RF AND MICROWAVE
`
`CIRCUIT DESIGN FOR
`
`WIRELESS
`
`COMMUNICATIONS
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`LAWRENCE E. LARSON, EDITOR
`
`~ ~l'itecf.i aoase P.tJDlisliers , o s r o H
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`~ o H o o N
`
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`

`Library of Congress Cataloging-in-Publication Data
`Larson, Lawrence E.
`RF and microwave circuit design for wireless communications/Lawrence E. Larson
`p. cm.
`Includes bibliographical references and index.
`ISBN 0-89006-818-6 (alk. paper)
`1. Wireless communication systems. 2. Radio circuits.
`TK5103.2.L37 1996
`621.384'12-<lcl0
`
`95-49987
`CIP
`
`British Library Cataloguing in Publication Data
`RF and microwave circuit design for wireless communications
`1. Radio circuits-Design 2. Microwave circuits-Design 3. Microwave communication
`systems 4. Wireless communication systems
`I. Larson, Lawrence E.
`621.3'8412
`
`ISBN 0-89006-818-6
`
`C 1996 ARTECH HOUSE, INC.
`685 Canton Street
`Norwood, MA 02062
`
`All rights reserved. Printed and bound in the United States of America. No part of this book
`may be reproduced or utilized in any form or by any means, electronic or mechanical, includ(cid:173)
`ing photocopying, recording, or by any information storage and retrieval system, without
`permission in writing from the publisher.
`All terms mentioned in this book that are known to be trademarks or service marks have
`been appropriately capitalized. Anech House cannot attest to the accuracy of this informa(cid:173)
`tion. Use of a term in this book should not be regarded as affecting the validity of any trade(cid:173)
`mark or service mark.
`
`International Standard Book Number: 0-89006-818-6
`Library of Congress Catalog Card Number: 95-49987
`
`10987654321
`
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`252 MICROWAVE & RF CIRCUIT DESIGN FOR WIRELESS COMMUNICATIONS
`
`This makes them uncomfortably large for use in wireless applications at frequencies
`below 2,400 MHz. Often, however, the structures can be modified to make them
`practical at low frequencies by either meandering the strips or loading them with
`dielectric material.
`Figure 5 .16 shows a simple transmission-line balun. It consists of a A/4 section
`of transmission line whose characteristic impedance Z0 is chosen to act as a trans(cid:173)
`former between the source and load impedances:
`
`Zo = ✓zszL
`
`(5.35)
`
`This balun is very sensitive to stray capacitance between the transmission line
`and ground. To account for this capacitance, we treat the conductors as coupled
`transmission-line sections, and their even-mode impedance accounts for the stray
`capacitance. Ideally, the capacitance is zero, causing the even-mode impedance to
`be infinite. The odd-mode impedance is half the transmission-line impedance; that
`is,
`
`Zoo = O.SZo = O.S✓Z,Zi
`
`(5.36)
`
`Analysis shows that the even-mode impedance should be at least ten times the
`odd-mode. This is often accomplished in microwave mixers by the use of a suspended
`substrate for the balun. At low frequencies, the even-mode impedance can be
`increased by using a twisted pair of conductors for the transmission line and inserting
`the conductors into a magnetic core to increase the even-mode inductance. This has
`two effects: first, it reduces the size of the balun; second, the balun operates as a
`1:1 transformer at low frequencies, improving the low-frequency response. (Of
`course, to have a good VSWR in this low-frequency range, the source and load
`impedances must be equal.)
`The transmission-line balun can be shortened by loading the input and output
`ends with capacitors. The optimum capacitance depends on the mode impedances
`and is best determined by numerical optimization. As an initial value, the line length
`should be ..V8 and the capacitors' reactances should be 0. 70720•
`
`Figure 5.16 A simple transmission-line balun.
`
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`Mixers for Wireless Applications 253
`
`Other transmission-line transformer combinations can be used as baluns. Figure
`5.17 shows a balun having a 1:4 impedance ratio with Z 0 == Z,. This balun is not
`fundamentally different from that of Figure 5 .16; it consists of two such baluns
`connected in parallel at the input and in series at the output. By selecting Z 0 = 0.52,,
`one could obtain a 1:1 transformation at the high-frequency end of its bandwidth.
`If the balun were wrapped on a magnetic core to improve its low-frequency response,
`the low-frequency impedance transformation would still be 1:4.
`Figure 5 .18 shows another 1 :4 balun. Both outputs of this balun are at ground
`potential for de, and provide a convenient de return for the mixer diodes.
`
`Zo
`
`Zo
`
`Figure 5.17 A 1:4 impedance-transforming transmission-line balun; 2 0 = Z,, ZL = 4 Z,.
`
`-
`
`-
`
`ZL
`
`f
`
`....:
`l/)
`(\J
`ci
`
`Zo
`
`Figure 5.18 A 1:4 impedance-transforming balun; 2 0 = Z,.
`
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