MICROWAVE
`
`Page 1 of 5
`
`ENCINEERING
`
`David M- Pozar
`
`ParkerVision Ex. 2035
`IPR2021-00985
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`ParkerVision Ex. 2035
`IPR2021-00985
`Page 1 of 5
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`EXECUTIVE EDITOR Charity Robey
`EDITORIAL ASSISTANT Susanne Dwyer
`MARKETING MANAGER Harper Mooy
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`SENIOR PRODUCTION EDITOR Monique Calello
`COVER DESIGNER David Levy
`Il..LUSTRATION STUDIOS Wellington & Vantage Art
`Il..LUSTRATION COORDINATOR Gene Aiello
`MANUFACTURING MANAGER Monique Calello
`
`This book was set in 10fl2 Tunes Roman by ETP HARRISON and
`printed and bound by R.R. Donnelley & Sons Company, Crawfordsville.
`The cover was printed by The Lehigh Press, Inc.
`
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`Copyright @ 1998, by John WIiey & Sons, Inc.
`
`All rights reserved. Published simultaneously in Canada.
`
`Reproduction or ttanslalion of any part of
`this work beyond that permitted by Sections
`107 and 108 of the 1976 United States Copyright
`Act without the permission of the copyright
`owner is unlawful. Requests for permission
`or further information should be addressed to
`the Permissions Department, John Wiley & Sons, Inc.
`
`library of Congress Cataloging in Publication Data
`Pozar, David M.
`Microwave engineering / David M. Pozar. -- 2nd ed.
`cm.
`p.
`ISBN 0-471-170%-8 (cloth : alk. paper)
`l. Microwaves. 2. Microwave devices. 3. Microwave circuits.
`I. Title.
`TK7876.P69 1998
`62l.381'3-dc20
`
`97-20878
`CIP
`
`Printed in the United States of America
`
`10 9 8 7 6 5 4
`
`ParkerVision Ex. 2035
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`10.2J)etsctors and Mixers
`
`565
`
`Saturation
`
`lV
`
`lOOmV
`
`lOmV
`
`lmV
`
`lOOµV
`
`IOµV
`
`I
`I
`-40 -30
`
`I
`30
`
`I
`40
`
`II
`
`logPin
`(dBm)
`
`FIGURE 10.15 Square-law region for a typical diode detector.
`
`Single-Ended Mixer
`A mixer uses the nonlinearity of a diode. to ,pnerate an output spectrum consisting
`of the sum and difference frequencies of two input signals. In a receiver application, a
`low-level RF signal and an RF local oscillator (LO) signal are mixed together to produce
`an intermediate frequency (IF), Jw = Ju:- Ao, and a much higher frequency, Ju:+ Ao,
`which is filtered out See Figure 10.16a. The IJlsignal usually has a frequ,mcy between
`10 and 100 MHz, and can be amplified with' a low-noise amplifier. This is called
`a heterodyne receiver, and is useful because it has much better sensitivity and n6ise
`characteristics (using an IF amplifier minimius 1/ J noise) than the direct detection
`scheme discussed in the previous section. A heterodyne system also has the advantage
`of being able to tune over a band by simply changing the LO frequency, without the
`need for a high-gain, wideband RF amplifier.
`As shown in Figure 10.16b, a mixer .can,alse be used in a transmitter to offset the
`frequency of an RF signal by an amount equal to Jn,. This is a convenient technique,
`as it allows the use of identical local oscillators in the transmitter and receiver; a single
`oscillator may serve this purpose in a radar or transceiver system.
`There are several types of mixer circuits, but the simplest is the single-ended mixer;
`single-ended mixers often are used as part of more sophisticated mixers. A typical
`single-ended mixer circuit is shown in Figure 10.17, where an RF signal,
`VRF{t) = 'Vr COS Wrt,
`
`1-0.36
`
`is combined with an LO signal,
`
`vr.o(t) = Vo cos Wot,
`and fed into a diode. The combiner may be a simple T-junction combiner, or a directional
`coupler. An RF matching circuit may precede the diode, and the diode may be biased
`through chokes that allow DC to pass while blocking RF. From (10.29), the diodc·current
`
`10.37
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`566
`
`Chapter 10: Active Microwave Circuits
`
`RF
`input
`
`(a)
`
`IRF=fw+IJF l..n._ fw±fJF R
`
`Local
`oscillator
`
`Sideband
`filter
`(optional)
`
`(b)
`
`FIGURE 10.16
`
`Frequency conversion in a receiver and transmitter. (a) Down-conversion in a
`heterodyne receiver. (b) Up-conversion in a transmitter.
`
`will consist of a constant DC bias term, and RF. and LO signals of frequencies Wr and
`w0 , due to the term which is linear in v. The v2 term will give rise to the following
`output current:
`
`G'
`d(Vr COS Wrt + Vo COS wc,t)2
`i =
`2
`= T(v~ cos 2wrt + 2VrVo cos Wrt cos wot+ ifo cos 2Wot)
`G'
`
`DC
`bias
`
`RF
`v,cos '41
`
`Combiner
`
`LO
`
`Matching
`network
`
`- - - -
`
`h
`~ - - -.... -♦Ol-,,•"1()---1 L1.. ~----
`O l± - - - -
`-u LP filter
`r
`
`V;COS(Ol,-Cll())t
`
`FIGURE 10.17 Single-ended mixer cin:uit.
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`10.2 Detectors and Mixers
`
`567
`
`10.38
`
`G' =
`4d[v;_ + tJ5 + v;_ COS 2wrt + tJ5 COS 2wot
`+ 2VrVO COS(Wr - WO)t + 2Vr'VO COS(Wr + WO)t].
`The DC terms can be ignored, and the 2wr and 2wo terms will be filtered out. The most
`important terms are those of frequency Wr ± wo.
`For a receiver or down-converter, the Wr -wo term will become the IF signal. Note
`that, for a given local oscillator frequency, there will be two RF frequencies that will mix
`down to the same IF frequency. If the RF frequency is Wr = wo + Wi, then the output
`frequencies of the mixer will be Wr ± wo = 2wo + Wi, and Wi; if the RF frequency is
`Wr = wo - Wi, the mixer output frequencies will be Wr ± wo = 2wo - Wi, and -wi. This
`latter output is called the image response of the mixer, and is indistinguishable from the
`direct response. It can be eliminated by RF filtering at the input of the mixer, but this
`is difficult because the desired RF frequency (wo + wi) is relatively close to the spurious
`image frequency at (wo - Wi), since generally wi < < wo. Another way to eliminate the
`image response is by using an image rejection mixer.
`In an up-converter, or modulation, application the two inputs will usually be a local
`oscillator and an IF oscillator, as in Figure 10.16b. The IF signal would be modulated
`with the desired information signal. Then the output will be wo ±wi, where Wi is the IF
`frequency. The frequency wo + wi is called the upper sideband (USB), while wo - Wi
`is called the lower sideband (LSB). Double sideband (DSB) modulation retains both
`sidebands, while single sideband (SSB) modulation removes one of the sidebands by
`filtering or by using an image rejection mixer (also called a single sideband modulator).
`Mixer design involves impedance matching the three ports, which is complicated by
`the fact that several frequencies and their harmonics are involved. Undesired harmonic
`power can be dissipated in resistive terminations, or blocked with reactive termina(cid:173)
`tions. Resistive loads increase the loss of the mixer, and reactive loads are usually very
`frequency sensitive. An important figure of merit for a mixer is the conversion loss,
`defined as
`
`_
`available RF input power dB
`L
`01
`C - 1 og - - - - - - - - - .
`IF output power
`
`10.39
`
`Practical mixers usually have a conversion loss between 4 and 7 dB. One factor that
`strongly affects the conversion loss of a mixer is the local oscillator signal ( or pump)
`power level; minimum conversion loss usually occurs for LO powers between O and
`10 dBm. This power level is large enough to violate the small-signal approximation of
`(10.29), so results using such a model may not be very accurate. Precise design requires
`numerical solution of the nonlinear equation that describes the diode characteristics [4].
`Because a mixer is often the first or second component in a receiver system, its noise
`characteristics can be of critical importance. When specifying the noise figure of a mixer
`(or a receiver that uses a mixer), a distinction must be made as to whether the input
`is a single sideband signal or a double sideband signal. This is because the mixer will
`produce an IF output for two RF frequencies (wo ± wi), and therefore collect noise power
`at both frequencies. When used with a DSB input, the mixer will have desired signals at
`both RF frequencies, while an SSB input provides the desired signal only at one of these
`frequencies. Thus the DSB noise figure will be 3 dB lower than the SSB noise figure.
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