ElEctromagnEtic WavEs
`
`Sevick’s Transmission Line
`Transformers
`Theory and practice
`5th Edition
`
`Raymond A. Mack and Jerry Sevick
`
`Sevick’s Transmission Line Transformers
`Theory and practice: 5th Edition
`
`Mack and Sevick
`
`Sevick’s Transmission Line
`Transformers
`Theory and practice
`5th Edition
`
`The long awaited revision of the classic book Transmission
`Line Transformers, by Jerry Sevick, is now in its fifth edition
`and has been updated and reorganised by Raymond Mack
`to provide communication engineers with a clear technical
`presentation of both the theory and practical applications
`of the transmission of radio communication.
`Sevick’s Transmission Line Transformers: Theory and
`Practice, 5th Edition reviews the underlying principles
`that promote a better understanding of transmission
`line transformers. Ideal for academics and practicing
`engineers, this edition is divided into two clear parts for
`easy reference. Part one is a review of the theory and
`new concepts, including a discussion on the magnetic
`properties that affect the core of a transmission line
`transformer. Part two essentially focuses on the “practice”
`element of the book title. This section has been updated
`to reflect the significant changes in component suppliers
`over the 30 years since the first edition of the book.
`Highlights of this title include the coverage of substantial
`background theory, recent work on fractional ratio
`transformers and high power Balun designs, and provides
`updated sources for transformer materials to reflect
`mergers, sales, and business failures over the past 20
`years. There is also expanded coverage of commercial
`sources of low impedance coaxial cable; expanded
`construction hints for purpose built rectangular parallel
`transmission lines; plus an updated test equipment
`chapter to reflect modern computer based experimenter
`grade test equipment sources. Ray has leveraged his
`experience with ferrite materials for switching power
`to explain the performance characteristics of the
`ferrite materials used for RF power transmission line
`transformers.
`
`raymond a. mack, W5IFS, received
`his Electrical Engineering degree, with
`emphasis on biomedical engineering,
`from Purdue University in 1975. His
`career in medical devices covered clinical
`chemistry analyzers, heart pacemakers,
`electro-surgery, and infant warming
`therapy. From 1999 he worked in digital
`television for eight years and is now
`working in the oil and gas industry at
`National Oilwell Varco. Ray has worked
`for QEX magazine for 12 years as a
`technical proofreader, editor, writes a
`column on software defined radio, and
`has authored Switching Power Supplies
`Demystified. Ray’s interests include
`alternative energy using switching power
`design, microwave system design,
`software defined radio, and DSP.
`Jerry sevick, W2FMI—renowned for
`his research and publications related to
`short vertical antennas and transmission
`line transformers—passed away in 2009.
`Jerry was a graduate of Wayne State
`University and later graduated from
`Harvard University with a doctorate in
`Applied Physics. In 1956, he joined AT&T
`Bell Laboratories and supervised groups
`working in high-frequency transistor
`and integrated-circuit engineering;
`later, he served as Director of Technical
`Relations at the company. During his
`career, he undertook the characterization
`and design of transformers for low
`impedance applications, resulting in this
`book, originally published in 1987.
`
`The Institution of Engineering and Technology
`www.theiet.org
`ISBN 978-1-89112-197-5
`
`Mack-STLT 5e 234x156mm.indd All Pages
`
`14/05/2014 11:58
`
`Exhibit 2005
`IPR2017-00391
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`

`

`Sevick’s
`Transmission Line
`Transformers
`Theory and Practice
`5th Edition
`
`Raymond A. Mack and Jerry Sevick
`
`Edison, NJ scitechpub.com
`
`Exhibit 2005
`IPR2017-00391
`
`

`

`Published by SciTech Publishing, an imprint of the IET.
`www.scitechpub.com
`www.theiet.org
`
`Copyright † 2001, 2014 by SciTech Publishing, Edison, NJ. All rights reserved.
`
`Fourth edition 2001
`Fifth edition 2014
`
`No part of this publication may be reproduced, stored in a retrieval system or transmitted in any
`form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise,
`except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without
`either the prior written permission of the Publisher, or authorization through payment of the
`appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA
`01923, (978) 750-8400, fax (978) 646-8600, or on the web at copyright.com. Requests to the
`Publisher for permission should be addressed to The Institution of Engineering and Technology,
`Michael Faraday House, Six Hills Way, Stevenage, Herts, SG1 2AY, United Kingdom.
`
`While the author and publisher believe that the information and guidance given in this work are
`correct, all parties must rely upon their own skill and judgement when making use of them.
`Neither the author nor publisher assumes any liability to anyone for any loss or damage caused
`by any error or omission in the work, whether such an error or omission is the result of
`negligence or any other cause. Any and all such liability is disclaimed.
`
`Editor: Dudley R. Kay
`
`10 9 8 7 6 5 4 3 2 1
`
`ISBN 978-1-89112-197-5 (hardback)
`ISBN 978-1-61353-046-7 (PDF)
`
`Typeset in India by MPS Limited
`Printed in the US by Lightning Source
`Printed in the UK by CPI Group (UK) Ltd, Croydon
`
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`IPR2017-00391
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`Chapter 1
`Transformer Basics
`
`1.1 Introduction
`
`There are two basic methods for constructing broadband impedance matching
`transformers. One employs the conventional magnetically coupled transformer
`that transmits energy to the output circuit by flux linkage; the other uses a trans-
`mission line transformer to transmit energy by transverse transmission line mode.
`Conventional transformers have been constructed to perform over wide band-
`widths by exploiting high magnetic efficiency of modern materials. Losses on the
`order of 1 dB can exist over a range from a few kilohertz to over 200 MHz.
`Throughout a considerable portion of this range, the losses are only 0.2 dB.
`Transmission line transformers exhibit far wider bandwidths and much greater
`efficiencies. The stray inductances and interwinding capacitances are generally
`absorbed into the characteristic impedance of the transmission line. The flux is
`effectively canceled out in the core with a transmission line transformer, so
`extremely high efficiencies are possible over large portions of the passband—
`losses of only 0.02–0.04 dB with certain core materials.
`A full model of a conventional transformer is presented in Figure 1-1. Multiple
`parasitic elements are affecting both low and high frequency operation. Low
`frequency operation is controlled by the magnetizing inductance (LM) in parallel
`with the ideal transformer. As frequency decreases, the current flows mostly
`through the low impedance inductance (LM) rather than the ideal transformer. High
`frequency operation is governed by the capacitances (CP, CS, and CPS), leakage
`inductances (LP and LS), and core losses (RC). As frequency increases, the output
`voltage and current become out of phase and the losses of the core increase. RP and
`RS are the copper losses of the respective windings. They increase with increasing
`frequency due to skin effect. RP and RS also increase with increasing temperature,
`so higher power applications will have higher losses.
`Figure 1-2 shows the construction of two conventional transformers on a
`double ‘‘U’’ core. The windings are physically separated on the core in the first
`example, so the only linkage from primary to secondary occurs through the shared
`flux in the core. CP and CS in the model occur because each turn of the winding is
`in proximity to the adjacent turns. A very small capacitance exists between each
`pair of turns, and each capacitor is in series with the next one around the winding.
`The capacitance can be quite small, but a capacitor of only 10 pF has an impedance
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`2
`
`Sevick’s Transmission Line Transformers
`
`RP
`
`LP
`
`CP
`
`RL
`
`RC
`
`LM
`
`CPS
`
`CPS
`
`LS
`
`RS
`
`CS
`
`Figure 1-1 The schematic shows a complete model of a magnetically coupled
`transformer.
`
`Figure 1-2 Two different methods of magnetically coupled transformer
`construction: (Left) This transformer minimizes capacitive coupling
`with all coupling by magnetic flux. (Right) This transformer has
`coupling by both capacitance and magnetic flux.
`
`of 159 at 100 MHz. Another method of transformer design in the figure winds the
`secondary on top of the primary. This construction reduces LP and LS but increases
`CPS. The other advantage of this construction is that flux linkage is improved at
`higher frequencies where the transformer tends to look more like an air core
`transformer with an absorber in the middle.
`A basic transmission line transformer with an unbalanced input and a balanced
`load is illustrated in Figure 1-3. Two pieces of equal length transmission line are
`connected in parallel at the input side and in series on the output side. If a trans-
`mission line is terminated in its characteristic impedance, the input side appears
`to be Z0 regardless of the length of the transmission line (within limits). In the
`example in Figure 1-3, Z0 and each half of the load are 100 W. The impedance on
`the input side is 50 W because we have two 100 W impedances in parallel.
`Oliver Heaviside used Maxwell’s equations in the late nineteenth century
`to develop the mathematical expressions for transmission lines. Those equations
`show that the load is isolated from the input on a transmission line that is longer
`than about 0.1 wavelength. At that point, the distributed inductance and distributed
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`Z0 = 100
`
`Z0 = 100
`
`A
`
`Transformer Basics
`
`3
`
`RL
`
`100
`
`RL
`
`100
`
`B
`
`Rg
`
`50
`
`+ –
`
`Figure 1-3 A schematic showing a Guanella 1:4 transformer. The connection
`between points A and B is used when a load is center tapped. For a
`200 W load the center tap is omitted.
`
`capacitance combine to produce the effect we know as characteristic impedance.
`The input energy is transmitted down the line as an electromagnetic field com-
`pletely contained within the transmission line. For that reason, placing a magnetic
`core around a transmission line will have no effect on the field inside the line.
`However, as the length becomes less than 0.1 wavelength, the field is no longer
`contained within the line so both conductors contribute magnetic flux in a core
`placed around the line. This external flux converts the line and core combination
`from a transmission line to a conventional transformer. Thus, the power ratings of
`transmission line transformers are determined more by the ability of the transmis-
`sion lines to handle the voltages and currents at high frequencies and by the
`properties of the core at low frequencies.
`The earliest presentation on transmission line transformers was by Gustav
`Guanella in 1944 [1]. He proposed the concept of coiling transmission lines to form
`a choke that would reduce the undesired mode in balanced-to-unbalanced (balun)
`matching applications. Before this time, this type of device was constructed from
`quarter- or half-wavelength transmission lines and, as such, had very narrow
`bandwidths. By combining coiled transmission lines in parallel-series arrange-
`ments, he was able to demonstrate broadband baluns with ratios of 1:n2, where n is
`the number of transmission lines.
`Other writers followed with further analyses and applications of the balun
`transformer [2–8]. In 1959, C. L. Ruthroff published another significant work on
`this subject [9]. By connecting a single transmission line such that a negative or a
`positive potential gradient existed along the length of the line, he was able to
`demonstrate a broadband 1:4 balun, or unbalanced-to-unbalanced (unun) transfor-
`mer. He also introduced the hybrid transformer in his paper. Many extensions
`and applications of his work were published and are included in the reference list
`[10–28]. The original Guanella article is reproduced in Appendix A, and the ori-
`ginal Ruthroff article is reproduced in Appendix B.
`In general, it can be said that the transmission line transformer enjoys
`the advantage of higher efficiency, greater bandwidth, and simpler construction.
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`4
`
`Sevick’s Transmission Line Transformers
`
`The conventional transformer, however, remains capable of DC isolation. The
`purpose of this chapter is twofold: to review Guanella’s and Ruthroff’s approa-
`ches and to present additional material to form a basis for the chapters that follow.
`Jerry Sevick lamented in the second edition of this book that many readers
`mistakenly consider the transformer designs in the book to be conventional mag-
`netically coupled transformers. I attribute this to the graphics that depict each
`conductor of the transmission line as an inductor. I have modified the graphics to
`show all two-conductor transmission lines as loaded wire lines or coaxial cables. In
`general, it is equally correct to build a transmission line transformer with coaxial
`cable as with a parallel line. However, some of the effects that Sevick has observed
`can be attributed to placing a magnetic material in proximity to a parallel wire
`transmission line. Until coax came into common use, it was well known that all
`metal must be kept away by at least four to five times the wire spacing to prevent
`distorting the signal in the parallel line. The result is that the two-, three-, and
`four-wire transmission lines more closely resemble coupled microstrip lines than
`parallel wire lines. Therefore, the core is an integral part of the circuit throughout
`the useful frequency range. Further, I believe Sevick was mistaken in his under-
`standing that many of the designs presented are strictly transmission line transfor-
`mers. The Ruthroff designs, in particular, rely on true magnetic transformer action
`for significant portions of their band of operation. However, his experimental work
`is still quite relevant!
`
`1.2 The Basic Building Block
`
`The single bifilar winding, shown in Figure 1-4, is the basic building block for
`understanding and designing transmission line transformers. Higher orders of
`windings (e.g., trifilar, quadrifilar) also perform in a similar transmission line
`fashion and will be discussed later.
`The circuit in Figure 1-4 can perform four different functions depending
`on how the output load, RL, is grounded: (1) a phase inverter when a ground is
`connected to terminal 4; (2) a balun when the ground is at terminal 5 or left off
`entirely (a floating load); (3) a simple delay line when a ground is at terminal 2; and
`(4) a ‘‘bootstrap’’ when þV1 is connected to terminal 2. The operation of these four
`
`RL1
`5
`RL2
`
`–+
`
`V2
`
`I2
`
`I2
`
`4
`
`2
`
`I1
`
`+
`V1
`–
`
`3
`
`1
`
`I1
`
`Rg
`
`+ –
`
`Figure 1-4 The schematic shows the transmission line transformer basic
`building block.
`
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`Transformer Basics
`
`5
`
`functions can be explained by simple transmission line theory and the choking
`reactance of the transmission lines. The latter, which isolates the input from the
`output, is usually obtained by coiling the transmission line around a ferrite core or
`by threading the line through ferrite beads. The objectives, in practically all cases,
`are to have the characteristic impedance (Z0) of the transmission line equal to the
`value of the load (RL), which is called the optimum characteristic impedance, and
`to have the choking reactance of the transmission line much greater than RL (and
`hence Z0). Meeting these objectives results in a ‘‘flat’’ line and hence maximum
`high frequency response and maximum efficiency since conventional transformer
`currents are suppressed. In the final analysis,
`the maximum high frequency
`response is determined by the parasitic elements not absorbed into the character-
`istic impedance of the line, and the efficiency is affected by the properties of the
`ferrites when used in transmission line transformer applications.
`A deeper understanding of transmission line transformers can be gained
`by noting the longitudinal potential gradients that exist with the following
`four circuits.
`
`1.2.1 Phase Inverter
`By connecting a ground to terminal 4, a negative potential gradient of V1 is
`established from terminal 3 to 4. The gradient from terminal 1 to 2 is V2. For a
`matched load, V1¼ V2. If the reactance of the windings (or a straight transmission
`line loaded with beads) is much greater than RL, then only transmission line cur-
`rents flow and terminal 2 is at a V2 potential. When the reactance is insufficient, a
`shunting, conventional current will also flow from terminal 3 to 4, resulting in a
`drop in the input impedance and the presence of flux in the core. As the frequency
`is decreased, the input impedance approaches zero.
`
`1.2.2 Balun
`By connecting a ground to terminal 5, a negative potential gradient (V1 V2/2) is
`established from terminal 3 to 4 and V2/2 from terminal 1 to 2. With a matched
`load, V1¼ V2 and the output is balanced to ground. When the reactance fails to be
`much greater than RL, conventional transformer current will flow and eventually,
`with decreasing frequency, the input impedance approaches RL/2. When the load is
`‘‘floating,’’ the currents in the two windings are always equal and opposite. At very
`low frequencies, where the reactance of the windings fails to be much greater than
`RL, the isolation of the load is inadequate to prevent conventional transformer
`current (which could be an antenna current) when the load is elevated in potential.
`This bifilar balun, which was first proposed by Guanella [1], is completely ade-
`quate for most l:l balun applications when the reactance of the windings (or beaded
`straight transmission lines) is much greater than RL.
`
`1.2.3 Delay Line
`By connecting the ground to terminal 2, the potential gradient across the bottom
`conductor is zero. With a matched load, the gradient across the top conductor
`is also zero. Under these conditions, the longitudinal reactance of the conductors
`
`Exhibit 2005
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