetic

More information

Student Name Instructor Name. High School or Vocational Center Grade. COMPETENCY RECORD FOR ARTICULATION Muskegon Community College Electronics

Student Name Instructor Name. High School or Vocational Center Grade. COMPETENCY RECORD FOR ARTICULATION Muskegon Community College Electronics Student Name Instructor Name High School or Vocational Center Grade COMPETENCY RECORD FOR ARTICULATION Muskegon Community College Electronics Please check below each skill the student has mastered as described,

More information

INTRODUCTION TO TRANSMISSION LINES DR. FARID FARAHMAND FALL 2012

INTRODUCTION TO TRANSMISSION LINES DR. FARID FARAHMAND FALL 2012 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

More information

45. The peak value of an alternating current in a 1500-W device is 5.4 A. What is the rms voltage across?

45. The peak value of an alternating current in a 1500-W device is 5.4 A. What is the rms voltage across? PHYS Practice Problems hapters 8- hapter 8. 45. The peak value of an alternating current in a 5-W device is 5.4 A. What is the rms voltage across? The power and current can be used to find the peak voltage,

More information

Reliability and Availability Aspects of. the IPHI Project

Reliability and Availability Aspects of. the IPHI Project Reliability and Availability Aspects of the IPHI Project Pierre-Yves Beauvais CEA/DSM/DAPNIA for the IPHI Team 18/02/2002 Pierre-Yves Beauvais, CEA Saclay 1 Table of contents Brief description of IPHI

More information

Practical aspects which affect an electrical measurement

Practical aspects which affect an electrical measurement Indian Journal of Engineering & Materials Sciences Vol. 14, April 2007, pp. 119-124 Practical aspects which affect an electrical measurement K B Ravat & S K Mahajan DC High Voltage Standard, National Physical

More information

LM386 Low Voltage Audio Power Amplifier

LM386 Low Voltage Audio Power Amplifier Low Voltage Audio Power Amplifier General Description The LM386 is a power amplifier designed for use in low voltage consumer applications. The gain is internally set to 20 to keep external part count

More information

APPLICATION NOTE AP050830

APPLICATION NOTE AP050830 APPLICATION NOTE AP050830 Selection and use of Ultrasonic Ceramic Transducers Pro-Wave Electronics Corp. E-mail: sales@pro-wave.com.tw URL: http://www.prowave.com.tw The purpose of this application note

More information

Selecting IHLP Composite Inductors for Non-Isolated Converters Utilizing Vishay s Application Sheet

Selecting IHLP Composite Inductors for Non-Isolated Converters Utilizing Vishay s Application Sheet VISHAY DALE www.vishay.com Magnetics Selecting IHLP Composite Inductors for Non-Isolated Converters INTRODUCTION This application note will provide information to assist in the specification of IHLP composite

More information

Cumbria Designs T-1. SSB/CW Filter kit (4.9152MHz) User Manual

Cumbria Designs T-1. SSB/CW Filter kit (4.9152MHz) User Manual Cumbria Designs T-1 SSB/CW Filter kit (4.9152MHz) User Manual CONTENTS 1 INTRODUCTION 2 2 CIRCUIT DESCRIPTION 2 3 ASSEMBLY 2 4 TESTING 4 The Steading Stainton PENRITH Cumbria CA11 0ES UK 1 Introduction

More information

APPLICATION NOTE ULTRASONIC CERAMIC TRANSDUCERS

APPLICATION NOTE ULTRASONIC CERAMIC TRANSDUCERS APPLICATION NOTE ULTRASONIC CERAMIC TRANSDUCERS Selection and use of Ultrasonic Ceramic Transducers The purpose of this application note is to aid the user in the selection and application of the Ultrasonic

More information

css Custom Silicon Solutions, Inc.

css Custom Silicon Solutions, Inc. css Custom Silicon Solutions, Inc. CSS555(C) CSS555/ PART DESCRIPTION The CSS555 is a micro-power version of the popular 555 Timer IC. It is pin-for-pin compatible with the standard 555 timer and features

More information

W03 Analysis of DC Circuits. Yrd. Doç. Dr. Aytaç Gören

W03 Analysis of DC Circuits. Yrd. Doç. Dr. Aytaç Gören W03 Analysis of DC Circuits Yrd. Doç. Dr. Aytaç Gören ELK 2018 - Contents W01 Basic Concepts in Electronics W02 AC to DC Conversion W03 Analysis of DC Circuits (self and condenser) W04 Transistors and

More information

VCO Phase noise. Characterizing Phase Noise

VCO Phase noise. Characterizing Phase Noise VCO Phase noise Characterizing Phase Noise The term phase noise is widely used for describing short term random frequency fluctuations of a signal. Frequency stability is a measure of the degree to which

More information

d di Flux (B) Current (H)

d di Flux (B) Current (H) Comparison of Inductance Calculation Techniques Tony Morcos Magnequench Technology Center Research Triangle Park, North Carolina 1 VCM Baseline: Geometry Axially-magnetized MQ3-F 42 NdFeB disk Br = 131kG

More information

Here, we derive formulas for computing crosstalk and show how to reduce it using well designed PCB layer stacks.

Here, we derive formulas for computing crosstalk and show how to reduce it using well designed PCB layer stacks. Crosstalk Ground and power planes serve to: Provide stable reference voltages Distribute power to logic devices Control crosstalk Here, we derive formulas for computing crosstalk and show how to reduce

More information

The Effects Of Cable On Signal Quality

The Effects Of Cable On Signal Quality The Effects Of Cable On Signal Quality By Jim Brown Audio Systems Group, Inc. jim@audiosystemgroup.com System designs often require output amplifier stages of microphones and line-level devices to drive

More information

Circuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49

Circuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49 Circuits with inductors and alternating currents Chapter 20 #45, 46, 47, 49 RL circuits Ch. 20 (last section) Symbol for inductor looks like a spring. An inductor is a circuit element that has a large

More information

The W5JCK Guide to the Mathematic Equations Required for the Amateur Extra Class Exam

The W5JCK Guide to the Mathematic Equations Required for the Amateur Extra Class Exam The W5JCK Guide to the Mathematic Equations Required for the Amateur Extra Class Exam This document contains every question from the Extra Class (Element 4) Question Pool* that requires one or more mathematical

More information