Design of a self-saturating magnetic amplifier utilizing high frequency excitation Item Type text; Thesis-Reproduction (electronic) Authors Perkins, Brayton Mills, 1924- Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 04/10/2021 10:04:12 Link to Item http://hdl.handle.net/10150/319332 DESIGN OF A SELF-SATURATING MAGNETIC AMPLIFIER UTILIZING HIGH FREQUENCY EXCITATION by Brayton M. Perkins A Thesis submitted to the faculty of the Department of Electrical Engineering in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in the Graduate College, University of Arizona 1956 Approved: C a t * * \ . / f f Z Director of Thesis Date 5 ^ This thesis has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the Library to be made available to borrowers under rules of the Library• Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or re­ production of this manuscript in whole or in part may be granted by the head of the major department or the dean of the Graduate College when in their judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGIpD: D1SIG-H OF A BH»F=>S&TOMflHa MM&mTXC 1SPL1FIER UTILIZING- H G H FREQUENCY EEGITATION . Drayton Perkiias transfer .fiiBotion for a self-saturating (with low eontrol eireuit resistanee) is .9 the elementary parallel-eonneeted saturable .reaetor amplifier as a basis0 Other equations pertaining to operation and.'design ©f a self~saturating amplifier3 with a high frequeney power supply ( 1 0 ko. to 5 0 ke0) g. rare d.©riTed„ A simplification of the tlm© eonstant arid the gain expression in the; transfer equation is earried out0 A sample design pro- .©edure'ls set up for the design of an amplifier by running relatively simple tests on proposed, core material and diodes and by using the equations developed; then an aetual design is earried out step: by step to.illustrate.tM sample procedure An experimental bridge self-saturating magmetie amplifier: was ©onstrueted from the design; and a eomparison of D 0G 0 input- output ©haraeteristies and frequeney response ©urves were made ''between' experimental results and these predieted by equations = Other ©omparisoris' are made 'eoneerning magnetie feedback and ©hange of input resistanee0 All results appear to eheek with­ in the limits of the approximations mad© in the equations.o AGKHOELEDG-Siirf. The author wishes to thank Professor 0o Eo Bunn for supervising the research and the preparation of this'thesis= The research was condnoted using the facilities of the Electrical Engineering Department at the University of Arizonao /v , , ' ' ; 0O1TEEES „ ' I M E H J O E E O H , Pag©; ,. Chapter lc THS SATOEABLS RMGTOR AS A COKTEOL DEVICE 1 . 1 o 1 « iBtretoetiom' . : \ , 1 l 0 2o" Diseussion of Core Materials . 2 lo3o laduetanoe as the Amplifier Controller 4 lo4o Method of Varying Induetanee 7 Chapter 2, Sm'-SAIUBikTIlMG MGKBTIC AIvlPLIPIlR TMNSFER . rnwgmow 1 1 2^1P Introduotion 11 2 o 2 o The Par all ei«- connect ed SR Magnetic. Amplifier 12 ■2*3*. : The General Transfer Function 21 2o4o Modification of the Transfer Function Time Constant 2S 2o 5o Ideal lnpu.t=output Characteristic for the Self^saturating Magnetic:Amplifier '32 2 0 6o The Modified Input-output Characteristic 4 0 2o7o Further Determination ©f the Transfer Funotion Variables 4 4 Chapter 3 = D E V m , O P m m OF DESIGN EQ.UATIONS AM) A DES1GM PR0C1DUR1 47 3ol» Introduction 47 3o2o Simplified Reference Gain 4$ 3<.3= Application of the Simplified Reference Gain function 53 3*4o Simplified. Time Constant 57 v ./ v.; ; ; , '3 = 5 =. SB Ixitation Reqmlremettts ■ - - 58 3 = 6 o A Sample Design Procedure 66 eripter: 4 EEPpiiMEZPii, aisJBfS . ' . 77 4*1 = Intx-saudtidn . - 77 • 4=%= ' Ixperimentai Test B@suits: on 6 @re Material 77 ' 4 o 3'6' Bzperimental $est;Bestilts on DleS.es . ■ 84 "4<r44 DeAlgm of a Bridge Self “Saturating Magnet! e ' - : isplifler / : . ; - 93 4o5»: Cpmpariaon of Implifier Ssperimeatal Besults ■ ■ ■ witli Deslgff.Sssults ■ ' - r;" : ' . :v;;101 - % 4o6o Discussion ©f Discrepancies Between Predicted lnput=output Dharaeteristioa. and Experimental ' : .. Besults . : ' : ■ , , 105; . 4o7= General Discussion of Other Experimental Data 110 Oliapter 5 O O E O m s i W , 44 / ".-v v ; - ^ ^ 11?:4;; 5=1*. Limitations and Advantages of High' Ereqneney ■ Operation ,; .: - 1 1 7 5=2= Other Remarks : 7 ; "' ; ' , - 1 1 8 ■ iPPiEDix 4 : ; ' 1 2 1 • ;'BlBH0dB4EW . :;y ■ ; ;v::: ; . v ' : : :M2 8 i d Ideal Hysteresis' Loop . - ; . : 3 . lo2 Non-ideal Hysteresis Loop : 3 1*3 Elementary Magnetic Amplifier J '5 16,4 Hermal Magnetization Oia,rir@ 4' : 5 1»5 Flux Density Components Present in Ferro- aagnetie Materials , ■ - ' .. g 2 01 Farallel-00nneeted SB Magnetic Amplifier ; . 13 202 Belationskip Between Core Flux ( }■ and SB . ■ . ‘ Toltag© i v ^ ; >T ; ' T 1 3 2 o 3 Average Value of SB Teltage ‘ 18 2Q4. - Eodp Ourrerits in a Parallel-eonneoted SB . ■: Amplifier . : i .i / ' 18, Zo 5 Sign convention for Amplifier Feedback . 22 2 C 6 S e r w Bloek Diagram of Farallel^eomeefed. ' SB Magnetic Amplifier ' ' : ; ■ 22 2o7 Servo Bloek Diagram of Self-saturating Magnetic , : Amplifier •; . ; . ; 2? 2oS Simplified Servo Bloek Diagram of Self- A ■ . saturating Magnetie Amplifier ' - 27- 2o9 Magnetic Amplifier Transfer Function Table 2 9 Sold Tke Equivalent Input Circuit of a Magnet!© ; -I" Amplifier ' - l i’: - 3 0 2 o 11 % e 'Bridge Self-saturating Magnetic Amplif ier y- for High"Frequency Operation 3 0 2ol2 Waveforms for the Bridge Self-saturating . Magnetic Amplifier ' 3 3 2 oX3 Magnetizing Gurrent Supplying Ezoitation .. _- -to - ^ v V "3;^:.: : ■" 35- : 2014 Magnetising Current Supplied, by SR& to ....... .. .. : 35 2oX5: : Saturation Load Current Path During a Half - ::: CyeXe of: Ezeitatio'n ■ / 39 2®X6 Beetifisr Heferse Current for Half=eyele of ' 42 : 'Sol ^ TypieaX D 0C 0 Input-output Char act eristic :: • 9 . : . Curve ef Self ^saturating Magnetic i,mpl i f i er 49 3o2 Straight Line Approximation of D 0C a Input- output Chara'etefistio with.no Feedback Present . 49 3o3- Straight Line Approximation of Input-output ,: . ' :: Characteristic (Showing Construction Lines for • ■ Graphical Determination of Characteristic with ■ . , Magnetie Feedback Only) • ", " .. 54 3o4 Straight Line Approximation of Input-output Characteristic (Showing Construction Lines.for Graphical Determination of Characteristic with , ■ : Rectifier Reverse Current Present.) : 5 6 3o5 Magnetizing Current of Self-saturating Magnetic 3o6. IxampXe'of 6 Sd and Even Punetions .' 6 0 3o7 Magnetizing; Current and its Fourier Approximation6 3 3 o-8 . Total Path of Magnetizing Current for a Half1 • Cycle of Power Supply Operation for the Bridge • Self-saturating Amplifier (Only Magnetizing : . 1 1 Current Flows. ' .t ,v- 65 " 3»9 . Flux Hecessary for Mormal Excitation of SB 6 5 3 10. Choi 6 ©, of Design DoG c Input-output Charact eristl c 6 8 : 3oil Example:of possible Core and Sinding Cross FIGURE " . lllnstratlom of Fe©dba.ek la Bridge Self= 3 o5-2 — Jt uL- t) w it> u * ‘ft ^ e* « ft ' 75 : " 4ol ; let hod of Measuring the jGop of Gore Material 79 4 o2 ■ Gore Magnetizing Current and Output 79 sis Loops for 2 Mil Super mall oy Tape 8 2 4°4 - Differential Permeability obtained from Parallelogram Approximation of Hysteresis 4»5 ;e Test oil Diodes at a Frequeney of 30 K e 0 83 4o 6 yariation of Differential Permeability with Fregneney for a Core Speeimen of 2 Mil Tape _ ' -- : S5 Hysteresis Loops (Parallelogram 1 for Sup email ©y at Two 8 6 408 Dynamie Hysteresis Loops Approximation) for Supermalloy at an ; Ff eq.u©ney of 30 K © 0 . -. 87 409 Mot hod of Determining Diode Equivalent 4ol0 Method of determining Average Value of A;'- Eeotifier Reverse Current ' 88 4 dll. .;F 6 f 8 of Three Different Diode 90 4*12 Photographs Showing Eeotifier Reverse Current 91 4ol3 ; Representative Plot'of Sinusoidal Load Current - : • Versus Eeotifier Reverse Current 4*14■ Reetifier Reverse Current for- Two Different ■ Diode. Types - - - 94 4sl5 Straight Line Approximation of Amplifier D 00 o Input”output Cliaraeteristi© FiGmih ' . : , ; :. pag@ ::- 4®16 'Amplifier Do Co Input=output Oharaeteristie '(& Bi©des>,. ' - : 1G2 46lf Gomparlsdii of i)eslgn Ireqmenef' HespoBse with Mzperimemtal Freqwiiey Reapeaae 103 . 4olB 4tepllfler Do Oo Xnput =• output Charaoterlstlo IB :Di©a©s) . - , 104; , ,, 4el9 Straight Line Approximation of Amplifier IX Co Input-”output. GharaeteristiQ (B Diodes) 106 4o20 Ampliiier i)0 Co Input-output Charaoteristie :, (C Diodes} ' , ' - ■ . 10? 4®21 Straight Line Approximation of Amplifier Do 0 0 . Xnput-dutput Charaeteristio { 0 Diodes) 108 4o22 A New Approach to Supermalloy Hysteresis Loop ■ r. ■ - - . Approximation - - - ' V ' ' 109 : 4®23 Photographs of Amplifier Output 111 4a24 Straight Line Approximation of Amplifier D* CB 1- , * ■. Input ^Output; Characteristic. (Infinite Gain) ■ ' -112 4o^$ Straight Dine Approximation of jWplifier Do: Ca ' . Input^output Characteri'sti.o.. (Finite Cain}, ■ 114 48.26 Effect of Input :Resistance on Frequency; : ;/: Bespohse of Self^saturating Kagneti© Amplifier - - ’ for a Saturation Angle i 1 of 127° • 1 1 5 - 4®2? Filter Used on Output of Experimental Amplifier 116 5*1 Experimental Amplifier DoCo Input-output Characteristic Showing How Assumption of no v : .Diode Reverse Current Results in Error» ; 120 Appendix 'ol A Toroid with IP Layers of Wire Wound in a I v Circular Manner - - .