Case 6:20-cv-00945-ADA Document 33-16 Filed 08/23/21 Page 1 of 8
`Case 6:20-cv-00945-ADA Document 33-16 Filed 08/23/21 Page 1 of 8
`
`
`EXHIBIT 15
`EXHIBIT 15
`
`

`

`-TECHNICAL
`
`Case 6:20-cv-00945-ADA Document 33-16 Filed 08/23/21 Page 2 of 8
`
`Peter A. Weisskopf
`Merit Microwave Corporation
`Phoenix, AZ
`
`harmonic sampling applications are
`presented.
`Basis of Subharmonic Sampling
`8ubharmonic sampling as a mi-
`crowave signal processing tech-
`nique may be best understood by
`studying sampling theory.The basic
`premise of sampling theory states
`that when a signal f(t) of bandwidth
`(Hz) is sampled at a rate of fe,
`which is greater than or equal to
`twice the signal bandwidth or
`no
`information contained in the original
`signal
`is lost. Furthermore, taking
`the Fourier transform of the sam-
`pling function
`fs(t)= f(t)8(t)
`where 8(t) is the periodic sampling
`function of pulse width 't and period
`1/fe, the spectrum of the sampled
`signal may be derived. This results
`in a summation of individual Fourier
`transforms each centered at a pos-
`itive and negative integer multiple of
`the sampling rate
`
`Fs(ro) = dF(ro) + dL sin
`(or-nee)
`For all n =±oo except n =0
`If the sampled signal
`is a base-
`band signal center at 0, then the
`reconstructed signal will be cen-
`tered at O. The frequencies of the
`first harmonic replica of the sam-
`
`Introduction
`instru-
`Modern microwave test
`ments owe much of their capabilities
`to powerful microwave signal proc-
`essing subsystemsthat employ high
`speed sampling circuitry. These
`, sampling heads, as they are often
`called, can be found at the heart of
`the latest sampling oscilloscopes,
`frequency counters, lime/frequency
`analyzers and vector network ana-
`iyzers.1-3 The sophisticationat which
`these instruments analyze compiex
`microwave signals is a testimony to
`the powerof sampling techniques for
`use in extracting frequency, phase
`and vector lntorrnatlon.s
`Outside of the test equipment in-
`dustry, sampling techniques have
`been employed by phase lock oscil-
`lator and synthesizer manufacturers
`for many years.s The emergence of
`commercially available sampling
`phase detectors is an indication of
`the need for these types of micro-
`wave signal processing compo-
`nents. Along with this demand
`comes the need for design and ap-
`plication information on microwave
`sampling hardware.
`In this paper the theory behind
`subharmonic sampling is explored
`and the physics of the sample-and-
`hold process are examined when
`applied to microwave frequencies.
`Through time domain analysis, the
`criteria for optimum sampling hard-
`ware performance is established.
`Finally, a variety of microwave sub-
`MICROWAVE JOURNAL. MAY 1992
`
`pled signal are centered at 0, ± fe.
`The succeeding replicas (± n X fe)
`decrease in amplitude at the rate of
`(sin n1td)/n1td. This theory is well .
`suited for such applications as dig-
`itized voice. For this application the
`subharmonic sampling of a micro-
`wave signal must be considered.
`In compliance with the gUidelines
`of the sampling theory,the spectrum
`that results from a bandlimited mi-
`crowave signal f(t) of bandwidth
`that is sampled at the rate fe, where
`and is also a subharmonic
`fe
`of f(t), or n X fe= f(t) is considered.
`In this case, the fundamental repli-
`cas of the sampled signal
`is cen-
`tered atf(t)with succeeding replicas
`of this reconstructed signal appear-
`ing at ± n X fe. The FFTs, shown in
`Figure 1a where k = 512, show the
`(sin XliXamplitude response of the
`sampled spectrum. The expanded
`FFT of Figure 1a, where k = 154,
`shows more clearly how the sam-
`pled RFInput is reconstructed atthe
`original frequency. The succeeding
`replicas of the RF input as shown
`are converted up and down in fre-
`quency and separated in frequency
`by the sampling rate Fe(Hz).
`Inthis sampling simulation,the RF
`input was sampled at a subharmon-
`ic rate of one-tenth f(t). This is ev-
`ident in the facllhatthere are indeed
`10 replicas of the sampled signal in
`either upper or lower sideband, of
`F(t). Typically, the baseband replica
`of F(t) located near DC, in this case
`
`239
`
`RPX-Farmwald Ex. 1023, p 1
`
`

`

`o
`
`L·T
`
`I
`SAMPLED SIGNAL 1 IF PERIOD
`[TIME)
`0.06 , - - - - - - - - - - ,
`wc
`
`00
`
`512
`k
`FFT SAMPLED SIGNAL
`(HARMONICS OF THE BASEBAND IF OUTPUn
`0.06
`r-RF INPUT 1(1)
`wc
`
`o
`
`FFT SAMPLED SIGNAL
`(HARMONICS OF THE BASEBAND IF OUTPUT)
`(a)
`
`wci:!:::i0.
`
`Case 6:20-cv-00945-ADA Document 33-16 Filed 08/23/21 Page 3 of 8
`tered at fIt) - n X fe. This level of
`performance may be achieved in
`actual microwave and millimeter-
`wave subharmonic sample-and-
`hold circuitry when the circuit cri-
`teria are met
`Subharmonic Sample-and-Hold
`Circuit Modeling and Optimization
`Fromthe ideal subharmonic sam-
`ple-and-hold model shown in Fig-
`ure 2, parameters that must be con-
`sidered during the design of a mi-
`crowave sampling circuit may be
`defined. The source represents the
`microwave signal
`to be sampled.
`The source, defined by the function
`f(s}= sin (20l + B)
`delivers a time variant voltage Vs of
`source impedance Rs Q. During the
`sampling cycle, the source signal is
`applied to the hold capacitor Chvia
`the gate. The sampling aperture (tal
`is the time the gate is closed. The
`resistance of the gate (Rd) has been
`included in the total source impe-
`dance (Rs).
`The parameters that come into
`play during the hold cycle include
`the hold capacitance (Ch) and the
`load impedance of the buffer ampli-
`fier R,. The hold time is the period
`of the sampling rate (fel minus the
`sampling aperture (t.).
`During the sample cycle, the gate
`closes for the duration of the sam-
`pling aperture and a charge is im-
`posed on the hold capacitor. The
`charge on the hold capacitor in
`coulombs can be expressed by
`q =Jf(i)*t dt
`Because the value for Vs is a time
`variant function (V(s) = sin(Olt}), the
`integral becomes
`
`o _"!,..........
`160
`k
`FFT SAMPLED SIGNAL
`(HARMONICS OFTHEBASEBAND IF OUTPUT)
`(b)
`
`o
`
`I
`SAMPLED SIGNAL 1 IF PERIOD
`[TIME)
`
`512
`k
`FFT SAMPLED SIGNAL
`(HARMONICS OF THE BASEBAND IF OUTPUn
`0.0
`
`DESIRED IF OUTPUT
`
`-
`
`Fig. 1 TIme domain analysis of Ihe sampling process; (a) fs(t) = f(t) X S(I) periodic
`sampling, and (b) periodic sampling and hold into high impedance buffer.
`
`GATE
`
`R,
`
`BUFFER
`
`R.
`
`SOURCE
`
`PULSE
`
`Fig. 2 An ideal subharmonic sampling model.
`
`is the desired output
`f(t} - 10 X fe,
`signal. Extracting this baseband
`signal does require some circuit im-
`provements.
`Sample-and-Hold Circuit Offers
`Improvements Over Sampling
`In order to perform sampling
`downconversion to baseband, the
`desired output of the FFT shown in
`Figure 1a would bethespectral rep-
`lica at f(t}- 10 X fe. This is because
`the signal was sampled at the one-
`tenth subharmonic. All of the other
`spectral images in the FFT need to
`be rejected. To improve this situa-
`tion, instead of multiplying F(t) by the
`periodic sampling function S(t), fIt)is
`240
`
`sampled when S(t} is high and f(t} is
`held when SIt) is low. This logic
`statement allows emulation of the
`sample-and-hold process.
`The output FFT spectrum of the
`defined subharmonic sample-and-
`hold process revealsits most signif-
`icant property, which is the ability to
`downconvert a microwave or rnm-
`wave signal to baseband with great
`efficiency and without loss offidelity.
`Any loss in fidelity is due to the
`phase noise of the sampling clock
`degraded by 20 log of n.The Fourier
`transforms of Figure 1b show how
`the sample-and-hold process con-
`verts most of the sampled energy to
`the baseband spectral replica cen-
`
`q = (la-to)
`Rs
`
`J
`
`(- .J!DL )dt
`sin(Olt)*e
`(Rs'Chl
`over the interval
`of tathrough to
`Integrating this function over the
`sampling aperture time for a given
`value of Ch and Rs yields the value
`for charge stored on the sampling
`capacitor in coulombs.
`The value of the hold capacitor Ch
`is of significance as it is a parameter
`that the designer can easily control.
`Insight into the most judicious
`choice of sampling capacitance
`can be obtained by evaluating the
`[Continued on page 2421
`
`MICROWAVE JOURNAL • MAY 1992
`
`WI
`
`RPX-Farmwald Ex. 1023, p 2
`
`

`

`and-h<
`pedarn
`The
`manife
`ability
`cult to
`functio
`the ou
`circuit.
`buffer
`lmped:
`contah
`much
`conver
`signal.
`Carr
`pedarn
`impres
`giga C
`device
`itances
`allelwi
`pacitai
`ciency
`Ina'
`detect,
`input
`hold c
`op-am
`pacita
`filter
`\
`1 MHz
`sports.
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`WQi
`
`Case 6:20-cv-00945-ADA Document 33-16 Filed 08/23/21 Page 4 of 8
`[From page 240J WEISSKOPF
`
`200
`
`150
`
`oS
`t.i 100
`
`(a)
`
`4.0
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`200
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`150
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`oS
`t.i 100
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`K.
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`4.0
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`3.0 .§.
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`2.0
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`2.0
`1.0
`0.2
`HOLDCAPACITOR (pO
`
`3.0
`2.0
`1.0
`0.2
`HOLDCAPACITOR (pO
`
`(b)
`
`Fig.3 Sampled voltage (Ve)and stored kinetic energy (Ke) per sample VS. hold
`capacitance; (a) source z transformer (50 to 25 il) and (b) source z transformer
`(50 to 12.5 OJ with RF" =18.5 GHz @ 5 dBm and sampling aperture =27 ps.
`
`C,
`
`BUFFER
`
`Fig. 4 An actual subharmonic sampling model.
`
`kinetic energy stored during the
`sample cycle, which is equal to
`K = (q2)
`Ch
`The voltage stored on the capacitor
`is equal to
`
`q
`V = -
`C Ch
`Figure 3 shows the effect of hold
`capacitance on the stored voltage
`Vc and the total kinetic energy for
`two values of Rs. The lower source
`Impedance delivers the same kinet-
`ic energy to a larger hold capacitor
`that the higher impedance can only
`deliver to a small capacitance. The
`only difference for these two cases
`is the voltage f:Jcl, which decreases
`by the square root ofthe impedance
`ratio or by the square root of two. By
`increasing the incident power on the
`sampling circuit by 3 dB, the original
`voltage will be restored and the ki-
`netic energy will be increased two
`fold. The hold circuit can achieve
`optimum performance with a larger
`capacitor.
`Thus, ilis important for the source
`to offer a low impedance to the gate-
`
`In the actual
`and-hold capacitor.
`sample-and-hold model, shown in
`Figure 4, the capacitor Cm has been
`included to demonstrate a matching
`structure that consists of Cm and Lm
`+ Lp• This LC network makes con-
`venient use of the series inductance
`of the bond wires in the sampling
`bridge diodes for the purpose of
`matching the 50 Q source impe-
`dance to the 10 Q gate impedance.
`Output Buffer Amplifier Design
`Establishes IF Response
`With Rs and Chestablished to give
`maximum kinetic energy for a given
`sampling aperture, the effects of the
`buffer amplifier impedance on the
`stored voltage during the hold cycle
`are considered. An ideal sample-
`and-hold buffer circuit should be
`capable of measuring the voltage
`stored on the hold capacitor for the
`duration of the hold cycle without
`discharging the capacitor. The ad-
`vantage of buffer circuitry, which
`can as nearly as possible meet this
`ideal requirement, is evident in the
`FFT of the ideal subharmonic sam-
`ple-and-hold simulation, as shown
`in Figure 1b. Next, one may com-
`pare this to the output of a sample-
`MICROWAVE JOURNAL' MAY 1992
`
`242
`
`CIRCLE 245
`
`RPX-Farmwald Ex. 1023, p 3
`
`

`

`Case 6:20-cv-00945-ADA Document 33-16 Filed 08/23/21 Page 5 of 8
`
`and-hold circuit that has a low im-
`pedance load,as shown in Figure 5.
`The resulting poor hold duration
`manifests itself as an increasing in-
`ability of the sample-and-hold cir-
`cuit to isolate the periodic sampling
`function discrete-line spectra from
`the output of the sample-and-hold
`circuit. On the other hand, if the
`buffer can be made to have a high
`impedance, the output signal will
`contain little harmonic energy and a
`much stronger baseband down-
`converted spectrum of the sampled
`signal.
`Commercially available high im-
`pedance buffer amplifiers offer very
`impressive input impedances in the
`giga ohm ranges. However, these
`devices can havestrayinput capac-
`itances of 3 pF. If connected in par-
`allel with the hold capacitor, this ca-
`pacitance would destroy the effi-
`ciency of the circuitry.
`Ina subharmonic sampling phase
`detector application, a 50 KQ series
`input resistance connecting the
`hold capacitor to a high impedance
`op-amp with 3 pF of stray input ca-
`pacitance would create a lowpass
`filter with a corner frequency at
`1 MHz. This limited frequency re-
`sponse is adequate for phase lock
`
`o
`
`L·T
`t
`SAMPLED SIGNAL 1 IF PERIOD
`(TIME)
`
`wC
`a.
`oo
`
`512
`k
`FFTSAMPLED SIGNAL
`(HARMONICS OFTHEBASEBAND IF OUTPUT)
`
`O.OS€
`i!l5a.
`11
`oIIIhiliMll.Ww,W,J..iIjl.Ii
`o
`154
`k
`FFTSAMPLED SIGNAL
`(HARMONICS OFTHE BASEBAND IF OUTPUT)
`
`Fig. 5 Timedomain analysis
`of periodic sampling and hold
`intoa lowimpedance buffer.
`MICROWAVE JOURNAL' MAY 1992
`
`loops that have bandwidths of less
`than 100 kHz. However, in micro-
`wavesignal processing,where sub-
`harmonic sampling is used to ex-
`tract information from a broadband
`modulated carrier or to downcon-
`vert a carrier to an IF frequency,the
`buffer amplifier will be required to
`have a frequency response as high
`as one-half the sampling rate.Inthis
`case, the buffer amplifier will need
`to have both high input impedance
`and very low input capacitance. A
`
`possible solution to this problem is
`to include the gate capacitance of a
`FET source follower Into the total
`required value of hold capacitance.
`Sampling Aperture Width
`Establishes InputRF Response
`Maximum kinetic energy will be
`transferred to the hold capacitor
`when the sampling aperture is one-
`half the period of the frequency of
`the the sampled carrier. Sampling a
`[Continued on page 244]
`
`I
`
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`Additional operating features
`different tape frequencies
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`acterlstlcs assure supe·
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`tion Converters.
`Model 1000ITC-6B is the IF to TapeConverter.
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`
`CIRCLE 34 ON READER SERVICE CARD
`
`243
`
`actual
`>wn in
`sbeen
`tching
`md L,
`s con-
`ctance
`mpling
`ose of
`impe-
`dance.
`gn
`to give
`a given
`s of the
`on the
`d cycle
`ample-
`.uld be
`voltage
`.for the
`without
`:he ad-
`which
`ieet this
`It in the
`ic sam-
`;shown
`Iy com-
`sample-
`MAY 1992
`
`RPX-Farmwald Ex. 1023, p 4
`
`

`

`Case 6:20-cv-00945-ADA Document 33-16 Filed 08/23/21 Page 6 of 8
`[From page 243] WEISSKOPF
`
`YOU
`DON'T HAVE
`
`TOFLIP
`
`MICROSTRIP
`
`SLOTLlNE)l- Ta
`
`MICROSTRIP
`
`MICROSTRIP
`
`<al
`
`RAW PULSE
`FROM SRD
`(b)
`
`RAW PULSE
`
`FROMSRD-lev -
`
`(c)
`
`Fig. 6 Pulse compression techniques;
`(a) back short reflected pulse inversion,
`(b) nonlinear transmission line
`and (c) anti-parallel displaced pulses.
`
`40 GHzcarrierwould requireasam-
`piing aperture of iess than 15 ps.
`With this in mind, and to the extent
`of what is practical in the generation
`olthe sampling aperture pulse, gen-
`erating a pulse that is too narrow is
`challenging above C-band.
`The best step recovery diodes
`(SRD) employed in pulse generation
`have a transition time of 35 ps, and
`a subsequent pulse width of 70 ps,
`Based on the above criteria, a sam-
`pling phase detector design that
`does not use a pulse compression
`technique will experience difficulty
`in operating at frequencies beyond
`7GHz.
`A number of techniques can be
`employed to achieve the required
`pulse compression needed to oper-
`ate at microwave and mm-wave fre-
`quencies. The ease at which the
`pulse compression hardware can
`be implemented is dependent on
`the type of 180· balun that is used
`to generate the balanced sampling
`aperture pulses to be applied to the
`sampling bridge diodes. The types
`of baluns that can find applications
`in sampling circuitry are generally
`those baluns employed in frequency
`mixers that offer multi-octave band-
`widths with good 180· balance.
`The most popular sampling phase
`detector balun is the floating dual
`resistive terminated balun found in
`
`the commercially availablesampling
`phase detectors. This balun offers
`minimum bandwidth at microwave
`frequencies, suffers from DC drift
`and is not easiIy adapted to puIse
`compression techniques.
`A more practical balun that offers
`muitioctave bandwidth is the slot-
`line-to-coplanar waveguide balun.
`Some very effective pulse compres-
`sion techniques can be applied to
`these types of E-plane circuits. A
`collection oftechniques is shown in
`Rgure 6.
`In the backshort circuit, the pulse
`travels in both directions at the mi-
`crostrip-to-slotline transition. When
`the pulse strikes the shorted end of
`the slotline,it is invertedand reflected
`where it combines with the trailing
`edge of the forward traveling pulse.
`The trailing inverted pulse clips the
`forward pulse, which shortens the
`effective sampling aperture.
`In Figure 6b, a nonlinear trans-
`mission line is used. The nonlinear
`transmission line uses varactor di-
`odes to generate a voltage depen-
`dent time delay.The higher voltages
`of the pulse waveform propagate
`faster, which leads to a steepening
`of the leading edge of the pulse,"
`The circuit shown in Figure 6c
`uses anti-parallel displaced pulses
`that are generated simultaneously.
`The trailing pulse that is inverted
`from the leading pulse serves to in-
`itiate the end of the sampling ap-
`erture. In this circuit, the aperture of
`the individual pulses is of minor sig-
`nificance as it is the spacing be-
`tween pulses that establishes the
`sampling aperture.
`
`24,0
`
`Sampling Circuit Applications
`Subharmonic Sampling Phase
`Lock Oscillators
`Perhaps the simplest and most
`common application for microwave
`sample-and-hold circuitry is in the
`sampling phase detector used to
`perform synchronization of a micro-
`eno
`wave oscillator with a high stability
`reference oscillator.
`In this hard-
`Hig
`ware,the sampling circuit is period-
`ically gated at a subharmonic of the
`voh
`microwave signal. During phase
`cati
`synchronization ofthe reference os-
`cillator with the microwave VCO, the
`ami
`sampling circuit measures the volt-
`bIOI
`age of the zero crossing of a single
`cos
`half cycle of the microwave signal.
`ma:
`[Continued on page 246]
`hig
`MICROWAVE JOURNAL. MAY 1992
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`CIRCLE 86
`
`244
`
`ro
`
`RPX-Farmwald Ex. 1023, p 5
`
`

`

`Case 6:20-cv-00945-ADA Document 33-16 Filed 08/23/21 Page 7 of 8
`[From page 244] WEISSKOPF
`
`z
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`
`Fig. 7 A complete sampling PLLmodule
`without the VCO.
`
`Fig.8 Sampling phasedetector performance; (a)typical gain
`and (b)temperature drift.
`
`RECOVERED CARRIER SUBHARMONIC
`
`---,
`
`III
`
`SPD6DQD
`
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`IJ
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`LIMITING
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`REFERENCE IN
`70 to 73 MHz
`
`Fig. 9 A schematic diagram of a sampling PLLmodule.
`
`Fig.10 A quadrature subharmonic sampling carrierrecovery loop
`fordirectdemodulation of a MPSKmicrowave carrier.
`
`246"._------------_...-
`
`MICROW.
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`Fig. 1
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`pled (
`conce
`wave
`the wi
`nator I
`tion fe
`FSKd
`quenc
`Concl
`Key
`head
`cusse
`sampi
`perfor
`micro'
`the !Yl
`esslru
`throu
`This I
`and d
`nique
`micro
`
`Referl
`1. W.
`SCIac
`nic
`19
`2. Aii
`qu
`icA>
`MICRC
`
`Any advance or retardation of phase
`is indicated by a negative or positive
`DC shift at the IF output of the sam-
`ple-and-hold circuit. When this sig-
`nal
`is applied to the VCO tuning
`structure, the phase of the VCO can
`be forced to track the phase of the
`reference oscillator at a precise in-
`teger sub harmonic.
`Figure 7 is a complete sampling
`phase detector module measuring
`1.2" X 1.9". This unit contains a
`sampling head that deiivers a phase
`detector response of 400 mV/ rad at
`18 GHz from a 0 dBm input signal.
`The sampling head topology is a
`coplanar structure that features
`pulse compression of
`the type
`shown in Figure 4a. The coplanar-
`to-slotline balun offers multioctave
`bandwidth and is well suited for
`sampling head appllcatlons.ts Ac-
`tual performance of
`the sampling
`phase detector is shown in Figure 8.
`
`Contained in the module is the ref-
`erence driver circuitry.
`loop filter.
`sweep and acquisition circuitry. ref-
`erence detector and lock detector
`circuitry. The module is tlesigned to
`be integrated with a VCO,such as a
`voltage tuned DRO. to form a com-
`plete PLO subsystem. as shown in
`Figure 9.
`Direct Demodulation of Microwave
`MPSK Carriers
`This commercial application em-
`ploys two sampling heads and is an
`example that performs a great deal
`of microwave signal processing with
`.a limited amountof microwave com-
`ponents.ln Figure 10,the concept of
`quadrature subharmonic sampling
`for the purpose of coherent direct
`demodulation of an MPSK modulat-
`ed microwave signal with sup-
`pressed carrier is introduced. Tradi-
`tionally,
`this application would re-
`
`quire a frequency converter with
`coherent microwave local oscilla-
`tors and a Costas ioop type of car-
`rier recovery system. The quadra-
`ture subharmonic sampling module
`performs frequency conversion to
`baseband as well as I and Q vector
`demodulation, simuitaneously. The
`carrier tracking oscillator is the
`sampling clock VCXO, which is op-
`erated at a subharmonic of the mi-
`crowave carrier. The microwave car-
`rier when split into quadrature and
`applied to the dual sampling down-
`converter module enables the I and
`Q signal to be generated, mixed and
`applied to the VCXo. The result of
`this is a quadrature subharmonical-
`Iy sampled carrier recovery loop
`(QSSCRL). The outputs of the
`QSSCRL can be digitized, which al-
`lows the remainder of the demodu-
`lation and decoding to be performed
`with conventional digital circuitry.
`MICROWAVE JOURNAL. MAY 1992
`
`RPX-Farmwald Ex. 1023, p 6
`
`

`

`Case 6:20-cv-00945-ADA Document 33-16 Filed 08/23/21 Page 8 of 8
`
`cos[(w1-nwO)t]
`FREQUENCY DIFFERENCE DC LEVEL
`1/2(w1-nwO)[1+cos2(w1
`
`-y-f'1::::>i:fff'[:::-:::'Jrli
`
`;
`
`1J2(w1-nwO)cos(w1-nwO)t
`dl DIFFERENTIATOR
`sin[(w1-nwO)I]
`
`aD
`
`) I DATA
`
`:AND
`ITA
`
`41C
`
`very loop
`ier.
`
`er with
`oscilla-
`of car-
`[uadra-
`module
`sion to
`I vector
`,Iy. The
`is the
`1 is op-
`the mi-
`wecar-
`ire and
`Idown-
`ie I and
`(ed and
`esult of
`onlcal-
`'y loop
`of the
`hich at-
`smodu-
`iormed
`luitry.
`!AY 1992
`
`Fig. 11 (a) A subharmonlcally sampled quadricorrelator and (b) its DC output V$. input
`frequency.
`
`Subharmonically Sampled
`Quadricorrelator
`The concept of quadrature sub-
`harmonic sampling for vector de-
`modulation is used in many signal
`processing applications. The circuit
`of Figure 11 shows how quadrature
`subharmonic sampling can be ap-
`plied to an old technique for a mod-
`ern application. The quadricorrela-
`tor is a type of wideband frequency
`discriminator first
`introduced in
`1954.9 The subharmonically sam-
`pled quadricorrelator allows this
`concept to be extended to micro-
`wave frequencies. Applications of
`the wideband frequency discrimi-
`nator might include veo lineariza-
`tion for microwave FM ew radar,
`FSK demodulation or precision fre-
`quency marker generation.
`Conclusion
`Key criteria for optimum sampling
`head performance have been dis-
`cussed. When applied to microwave
`sampling hardware,
`the ability to
`perform vector demodulation of a
`microwave carrier is one example of
`the types of microwave signal proc-
`essing that can be accomplished
`through subharmonic sampling.
`This blend of microwave circuitry
`and digital signal processing tech-
`niques represents the new age of
`microwave signal processing.•
`
`References
`1. W.M. Grove, "Sampling for Oscillo-
`scopes and Other RF Systems:' Trans-
`actions on Microwave Theoryand Tech-
`niques, Vol. MTT-14, No. 12, December
`1966.
`2. Ali Bologlu, "A 26.5 GHz Automatic Fre-
`quency Counterwith EnhancedDynam-
`ic Range," Hewlett-Packard Journal,
`April 1960.
`MICROWAVE JOURNAL • MAY 1992
`
`3. Mohammed M. Sayed, "40 GHz Fre-
`quency Converter Heads," Hewlett-
`Packard Journal,Vol.31, Aprli 1980.
`4. Chu-Sun Yen,"Phase-Locked Sampling
`Instruments," IEEE Transactions on In-
`strumentation and Measurement,
`March-June, 1965.
`5. Brian E. Gllcrlst, Rodger D. Fildes and
`John G. Galli, "The Use of Sampling
`Techniques for Miniaturized Microwave
`Synthesizer Applications," lEE MTT-S
`Digest, 1982,
`6. Wesley C. Whitely, William E. Kunz and
`William J. Anklam, "50 GHz Sampler Hy-
`brid Utilizing a Small Shockline and an
`Internal SRD:' IEEE MTT-S Digest, Vol.
`111991. p. 895.
`7. H. Ogawa, M. Aikawa and M. Akalke,
`"Integrated Balanced BPSK and QPSK
`Modulators for the Ka-Band,'
`lEE Trans-
`actions on Microwave Theory and Tech-
`niques, Vol.MTT-30, March 1982, p. 227.
`8. Gupta, Ramesh and Bahl, Microstrip
`Lines and Siotlines, Artech House, 1979,
`p.293.
`9. Donald Richman, "The DC Quadricorre-
`lator. A Two-Mode Synchronization Sys-
`tem," Proceedings of the IRE, Vol. 42,
`January 1954, pg. 266-299.
`
`Peter A. welaakopf
`received his BSEE
`from George Mason
`University in 1987.
`Prior to graduation,
`he was involved in
`mm-,¥ave system
`development at
`In-
`novative Concepts
`fnc. for the NavalRe-
`search Laboratory.
`Washington DC. Af-
`tergraduation, he worked for M/A-COMAAD,
`where he designed phase locked DROs and
`microwave synthesizers. In 1990, he founded
`Merit Microwave in Phoenix, Arizona, where
`he is in engaged in the development of mi-
`crowave and mm-wave signal processing
`components Bnd systems.
`FAST AND EASY!
`That's what our Reader Service Cards
`mean to you when you want more
`information. You will find them near the
`back of every issue.
`
`•
`
`Ih-F....
`E\ 1'--
`
`-'
`
`CIRCLE 95
`
`247
`
`RPX-Farmwald Ex. 1023, p 7
`
`