(RF) Harmonic Measurement System

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Article Hardware Design of a High Dynamic Range Radio Frequency (RF) Harmonic Measurement System

Ram M. Narayanan 1,* ID , Kyle A. Gallagher 2, Gregory J. Mazzaro 3 ID , Anthony F. Martone 2 and Kelly D. Sherbondy 2

1 School of Electrical Engineering and Computer Science, The Pennsylvania State University, University Park, PA 16802, USA 2 U.S. Army Research Laboratory, Sensors Directorate, Adelphi, MD 20783, USA; [email protected] (K.A.G.); [email protected] (A.F.M.); [email protected] (K.D.S.) 3 The Citadel, Department of Electrical & Computer Engineering, Charleston, SC 29409, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-814-863-2602

Received: 15 July 2018; Accepted: 17 August 2018; Published: 19 August 2018

Abstract: Radio frequency (RF) circuit elements that are traditionally considered to be linear frequently exhibit nonlinear properties that affect the intended operation of many other RF systems. Devices such as RF connectors, antennas, attenuators, resistors, and dissimilar metal junctions generate nonlinear distortion that degrades primary RF system performance. The communications industry is greatly affected by these unintended and unexpected nonlinear distortions. The high transmit power and tight channel spacing of the communication channel makes communications very susceptible to nonlinear distortion. To minimize nonlinear distortion in RF systems, specialized circuits are required to measure the low level nonlinear distortions created from traditionally linear devices, i.e., connectors, cables, antennas, etc. Measuring the low-level nonlinear distortion is a difﬁcult problem. The measurement system requires the use of high power probe signals and the capability to measure very weak nonlinear distortions. Measuring the weak nonlinear distortion becomes increasingly difﬁcult in the presence of higher power probe signals, as the high power probe signal generates distortion products in the measurement system. This paper describes a circuit design architecture that achieves 175 dB of dynamic range which can be used to measure low level harmonic distortion from various passive RF circuit elements.

Keywords: high dynamic range measurements; harmonic measurement system; nonlinear distortion; harmonic radar; passive RF components

1. Introduction and Motivation Nonlinearities in RF and microwave systems can take many forms. Historically, nonlinearities are found in circuit elements such as diodes, transistors, ampliﬁers, mixers, and others. In addition, nonlinearities have been found in other circuit components and are generated by different mechanisms. One of the less common nonlinear mechanisms is passive intermodulation (PIM) distortion, which occurs in antennas [1,2], cables, connectors [2–4], metal-to-metal junctions [5,6], and various components [7,8]. A recent development has led to the exploitation of nonlinearities in electronic circuits to detect and track nonlinear targets [9–15]. Circuit elements exhibit nonlinear properties either by design or by consequence. By design, P-N junctions, such as diodes, are inherently nonlinear, and this property is exploited for their use in frequency mixers, which are used to upconvert or downconvert signals from one frequency to another.

Instruments 2018, 2, 16; doi:10.3390/instruments2030016 www.mdpi.com/journal/instruments Instruments 2018, 2, 16 2 of 16

The operation of mixing two signals together to create a new frequency is a nonlinear operation. By consequence, many RF and microwave circuit elements exhibit unintended nonlinear properties. An example is the RF amplifier. Amplifiers are intended to operate linearly, boosting the input signal without creating extraneous frequencies at the output. In practice, creating a linear amplifier is not possible and additional frequency content is generated that distorts the desired signal. Much research has been done to linearize amplifiers [16–20]. The unintended frequency content generated by the nonlinear properties of the amplifier interferes with other radar and communication systems [21–23], as well as affect the sensitivity of the receiver. There are other nonlinear effects that are subtler and do not manifest as often. Among these is PIM, which is observed when high power signals interact with components that are weakly nonlinear. Such components do not exhibit measurable nonlinear distortion under normal conditions. In communication systems, the PIM produced can fall close to the fundamental band and interfere with adjacent communication channels [24,25]. To combat this, much research has gone into linearizing communication systems [3,24,26]. For close-in intermodulation distortion (IMD), the frequency separation between the fundamental signal and PIM is too small to effectively filter out. Additionally, the communication channels change frequency quickly to accommodate multiple users. So, adaptable filters with large Q values would be needed; however, reconfigurable, high Q filters do not exist. For this reason, adaptive techniques are used to predict and cancel the nonlinearities. Such techniques include predistortion, feedforward linearization, channel equalization, etc. [27–32]. Measuring weakly nonlinear RF circuit components requires specialized RF hardware [3], which itself must be highly linear and devoid of any self-generated nonlinearities. If the measurement system is not highly linear, the measurements will reflect the distortions caused by the test hardware in addition to the device under test (DUT). Commercially-available high dynamic range PIM measurement systems are accessible today [33,34]. These systems are typically designed for specific frequencies, usually around the cell band. They use a two-tone test setup and achieve up to 170 dBc of dynamic range using high Q filters that are fixed in frequency, but lack frequency agility. A commercially-available nonlinear vector network analyzer, PNA-X, demonstrates far more flexibility than the fixed frequency PIM testing systems, and has the ability to vary tone spacings and tone amplitudes [35]. The PNA-X system also tracks intermodulation (IM) products and harmonics, keeping track of all the nonlinear terms [36]. However, it lacks the dynamic range necessary to measure nonlinear distortion from weakly nonlinear devices, as they are specified to generate harmonics lower than 60 dBc [37]. Feedforward cancellation systems have been developed that enable close-in PIM to be measured with a 160-dBc dynamic range, measured from the probe signal power to the spurious free IM frequency [16,38–40]. The systems achieve a large dynamic range by taking great care to linearize their measurement system, which requires high levels of isolation between nonlinear circuit elements in the test setup to the DUTs. These systems also employ an adaptable cancellation system that removes the probe signals before PIM measurements are made. The linearization, isolation, and removal of the probe signal are essential to any high dynamic range measurement system. The downside to constructing such a test setup is the complexity of the system. These systems require iterative feedback from the receiver to cancel the fundamental probe signal. They also require an optimization algorithm to maximize the cancellation of the probe signal to maximize the dynamic range of the measurements. This paper describes an alternate approach to measuring low level nonlinear distortion from weakly nonlinear targets. The measurement system uses the second harmonic to characterize the nonlinearities of passive RF circuit elements. The measurement system achieves the high dynamic range, of the order of 175 dBc, necessary to measure weakly nonlinear devices while covering a 20% bandwidth, something the PNA-X and other commercially-available systems cannot accomplish. The measurement system is also low complexity, not requiring complicated feedforward cancellation circuits. Instruments 2018, 2, 16 3 of 16

Instruments 2018, 3, x FOR PEER REVIEW 3 of 16 Section1 introduces the mathematics required to characterize nonlinearities from circuit elements. instrumentation.Section2 describes Section basic harmonic 3 considers measurement issues in creating techniques a high to dynamic linearize range standard harmonic RF instrumentation. measurement system.Section3 Section considers 4 discusses issues in the creating high adynamic high dynamic range harmonic range harmonic measurement measurement system system. constructed Section that4 achievesdiscusses 175 the highdBc of dynamic dynamic range rang harmonice. Section measurement 5 presents the system results constructed obtained thatfrom achieves the measurement 175 dBc of systemdynamic of range.various Section RF system5 presents compon theents. results Section obtained 6 concludes from the the measurement paper. system of various RF system components. Section6 concludes the paper. 2. Nonlinear Device Modeling and Characterization 2. Nonlinear Device Modeling and Characterization To accomplish the goal of characterizing nonlinearities generated by RF circuit components, a nonlinearTo accomplish system model the goal is needed. of characterizing The model nonlinearities must characterize generated the nonlinear by RF circuit properties components, of the devicesa nonlinear and systempredict modelthe behavior is needed. of the The devices model un mustder characterizedifferent conditions. the nonlinear Having properties the ability of the to predictdevices andthe predictnonlinear the response behavior ofof theweakly devices nonlinear under different devices conditions. enables a Havingsystem thedesigner ability toto predictbetter predictthe nonlinear how much response distortion of weakly will nonlinearbe present devices in the system. enables Therefore, a system designer the input-output to better predictrelationship how formuch nonlinear distortion devices will beneeds present to be in defined. the system. Therefore, the input-output relationship for nonlinear devicesIn general, needs to nonlinear be deﬁned. systems do not satisfy the linearity property, i.e., superposition and scaling properties.In general, The nonlinearoutput of systemsnonlinear do systems not satisfy contai thens linearity signals property, that cannot i.e., be superposition represented andas a scaling linear properties.combination The of outputthe input of nonlinearsignals. These systems signals contains cansignals be at thatdifferent cannot frequencies be represented than asthe a linearinput frequencies.combination In of this the paper, input nonlinear signals. Thesesystems signals are modeled can be using at different the power frequencies series [7,8,41–43], than the which input isfrequencies. represented In as this paper, nonlinear systems are modeled using the power series [7,8,41–43], which is represented as ∞∞ ∞ ∞ n y ==yaxn, (1) y = yn =nnanx , (1) ∑nn==00∑ n=0 n=0 where xxis is the the input input signal, signal,y isy the is outputthe output signal, signal, and andan is a then is scale the factorscale factor coefﬁcient coefficient of the ofnth the order nth ordernonlinearity. nonlinearity. When the input to a nonlinear system is a single frequency, the output consists of harmonics of that frequency occurring at integer multiples of of th thee fundamental frequency. frequency. With a single frequency input to the power series given by x ==+x0 cos(ωθω0t + θ), the output can be shown to be [44] input to the power series given by xx00cos( t ) , the output can be shown to be [44]

∞ ∞ n n y = =+cnx cos(nωωθ0t + nθ). (2) y ∑cxn0 00cos( n t n ) . (2) n=0n=0

The amplitude of the frequency domain representati representationsons of Equation (2) is illustrated graphically in Figure 1 1.. Generally,Generally, the the output output amplitude amplitude drops drops as as the the harmonic harmonic order order nnincreases. increases.

Figure 1. IllustrationIllustration of of the the output output due to a single frequency input into a nonlinear system.

Equation (2) expresses the nonlinear system input-output relationship in terms of voltage. Equation (2) expresses the nonlinear system input-output relationship in terms of voltage. Engineers typically prefer to use power units; therefore, the voltage expression is converted to power. Engineers typically prefer to use power units; therefore, the voltage expression is converted to power. = 2 The average power of a sinusoidal signal is given by PVave2 peak2 Z 0 , where Vpeak is the peak The average power of a sinusoidal signal is given by Pave = Vpeak/2Z0, where Vpeak is the peak voltage voltageand Z0 is and the systemZ0 is the characteristic system characteristic impedance. impedance. Thus, the power Thus, in the the power harmonics in the can harmonics be represented can be in representeda decibel (dB) in scale a decibel as: (dB) scale as: Pout,n[dBm] = nP [dBm] + Dn, (3) =+in PnPDout,nn[dBm] in [dBm] , (3) where Pout,n is the output power at the nth harmonic, Pin is the input power at the fundamental (1−n) wherefrequency Pout, (n =is 1),theD outputn is a coefﬁcient power at expressedthe nth harmonic, in dBm Pin, andis the dBm input represents power at power the fundamental expressed in decibels relative= to one milliwatt. (1−n) frequency ( n 1 ), Dn is a coefficient expressed in dBm , and dBm represents power expressed in decibels relative to one milliwatt. The implications of Equation (3) are that the output-to-input power ratio for the nth harmonic follows an n:1 relationship in a dB scale. Therefore, a 1-dB increase in the input creates a 2- and 3-

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InstrumentsThe implications 2018, 3, x FOR ofPEER Equation REVIEW (3) are that the output-to-input power ratio for the nth harmonic4 of 16 follows an n : 1 relationship in a dB scale. Therefore, a 1-dB increase in the input creates a 2- and 3-dB dB increase in output power for the second and third harmonics, respectively. In general, the D increase in output power for the second and third harmonics, respectively. In general, the Dn valuesn arevalues frequency-dependent are frequency-dependent and characterize and characterize the nth the order nth nonlinear order nonlinear properties properties of a device. of a device. A more A commonlymore commonly found characterizationfound characterization of a device’s of a device’s nonlinear nonlinear properties properties is its output is its output intersect intersect point OIP pointn, whichOIPn , is which the intersection is the intersection point at point which at the which 1:1 slope the 1:1 of slope the linear of the response linear response intersects intersects the n : 1 slopethe n of:1 theslopenth of order the n nonlinearity.th order nonlinearity. This is shown This inis Figureshown2 in for Figure the second 2 for the harmonic, second i.e.,harmonic,n = 2. i.e., n = 2 .

Figure 2. IllustrationIllustration of of the relationship between OIPOIP22and andD 2D. 2 .

TheThe relationship relationship between betweenD nDandn and OIP OIPn cann canbe found be found by manipulating by manipulati Equationng Equation (3) to (3) yield: to yield:

Dn=−(1 )OIP + nD. Dn = (nn1 − n)OIPn + nD1.1 (4)(4)

3. Issues in Creating a High Dynamic Range Harmonic Measurement System 3. Issues in Creating a High Dynamic Range Harmonic Measurement System To measure harmonics generated by devices that are not traditionally nonlinear, a high dynamic To measure harmonics generated by devices that are not traditionally nonlinear, a high dynamic range (DR) measurement system must be developed. The measurement system must create a highly range (DR) measurement system must be developed. The measurement system must create a highly linear probe signal and must have the ability to measure very weak nonlinear signals in the presence linear probe signal and must have the ability to measure very weak nonlinear signals in the presence of the large fundamental probe signal. of the large fundamental probe signal. There are two important aspects of designing a high DR harmonic measurement system: (1) the There are two important aspects of designing a high DR harmonic measurement system: (1) the use of a high DR receiver to measure the weak nonlinear signals in the presence of the high power use of a high DR receiver to measure the weak nonlinear signals in the presence of the high power probe signal; and (2) generation of a highly linear probe single used to probe a DUT. Both the receiver probe signal; and (2) generation of a highly linear probe single used to probe a DUT. Both the receiver and probe single generator have their unique problems that must be addressed to generate high fidelity, and probe single generator have their unique problems that must be addressed to generate high linearized signals. This section addresses these problems. fidelity, linearized signals. This section addresses these problems. 3.1. Creating a Highly Linear Harmonic Receiver 3.1. Creating a Highly Linear Harmonic Receiver The first problem in creating a highly linear harmonic receiver is that the measurement hardware is itself nonlinear.The first Theproblem RF front in endcreating of a spectrum a highly analyzer linear consistsharmonic of nonlinearreceiver devicesis that suchthe measurement as amplifiers andhardware mixers. is For itself the nonlinear. results presented The RF front in this end paper, of a spectrum a National analyzer Instruments consists (NI) of ( Austin,nonlinear TX, devices USA) PXIe-5668Rsuch as amplifiers spectrum and analyzer mixers. is For used. the The results 5668R presen is specifiedted in tothis generate paper, a secondNational harmonic Instruments >69 dBc(NI) down(Austin, from TX, the USA) fundamental, PXIe-5668R between spectrum 700 analyzer to 1000 MHzis used. with The 0-dBm 5668R input is specified power to [45 generate]. Although a second the dataharmonic sheet specifies>69 dBc down >69 dBc, from the the measured fundamental, self-generated between second700 to 1000 harmonic MHz iswith 80 dBc.0-dBm This input 80 dBc power of dynamic[45]. Although range isthe sufficient data sheet tomake specifies harmonic >69 dBc, measurements the measured of self-generated strongly nonlinear second devices, harmonic such is as 80 amplifiers,dBc. This 80 mixers, dBc of and dynamic diodes, range but is is inadequate sufficient to to make make harmonic measurements measurements of weakly of nonlinear strongly elements.nonlinear Thedevices, first example such as ofamplifiers, this shown mixers in Figure, and3 diodes,, which but depicts is inadequate an ideal probe to make signal measurements entering an amplifier. of weakly Innonlinear Figure3, elements. “DUT” stands The first for example “device underof this test”,shown “HPF” in Figure stands 3, which for “high-pass depicts an filter”, ideal probe and “LPF” signal standsentering for an “low-pass amplifier. filter”. In Figure The DUT 3, “DUT” is a Mini-Circuits stands for “device amplifier under ZX60-3018G-S+. test”, “HPF” The stands fundamental for “high- andpass harmonic filter”, and responses “LPF” stands are made for “low-pass on the PXIe-5668R filter”. The spectrum DUT is a analyzer. Mini-Circuits The choice amplifier of filters ZX60-3018G- is very importantS+. The fundamental in architecting and a reliableharmonic harmonic responses measurements are made on system the PXIe-5668R [46]. spectrum analyzer. The choice of filters is very important in architecting a reliable harmonic measurements system [46].

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Figure 3. Measuring the second harmonic output of an ampliﬁer using an ideal linear source. FigureFigure 3.3. MeasuringMeasuring thethe secondsecond harmonicharmonic outputoutput ofof anan amplifieramplifier usingusing anan idealideal linearlinear source.source.

ThreeThree differentdifferent low-pass low-passlow-pass filter filterfilter options optionsoptions are areare tested testedtested using usingusing the thethe setup setupsetup in in Figurein FigureFigure3. These 3.3. TheseThese include: include:include: (1) no(1)(1) nofilter;no filter;filter; (2) (2)(2) a Mini-Circuits aa Mini-CircuitsMini-Circuits reflective reflectivereflective filter filterfilter VLF-1200; VLF-VLF-1200;1200; and andand (3) (3)(3) a aa Mini-Circuits Mini-CircuitsMini-Circuits diplexer diplexerdiplexer RPB-272. RPB-272.RPB-272. WhenWhen nono filter filterfilter is is used, used, the the dynamic dynamic range range of of the the test test se setupsetuptup isis setset byby thethe spectrumspectrum analyzer,analyzer, namelynamely 8080 dBc.dBc. TheThe dynamicdynamicdynamic range rangerange of ofof test testtest setup setupsetup is increasedisis increasedincreased by filteringbyby filteringfiltering out theoutout fundamental thethe fundamentalfundamental frequency frequencyfrequency before beforebefore it enters itit enterstheenters spectrum thethe spectrumspectrum analyzer. analyzer.analyzer. For every ForFor 1-dBeveryevery attenuation 1-dB1-dB atteattenuationnuation of the fundamental,ofof thethe fundamental,fundamental, the self-generated thethe self-generatedself-generated second secondharmonicsecond harmonicharmonic of the spectrum ofof thethe spectrumspectrum analyzer decreasesanalyzeranalyzer decreases 2decreases dB. This 2 follows2 dB.dB. ThisThis from followsfollows the relationship fromfrom thethe relationship inrelationship Equation (3). inin EquationAEquation commercial (3).(3). AA off-the-shelf commercialcommercial (COTS) off-the-shelfoff-the-shelf Mini-Circuits (COTS)(COTS) high-passMini-CircuitsMini-Circuits filter high-passhigh-pass VHF-1200 filterfilter would VHF-1200VHF-1200 be a natural wouldwould choice, bebe aa naturalbutnatural most choice,choice, COTS butbut filters mostmost attenuate COTSCOTS filtersfilters the stop attenuateattenuate band frequencies thethe stopstop bandband by creatingfrequenciesfrequencies an impedance byby creatingcreating mismatch. anan impedanceimpedance The mismatch.resultmismatch. of the TheThe mismatch resultresult ofof isthethe that mismatchmismatch the undesired isis thatthat thethe frequencies undesiredundesired are frequenciesfrequencies reflected andareare reflectedreflected not passed andand through notnot passedpassed the throughfilter.through The thethe impact filter.filter. of TheThe this impactimpact is examined ofof thisthis later.isis examinedexamined To attenuate later.later. theToTo attenuateattenuate fundamental thethe fundamental frequencyfundamental and frequencyfrequency to reduce andand the toreflectionto reducereduce backthethe reflectionreflection into the DUT, backback aintointo diplexer thethe DUT,DUT, is used. aa dipldipl Theexerexer low isis frequency used.used. TheThe port lowlow is frequencyfrequency terminated portport in 50isis terminatedterminatedΩ. For this insetup,in 5050 ΩΩ the.. ForFor probe thisthis setup,setup, signal thethe is set probeprobe to 800 signalsignal MHz isis andsetset toto the 800800 probe MHzMHz signal andand thethe power probeprobe is signal calibratedsignal powerpower to beisis calibratedcalibrated−20 dBm to atto bethebe −− input2020 dBmdBm to at theat thethe amplifier. inputinput toto thethe amplifier.amplifier. TheThe resolution resolution bandwidth bandwidth (RBW) (RBW) on on the the spectrum spectrum analyzer analyzer was was set set to to 800 800 Hz Hz and and the the internalinternal attenuatorattenuator waswaswas set setset to toto 30 3030 dB. dB.dB. The TheThe results resultsresults in Table inin TablTabl1 illustrateee 11 illustrateillustrate the following thethe followingfollowing two concepts: twotwo concepts:concepts: (1) the spectrum (1)(1) thethe spectrumanalyzerspectrum has analyzeranalyzer the dynamic hashas thethe dynamic rangedynamic to measurerangerange toto measur themeasur secondee thethe harmonic secondsecond harmonicharmonic response rere fromsponsesponse the fromfrom Mini-Circuits thethe Mini-Mini- Circuitsamplifiers;Circuits amplifiers;amplifiers; and (2) the andand reflective (2)(2) thethe reflecreflec filtertivetive alters filterfilter the altersalters test setup thethe testtest and setupsetup yields anan falsedd yieldsyields results. falsefalse If results.results. the input IfIf thethe power inputinput to powerthepower spectrum toto thethe spectrumspectrum analyzer isanalyzeranalyzer 0 dBm, is theis 00 dBm, spectrumdBm, thethe spectrspectr analyzerumum willanalyzeranalyzer generate willwill agenerategenerate second harmonicaa secondsecond harmonicharmonic on the order onon theofthe− orderorder90 dBm. ofof −− Therefore,9090 dBm.dBm. Therefore,Therefore, the reading thethe of readingreading−36.3 dBm ofof −−36.336.3 is well dBmdBm above isis wellwell the aboveabove self-generation ththee self-generationself-generation level of the levellevel setup ofof theandthe setupsetup it is a andand valid itit reading.isis aa validvalid reading.reading.

TableTable 1.1. FilterFilter testing testing results results toto improveimprove dynamicdynamic range.range.

FilterFilterFilter TypeType Type Power Power Power at at 800 800 MHzMHz Power Power Power atat 160016001600 MHz MHzMHz NoneNoneNone −−0.30.30.3 dBmdBm dBm −−36.336.3 dBmdBm ReflectiveReflectiveReﬂective −−39.339.339.3 dBmdBm dBm −−29.529.5 dBmdBm DiplexerDiplexerDiplexer −−42.642.642.6 dBmdBm dBm −−38.638.6 dBmdBm

ToTo measure measure lowerlower lower levellevel level harmonics,harmonics, harmonics, thethe the dynamicdynamic dynamic rangrang rangeee ofof thethe of thesystemsystem system needsneeds needs toto bebe to increased.increased. be increased. ThisThis canThiscan bebe can donedone be done byby usingusing by using aa filter.filter. a filter. WhenWhen When aa reflectivereflective a reflective filtfilt filtererer isis isused,used, used, thethe the undesiredundesired undesired probeprobe probe signalsignal signal isis reflectedreflected reflected causingcausing a a reverse reverse traveling traveling wave wave that that enters enters the the output output port port of of the the DU DUT.DUT.T. Once Once the the probe probe signal signal enters enters thethe output output portport ofof thethe DUT,DUT, the thethe probe probeprobe signal signalsignal generates generageneratestes additional additionaladditional nonlinearities. nonlinearities.nonlinearities. The TheThe results resultsresults in inin Table TableTable1 1show1 showshow more moremore than thanthan a aa 7-dB 7-dB7-dB increase increaseincrease in inin the thethe measured measuredmeasured second sesecondcond harmonic harmonicharmonic whenwhen thethe reflective reflectivereflective filter filterfilter is is used.used. FigureFigure 4 44 illustrates illustratesillustrates this thisthis reflectionreflectionreflection and andand additional additionaladditional generation gegenerationneration of ofof the thethe second secondsecond harmonic harmonicharmonic when whenwhen a aa reflectivereflectivereflective filterfilterfilter is is used. used.

FigureFigure 4. 4. MeasuringMeasuring the the secondsecond harmonicharmonic output output of of anan amam amplifierplifierplifier with with aa reflectivereflective reflective filter filterfilter showing showing errors errors ininin the the measurement measurement setup. setup.

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Instruments 2018, 3, x FOR PEER REVIEW 6 of 16 In Figure4, the blue lines represent the probe signal at fundamental frequency, the red lines In Figure 4, the blue lines represent the probe signal at fundamental frequency, the red lines representrepresent the second the second harmonic harmonic signal, signal, and and the the dashed dashed lines lines represent represent thethe signals that that are are generated generated by the reﬂectedby the reflected probe signal. probe Forsignal. the For measurements the measurements taken taken in Table in Table1, the 1, setup the setup was calibratedwas calibrated to remove to the cableremove loss the and cable the loss loss and through the loss the through ﬁlter atthe the filt seconder at the harmonic.second harmonic. The VHF-1200 The VHF-1200 and RBF-272and RBF- were chosen272 to were have chosen similar to losseshave similar at 800 losses and 1600at 800 MHz, and 1600 the MHz, fundamental the fundamental frequency frequency of the probe of the signalprobe and its secondsignal harmonic and its second under harmonic test, respectively. under test, respectively. The return lossThe (returnS11) for loss both ( S11 the) for VHF-1200 both the VHF-1200 and RBF-272 are shownand RBF-272 in Figure are5 shown. in Figure 5.

FigureFigure 5. S-parameters 5. S-parameters of the of Mini-Circuitsthe Mini-Circuits VHF-1200 VHF-1200 high-pass high-pass filter filter and and RBF-272 RBF-272 diplexer diplexer inin thethe high high pass configuration. pass configuration. Although the high-pass filter is not needed for this amplifier example, filtering is needed to Althoughincrease the the dynamic high-pass range filter to greater is not neededthan 160 fordBc, this the amplifier dynamic example,range needed filtering to measure is needed to increasenonlinearities the dynamic from passive range circuit to greater components than. 160The dBc,amount the of dynamic attenuation range needed needed to achieve to measure a nonlinearitiesdesired dynamic from passiverange of circuitDRd with components. a current dynamic The amount range of ofDR attenuationc is given by: needed to achieve a desired dynamic range of DR with a current dynamic range of DRc is given by: d DR−+ DR 10 = dc AH , (5) DR − DR2 + 10 A = d c , (5) H 2 where AH is the attenuation needed by the high pass filter at the fundamental frequency. The expression is given in a dB scale. An extra 10 dB is added to the desired dynamic range to ensure that where AH is the attenuation needed by the high pass filter at the fundamental frequency. The expression is giventhe self-generated in a dB scale. nonlinearities An extra 10 are dB at least is added a factor to of the 10 desiredless than dynamicthe desired range minimum to ensure detectable that the nonlinearity. Equation (5) also predicts that the dynamic range is increased by 2 dB for every 1 dB of self-generated nonlinearities are at least a factor of 10 less than the desired minimum detectable attenuation in the high-pass filter. nonlinearity. Equation (5) also predicts that the dynamic range is increased by 2 dB for every 1 dB of This section has demonstrated the importance of properly linearizing the receive section of a attenuationharmonic in measurement the high-pass system. filter. In this section, it was assumed that the probe signal was ideal, i.e., it Thiscontained section no hasmeasurable demonstrated second theharmonic. importance The next of properly section linearizingshows how theto ensure receive proper section of a harmoniclinearization measurement of the probe system.signal and Inillustrates this section, a potential it wasissue assumedwhen constructing that the the probe measurement signal was ideal,setup. i.e., it contained no measurable second harmonic. The next section shows how to ensure proper linearization of the probe signal and illustrates a potential issue when constructing the measurement3.2. Creating setup. a Harmonic Free Probe Signal In the previous section, it was assumed that the probe signal was ideal, i.e., it contained no 3.2. Creatingsecond harmonic. a Harmonic This Free is not Probe physically Signal possible and this section demonstrates how to create a probe signal that is “ideal enough” to measure weakly nonlinear targets. In the previous section, the In the previous section, it was assumed that the probe signal was ideal, i.e., it contained no second fundamental frequency needed to be attenuated in the receiver to measure the second harmonic harmonic. This is not physically possible and this section demonstrates how to create a probe signal accurately. In this section, the second harmonic must be removed from the probe to ensure that the that ismeasured “ideal enough” harmonic to is measure coming solely weakly from nonlinear the DUT and targets. not the In theprobe previous signal. If section, the second the harmonic fundamental frequencyis not neededadequately to beattenuated attenuated from in the the probe receiver signal to, measurethe measurement the second system harmonic generates accurately. a false, self- In this section,created the secondsecond harmonic. harmonic This must problem be removed is viewed from as theco-site probe interference. to ensure that the measured harmonic is coming solely from the DUT and not the probe signal. If the second harmonic is not adequately attenuated from the probe signal, the measurement system generates a false, self-created second harmonic. This problem is viewed as co-site interference. Instruments 2018,, 23,, 16x FOR PEER REVIEW 7 of 16

3.2.1. Filter Considerations 3.2.1. Filter Considerations The amount of second harmonic present in probe signal can never reach zero, or −∞ dB. Therefore,The amount it can only of second be attenuated harmonic to present the noise in probe floor signalof the measurement can never reach setup. zero, As or − in∞ SectiondB. Therefore, 3.1, the itlinearity can only of bethe attenuated measurement to the system noise can floor be of increase the measurementd by filtering. setup. The As NI inPXI-5651 Section signal3.1, the generator linearity ofused the is measurement specified to produce system less can bethan increased 25 dBc of by se filtering.cond harmonic The NI when PXI-5651 the output signal power generator is 0 useddBm is[47]. specified We assumed to produce this va lesslue than does 25 not dBc change of second too much harmonic when when the output the output power power is increased is 0 dBm to [+1047]. WedBm. assumed With +10 this dBm value of doesoutput not power, change the too 5651 much signal when generator the output will power produce is increased less than to−15 +10 dBm dBm. of Withsecond +10 harmonic, dBm of output thereby power, providing the 5651 25 dBc signal of dynamic generator range. will produceThus, if this less generator than −15 is dBm used of without second harmonic,any filtering, thereby accurate providing second 25 harmonic dBc of dynamic measurements range. Thus,are made if this to generator−5 dBm, including is used without the 10-dB any filtering,safety factor accurate for signal-to-interference second harmonic measurements ratio, which is are not made very to useful−5 dBm, when including trying to the make 10-dB sensitive safety factorharmonic for signal-to-interferencemeasurements. To increase ratio, which the dynamic is not very rang usefule of the when receiver, trying a tolow-pa makess sensitive filter is harmonicused. For measurements.the probe signal, To the increase improvement the dynamic in dynamic range range of the is receiver, a 1:1 ratio. a low-pass So, if the filter signal is used.generator For theprovides probe signal,a 25-dBc the dynamic improvement range and in dynamic 160 dBc rangeis desired, is a 1:1 the ratio. attenuation So, if the required signal generator for the low provides pass filter a 25-dBc is 145 dynamicdB. The general range andexpression 160 dBc for is the desired, attenuation the attenuation needed by requiredthe low pass for filter the low is: pass filter is 145 dB. The general expression for the attenuation needed=−+ by the low pass filter is: ALdgDR DR 10 , (6)

AL = DRd − DRg + 10 (6) where AL is the attenuation required of the low-pass filter at the second harmonic and DR g is the wheredynamicAL rangeis the of attenuation the signal generator. required ofAgain, the low-passa 10-dB safety filter factor at the is second built in harmonic to ensure and10 dBDR ofg signal-is the dynamicto-interference range ratio. of the signal generator. Again, a 10-dB safety factor is built in to ensure 10 dB of signal-to-interferenceMost COTS filters ratio. do not provide greater than 100 dB of attenuation required to linearize the probeMost signal. COTS Therefore, filters domultiple not provide filters need greater to be than cascaded 100 dB to of achieve attenuation the large required attenuation to linearize required. the probeAs stated signal. in Section Therefore, 3.1, most multiple COTS filters filters need are to reflective, be cascaded and to attenuation achieve the is largeachieved attenuation in the stop required. band Asby statedan impedance in Section mismatch 3.1, most COTScausing filters the arestop reflective, band frequencies and attenuation to reflect is achieved backwards in the and stop not band pass by anthrough impedance it. This mismatch reflective causing nature theof filters stop bandcauses frequencies problems. to reflect backwards and not pass through it. ThisThe reflective Mini-Circuits nature low-pass of filters filter, causes Model problems. # VLF-1200, has a cut off frequency of 1 GHz. However, the stopThe band Mini-Circuits of this filter low-pass does filter,not meet Model the# >1 VLF-1200,00-dB attenuation has a cut offrequirement. frequency ofTherefore, 1 GHz. However, multiple thefilters stop need band to ofbe thiscascaded filter doesto increase not meet the the stop >100-dB band attenuation. attenuation Figure requirement. 6 shows Therefore, the measured multiple and filters need to be cascaded to increase the stop band attenuation. Figure6 shows the measured and theoretical S21 response when two VLF-1200 filters are cascaded. The theoretical cascaded S21 theoretical |S21| response when two VLF-1200 filters are cascaded. The theoretical cascaded |S21| response was computed as a product of the individual S21 responses. response was computed as a product of the individual |S21| responses.

| | FigureFigure 6. 6.Measured Measured and andtheoretical theoretical SS2121 response response whenwhen two VLF-1200 low-pass low-pass filters ﬁlters are are cascaded. cascaded.

When the two reflectivereflective low-pass filtersfilters are cascaded,cascaded, the measuredmeasured and theoretical responses do not closely match. This point is further investigated in [48], [48], where three reflective reflective low pass filtersfilters are cascaded. The measured results when three lo low-passw-pass filters filters are cascaded show more discrepancy when compared toto thethe theoreticaltheoretical response.response.

Instruments 2018, 3, x FOR PEER REVIEW 8 of 16 Instruments 2018, 2, 16 8 of 16 Using a number of cascaded reflective filters causes large variations in the measurement system’s dynamic range as a function of frequency. If the measurement system operates at a single Using a number of cascaded reflective filters causes large variations in the measurement system’s frequency, a null in the cascaded frequency response can be used. If measurements are taken over a dynamic range as a function of frequency. If the measurement system operates at a single frequency, bandwidth of frequencies, the fluctuations in the frequency response would not permit reliable, a null in the cascaded frequency response can be used. If measurements are taken over a bandwidth repeatable, and accurate measurements. of frequencies, the fluctuations in the frequency response would not permit reliable, repeatable, and3.2.2. accurate Diplexer measurements. Considerations 3.2.2.This Diplexer leads Considerations us to the choice of microwave diplexers for accomplishing the filtering operation. Diplexers are three-port devices which separate power entering a common input into two frequency This leads us to the choice of microwave diplexers for accomplishing the filtering operation. bands; or conversely, they combine two frequency bands arriving separately into a common output Diplexers are three-port devices which separate power entering a common input into two frequency [49]. Diplexers in which there are adequate guard bands between channels may be designed by bands; or conversely, they combine two frequency bands arriving separately into a common output [49]. suitably connecting two separate, doubly-terminated filters onto a T-junction. These devices are Diplexers in which there are adequate guard bands between channels may be designed by suitably typically employed to connect the transmit and receive filters of a transceiver to a single antenna connecting two separate, doubly-terminated filters onto a T-junction. These devices are typically through a suitable three-port junction [50,51]. Diplexers are designed to have low PIM and, therefore, employed to connect the transmit and receive filters of a transceiver to a single antenna through a will have low harmonic distortion. With that said, they will generate their own harmonics, but these suitable three-port junction [50,51]. Diplexers are designed to have low PIM and, therefore, will have will be very low, on the order of high-quality cables and connectors, i.e., <−170 dBc. The harmonics low harmonic distortion. With that said, they will generate their own harmonics, but these will be very generated by the diplexers, cables, and connectors will set a fundamental limit on the dynamic range low, on the order of high-quality cables and connectors, i.e., <−170 dBc. The harmonics generated by of the system. the diplexers, cables, and connectors will set a fundamental limit on the dynamic range of the system. As such, they have the ability to be configured differently for different applications. Diplexers As such, they have the ability to be configured differently for different applications. Diplexers can can be used as a low-pass filter by terminating the high frequency port in 50 Ω and using the common be used as a low-pass filter by terminating the high frequency port in 50 Ω and using the common port and low frequency port. Unlike reflective filters, diplexers can be cascaded to increase their stop port and low frequency port. Unlike reflective filters, diplexers can be cascaded to increase their stop band attenuation. To cascade diplexers in a low-pass configuration, we terminate the high frequency band attenuation. To cascade diplexers in a low-pass configuration, we terminate the high frequency port and connect the common port to the low-pass port of the next diplexer. By connecting the low- port and connect the common port to the low-pass port of the next diplexer. By connecting the frequency port of one diplexer to the common port of another diplexer, the reflections between low-frequency port of one diplexer to the common port of another diplexer, the reflections between cascaded diplexers is reduced, when compared to the reflections when reflective filters are cascaded. cascaded diplexers is reduced, when compared to the reflections when reflective filters are cascaded. By terminating the high-frequency port, the stop band frequencies have a path to 50 Ω and the By terminating the high-frequency port, the stop band frequencies have a path to 50 Ω and the cascaded cascaded network is well-behaved. Figure 7 shows the S response when two diplexers are network is well-behaved. Figure7 shows the |S21| response21 when two diplexers are cascaded in a low-passcascaded configuration.in a low-pass configuration.

FigureFigure 7.7. Measured and theoretical |SS2121 | responseresponse whenwhen twotwo RBF-272RBF-272 diplexersdiplexers inin low-passlow-pass ﬁlterfilter conﬁgurationconfiguration areare cascaded.cascaded.

FigureFigure7 7 shows shows that that when when two two diplexers diplexers areare cascaded,cascaded, thethe measuredmeasured |SS2121 | closelyclosely matchesmatches thethe theoreticaltheoretical response.response. ComparingComparing FiguresFigures6 6 and and7 ,7, we we note note that that cascading cascading diplexers diplexers is is more more desirable desirable thanthan cascadingcascading reﬂectivereflective ﬁltersfilters forfor increasingincreasing stopstop bandband attenuation.attenuation.

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4. System Hardware Design Using the information from the previous sections, a higher power, high dynamic range harmonic measurement system was constructed.constructed. The measurement system was developed to measure second harmonic, nn = 22,, responses responses from from weakly nonlinear targets. The The system system also also collects collects data data on the linear, fundamentalfundamental ((nn== 1)) responses fromfrom DUTs.DUTs. TheThe system was designed to measure both the pass through and reﬂected,reflected, linear and secondsecond harmonicharmonic response.response. This allows for full characterization of devices. The linear frequency range spans 800 to 1000 MHz and the the second second harmonic harmonic frequency frequency range is 1600 to to 2000 2000 MHz. MHz. A A block block diagram diagram of of the the measurem measurementent system system is shown is shown in Figure in Figure 8. Note8. Note that that the thesecond second diplexer diplexer is flipped is ﬂipped to give to give the the harmonics harmonics traveling traveling in in the the reverse reverse direction direction a a path path to to a 50-50-Ω termination. WhereverWherever possible, possible, all inputsall inputs and outputsand outputs are terminated are terminated in 50 Ω atin both 50 theΩ fundamentalat both the frequencyfundamental and frequency second harmonic. and second harmonic.

Figure 8.8. BlockBlock diagram diagram of theof the linear/nonlinear linear/nonlinear measurement measurement system system with specificwith specific test locations test locations marked. marked. A NI PXI-5651 signal generator is used to create the probe signal. Next, Mini-Circuits RBF-272 A NI PXI-5651 signal generator is used to create the probe signal. Next, Mini-Circuits RBF-272 diplexers are used in a low pass configurations to linearize the probe signal, filter out any second diplexers are used in a low pass configurations to linearize the probe signal, filter out any second harmonic generated by the signal generator. To boost the power of the probe signal, a ZHL-30W-252-S+ harmonic generated by the signal generator. To boost the power of the probe signal, a ZHL-30W-252- Mini-Circuits power amplifier (PA) is used. The probe signal is amplified to 10 W (+40 dBm). The power S+ Mini-Circuits power amplifier (PA) is used. The probe signal is amplified to 10 W (+40 dBm). The amplifier is a nonlinear device and generates significant harmonics that need to filtered. Since the power amplifier is a nonlinear device and generates significant harmonics that need to filtered. Since fundamental frequency power is at 10 W, high power custom diplexers, manufactured by Reactel, the fundamental frequency power is at 10 W, high power custom diplexers, manufactured by Reactel, are used. are used. The high power diplexers are rated up to 100 W continuous wave input power. They are cavity The high power diplexers are rated up to 100 W continuous wave input power. They are cavity diplexers that provide greater than 80 dB of rejection in the stop band. The passband attenuation is diplexers that provide greater than 80 dB of rejection in the stop band. The passband attenuation is less than 0.4 dB. Section 3.2 demonstrated the need for a highly linear probe signal; therefore, two such less than 0.4 dB. Section 3.2 demonstrated the need for a highly linear probe signal; therefore, two diplexers are cascaded to attenuate the self-generated harmonics below the noise floor. In addition such diplexers are cascaded to attenuate the self-generated harmonics below the noise floor. In to the diplexers, an isolator is used to isolate the power amplifier output from the DUT and avoid addition to the diplexers, an isolator is used to isolate the power amplifier output from the DUT and mismatches. The insertion loss of the isolator is 0.2 dB. Thus, the power delivered to the DUT was avoid mismatches. The insertion loss of the isolator is 0.2 dB. Thus, the power delivered to the DUT approximately +39 dBm. was approximately +39 dBm. Test results from a single diplexer are presented in Figure9. The data in Figure9 show the Test results from a single diplexer are presented in Figure 9. The data in Figure 9 show the diplexers’ ability to pass the fundamental frequencies, from 800 to 1000 MHz, and attenuate the second diplexers’ ability to pass the fundamental frequencies, from 800 to 1000 MHz, and attenuate the harmonics, from 1600 to 2000 MHz. second harmonics, from 1600 to 2000 MHz. Figure9a shows that one cavity diplexer attenuates all harmonics, from 1600 to 2000 MHz, by at Figure 9a shows that one cavity diplexer attenuates all harmonics, from 1600 to 2000 MHz, by at least 80 dB with less than 0.4 dB attenuation at the fundamental frequencies, from 800 to 1000 MHz. least 80 dB with less than 0.4 dB attenuation at the fundamental frequencies, from 800 to 1000 MHz. The high frequency path of the diplexer was also tested and the results are shown in Figure9b. Again, The high frequency path of the diplexer was also tested and the results are shown in Figure 9b. Again, the diplexer attenuates the unwanted fundamental frequencies (here it is from 800 to 1000 MHz) by the diplexer attenuates the unwanted fundamental frequencies (here it is from 800 to 1000 MHz) by more than 80 dB and it passes the desired harmonic frequencies, 1600 to 2000 MHz, with less than more than 80 dB and it passes the desired harmonic frequencies, 1600 to 2000 MHz, with less than 0.4 0.4 dB of loss. Since the diplexers have very little loss in the pass band, they do not absorb a significant dB of loss. Since the diplexers have very little loss in the pass band, they do not absorb a significant amount of pass band energy. amount of pass band energy.

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(a) (b)

Figure 9. Measured S21 response for Reactel diplexers for various ports: (a) low-frequency port; and Figure 9. Measured |S21| response for Reactel diplexers for various ports: (a) low-frequency port; and (b) high-frequency(b) high-frequency port. port. (a) (b) A measured link-budget for a 900-MHz tone, used as the probe signal, is presented in Table 2. S response for Reactel diplexers for various ports: (a) low-frequency port; and ANote measuredFigure from 9. Table Measured link-budget 2 that going21 for from a 900-MHz D to E for tone,the second used harmonic as the probe shows signal, a loss of is 113.4 presented dB. However, in Table 2. Note fromaccording(b Table) high-frequency to2 thatFigure going 9a, port. the from loss D is to seen E for to thebe around second 95 harmonic dB. This discrepancy shows a loss is ofprobably 113.4 dB. due However, to the according to Figure9a, the loss is seen to be around 95 dB. This discrepancy is probably due to the fact fact that the S21 measurements are made on a network analyzer and the results in Figure 9a are A measured link-budget for a 900-MHz tone, used as the probe signal, is presented in Table 2. that thelikely|S21 limited| measurements by the network are madeanalyzer’s on anoise network floor or analyzer the internal and coupling. the results in Figure9a are likely limitedNote by from the networkTable 2 that analyzer’s going from noise D to floorE for the or thesecond internal harmonic coupling. shows a loss of 113.4 dB. However, according to Figure 9a, the loss is seen to be around 95 dB. This discrepancy is probably due to the Table 2. Measured link-budget for the harmonic distortion measurement system, in dBm, at different fact that the S measurements are made on a network analyzer and the results in Figure 9a are Table 2.locationsMeasured marked21 link-budget in Figure 8. for the harmonic distortion measurement system, in dBm, at different locationslikely limited marked by the in Figure network8. analyzer’s noise floor or the internal coupling. Frequency A B C D E F 900 MHz −7.7 −8.3 −8.9 +40.5 +40.2 +40.1 Table 2. MeasuredFrequency link-budget for A the harmonic B distorti Con measurement D E system, in F dBm, at different locations marked in 1800Figure MHz 8. −40.8 −94.7 <−130 +22.4 −91 <−130 900 MHz −7.7 −8.3 −8.9 +40.5 +40.2 +40.1 Photographs1800 ofFrequency the MHz NI chassis −40.8 Aand the−94.7B RF comp <−C130 onents+22.4D (Mini-Circuits E− 91 Fand< −130 Reactel diplexers and power amplifier) are 900shown MHz in Figures−7.7 10 −and8.3 11, −respectively.8.9 +40.5 +40.2 +40.1 1800 MHz −40.8 −94.7 <−130 +22.4 −91 <−130 PhotographsThe receiver of the hardware NI chassis is straightforward. and the RF components The probe (Mini-Circuitssignal, at the fundamental and Reactel frequency, diplexers is and separated from the second harmonic using another high power diplexer. The fundamental frequency power amplifier) are shown in Figures 10 and 11, respectively. passingPhotographs through theof the DUT NI is chassis measured and atthe port RF 3comp in Figureonents 11. (Mini-Circuits The output second and Reactel harmonic diplexers is measured and Thepowerat port receiver amplifier) 4. The hardwarespectrum are shown analyzer is in straightforward. Figures has an10 80-dBcand 11, dynamicrespectively. The probe range; signal, coupling at the this fundamentalwith the 80-dB frequency,of loss is separatedprovidedThe from receiver by the the secondhardware Reactel harmonic diplexer is straightforward. usingyields anothera system The highprobe dynamic power signal, range diplexer. at theof fundamentalover The 200-dBc, fundamental frequency, according frequency isto passingseparatedEquation through from (5). the However,the DUT second is measuredthe harmonic theore ticalatusing port 200-dBc another 3 in Figure dynamic high power11 .range The diplexer. output is unachievable, The second fundamental harmonic as in practice, frequency is measured the at portpassingsystem 4. The through would spectrum bethe noise DUT analyzer islimited measured hasbefore at an port200-dBc 80-dBc 3 in Figurecan dynamic be 11. achieved. The range; output The coupling second noise harmonicfloor this of with the is measuredreceiver the 80-dB is of loss providedatmeasured port 4. The by to thespectrumbe less Reactel than analyzer diplexer135 dBm. has yieldsWithan 80-dBc the a systemprobe dynamic signal dynamic range; measured coupling range to ofbe this overgreater with 200-dBc, thethan 80-dB 40 accordingdBm of loss and to Equationprovidedthe noise (5). However,byfloor the below Reactel the 135 diplexer theoreticaldBm, the yields system’s 200-dBc a system dynami dynamic dynamicc range range is range estimated is unachievable,of over to be 200-dBc, greater as thanaccording in practice,175 dB. to the Equation (5). However, the theoretical 200-dBc dynamic range is unachievable, as in practice, the system would be noise limited before 200-dBc can be achieved. The noise floor of the receiver is system would be noise limited before 200-dBc can be achieved. The noise floor of the receiver is measured to be less than 135 dBm. With the probe signal measured to be greater than 40 dBm and the measured to be less than 135 dBm. With the probe signal measured to be greater than 40 dBm and noisethe floor noise below floor135 below dBm, 135 thedBm, system’s the system’s dynamic dynami rangec range is estimated is estimated to to be be greater greater thanthan 175 dB. dB.

Figure 10. Photographs of the NI chassis with computer, signal generator, and spectrum analyzer.

Figure 10. Photographs of the NI chassis with computer, signal generator, and spectrum analyzer. Figure 10. Photographs of the NI chassis with computer, signal generator, and spectrum analyzer.

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Figure 11. Photograph of the diplexers and 10-W power amplifier.

5. System Test Results The high dynamic range measurement system described in Section 4 was used to measure the second harmonic response from a variety of circuit elements. The passive devices tested are shown in Figure 12.

Figure 11. Photograph of the diplexers and 10-W power amplifier. ampliﬁer. Figure 11. Photograph of the diplexers and 10-W power amplifier. 5. System Test Results 5. System Test Results The high dynamic range measurement system described in Section 4 was used to measure the The high dynamic range measurement system described in Section4 was used to measure the secondThe harmonic high dynamic response range from measurement a variety of systemcircuit elements.described Thein Section passive 4 deviceswas used tested to measure are shown the second harmonic response from a variety of circuit elements. The passive devices tested are shown in secondin Figure harmonic 12. response from a variety of circuit elements. The passive devices tested are shown Figurein Figure 12 .12.

Figure 12. Devices tested for second harmonic characterization.

The two port devices were tested for their input and output harmonic generation while the one- port devices could only be tested for their reflected harmonic generation. Test setups for the harmonic through and harmonic reflection measurements are shown in Figures 13 and 14, respectively. Since the spectrum analyzer only has one input port, the fundamental and second harmonic at the output of the DUT need to be measured via two separate measurements. Therefore, the loading conditions of the twoFigure measurements 12. Devices are tested slightly for second different. harmonic The spectrcharacterization.um analyzer is matched to 50 Ω Figure 12. Devices tested for second harmonic characterization. throughout the bandsFigure of interest 12. Devices with testedan input for secondreflection harmonic coefficient characterization. S11 of less than 20 dB, which The two port devices were tested for their input and output harmonic generation while the one- provides a 99% power transfer. The differences between the loading conditions for the fundamental port devicesThe two could port devicesonly be weretested tested for their for reflectedtheir input harmonic and output generation. harmonic Test generation setups for while the harmonic the one- and Thesecond two harmonic port devices measurements were tested is therefore for their inputexpected and to output be negligible harmonic compared generation to using while a 50 the Ω portthrough devices and couldharmonic only reflectionbe tested formeasurements their reflected ar harmonice shown in generation. Figures 13 Test and setups14, respectively. for the harmonic one-porttermination. devices Thus, could we believe only be that tested any for mismat their reﬂectedches between harmonic the two generation. measurement Test setupssetups forwould the throughSince and the harmonic spectrum reflection analyzer measurementsonly has one input are shown port, the in Figuresfundamental 13 and and 14, secondrespectively. harmonic at harmonicresult in an through insignificant and harmonic difference reﬂection in nonlinear measurements distortion are generated. shown in Figures 13 and 14, respectively. the outputSince theof the spectrum DUT need analyzer to be onlymeasured has one via input two separateport, the measurements.fundamental and Therefore, second harmonic the loading at theconditions output of thethe twoDUT measurements need to be measured are slightly via twodifferent. separate The measurements. spectrum analyzer Therefore, is matched the loading to 50 Ω conditions of the two measurements are slightly different. The spectrum analyzer is matched to 50 Ω throughout the bands of interest with an input reflection coefficient S11 of less than 20 dB, which throughout the bands of interest with an input reflection coefficient S of less than 20 dB, which provides a 99% power transfer. The differences between the loading conditions11 for the fundamental providesand second a 99% harmonic power measurements transfer. The differences is therefore between expected the to loadingbe negligible conditions compared for the to fundamentalusing a 50 Ω andtermination. second harmonic Thus, we measurements believe that any is therefore mismatches expected between to be the negligible two measurement compared to setups using woulda 50 Ω termination.result in an insignificant Thus, we believe difference that in any nonlinear mismat distortionches between generated. the two measurement setups would result in an insignificant difference in nonlinear distortion generated.

FigureFigure 13.13. TestTest setupsetup forfor harmonicharmonic throughthroughmeasurement. measurement.

Since the spectrum analyzer only has one input port, the fundamental and second harmonic at the output of the DUT need to be measured via two separate measurements. Therefore, the loading conditions of the two measurements are slightly different. The spectrum analyzer is matched to 50 Ω throughout the bands of interest with an input reﬂection coefﬁcient |S11| of less than 20 dB,

Figure 13. Test setup for harmonic through measurement. Figure 13. Test setup for harmonic through measurement.

Instruments 2018, 2, 16 12 of 16 which provides a 99% power transfer. The differences between the loading conditions for the fundamental and second harmonic measurements is therefore expected to be negligible compared to using a 50 Ω termination. Thus, we believe that any mismatches between the two measurement setups wouldInstruments result 2018 in, 3 an, x FOR insigniﬁcant PEER REVIEW difference in nonlinear distortion generated. 12 of 16

FigureFigure 14. 14.Test Test setup setup for for harmonic harmonic reﬂection reflection measurement. measurement.

The test results are summarized in Table 3. The values are shown for D in Equation (3), the The test results are summarized in Table3. The values are shown for D2 in Equation2 (3), the units forunits which for which are dBm are− 1dBm. A lower−1. A lower value, value, i.e., more i.e., more negative, negative, indicates indicates better better harmonic harmonic suppression. suppression.

TableTable 3. 3.Harmonic Harmonic generation generation results results from from various various passive passive devices devices shown shown in in Figure Figure 12 12..

Device D (dBm−1 −1) D (dBm−−11) Device D2,ref 2,(dBmref ) D2,through2,through (dBm ) OpenOpen circuit circuit −215.0−215.0 —— N(m)-N(m)N(m)-N(m) adaptor adaptor (new) (new) −210.0−210.0 −−210.0 MixerMixer −30.0−30.0 −−40.0 − − 10-dB10-dB attenuator attenuator 153.6−153.6 −155.4 Circulator (terminated in 50 Ω) −121.3 −104.0 CirculatorCirculator (open-circuited) (terminated in 50 Ω) −108.4−121.3 −104.0 — N(m)-SMA(f)Circulator adaptor(open-circuited) (old) −190.8−108.4 —— N(m)-SMA(f)Open SMA connector adaptor (old) −202.0−190.8 —— Open SMAOpen connector SMA connector with solder −196.5−202.0 —— Open SMA connector with solder and steel −174.9 — Open SMA connector with solder −196.5 — Open SMA connector with solder and steel −174.9 — The results from the open circuit and new N(m)-N(m) adaptor show the minimum detectable D2 coefficientThe results the from setup the can open measure. circuit The and open new circuitN(m)-N(m) and new adaptor adaptor show test the cases minimum are the detectable baseline measurements used for monitoring the spurs created at the second harmonic and the noise floor, D2 coefficient the setup can measure. The open circuit and new adaptor test cases are the baseline which determines the system dynamic range. Any significant contributions from the higher-order measurements used for monitoring the spurs created at the second harmonic and the noise floor, harmonics to the second harmonic would be indicated in this measurement. The observations from which determines the system dynamic range. Any significant contributions from the higher-order this measurement indicated that distortion created from these higher order harmonics are below the harmonics to the second harmonic would be indicated in this measurement. The observations from noise floor. this measurement indicated that distortion created from these higher order harmonics are below the Since a mixer, by design, is a nonlinear component whose nonlinearity is essential for frequency noise floor. conversion [52], it shows much higher D values. Attenuators typically consist of resistors connected Since a mixer, by design, is a nonlinear2 component whose nonlinearity is essential for frequency in T- or Π-configurations with dissimilar metal contacts, which results in D values of about 60 dB conversion [52], it shows much higher D values. Attenuators typica2lly consist of resistors higher than the detection floor. The intense RF2 magnetic field across the ferrite disk excites nonlinear behaviorconnected in ain circulator T- or Π-configurations [53], which explains with dissimilar its higher values.metal contacts, The old, which i.e., well-used, results in adaptor D2 values shows of aboutabout 20-dB 60 dB increase higher inthanD2 comparedthe detection to the floor. new The adaptor, intense which RF maymagnetic be ascribed field across to possible the ferrite corrosion disk causedexcites bynonlinear wear and behavior tear and in environmental a circulator [53], effects. which Connectors explains terminatedits higher values. in solder The and old, steel i.e., show well- higherused, adaptorD2 values shows compared about to 20-dB the unterminated increase in D connector2 compared due to thethe effectnew adaptor, of the dissimilar which may metal be contacts,ascribed withto possible steel adding corrosion about caused a 20-dB by higher wear value, and consistenttear and withenvironmental the results effects. reported Connectors in [54,55]. The mixer serves as a reference for traditionally nonlinear devices. Table3 shows that the nonlinear terminated in solder and steel show higher D2 values compared to the unterminated connector due response from the mixer is about 90 dB over the circulator, about 120 dB over the attenuator, and about to the effect of the dissimilar metal contacts, with steel adding about a 20-dB higher value, consistent 145–170 dB over the adaptors, at an input of 0 dBm. with the results reported in [54,55]. The mixer serves as a reference for traditionally nonlinear devices. Table 3 shows that the nonlinear response from the mixer is about 90 dB over the circulator, about 120 dB over the attenuator, and about 145–170 dB over the adaptors, at an input of 0 dBm.

Instruments 2018, 2, 16 13 of 16

6. Conclusions As the frequency spectrum gets more crowded and the demand for wireless communication increases, nonlinear distortions generated by passive elements become more relevant. Commercially-available nonlinear measurement systems are expensive and either lack the dynamic range needed to make the sensitive measurements or are fixed in frequency and do not provide the flexibility required. Robust feed-forward systems have been constructed that provide both the ﬂexibility and dynamic range needed to made the sensitive measurements, but these systems are complex and require iterative tuning and optimization algorithms. This paper has presented an alternate method for characterizing nonlinear distortion from weakly nonlinear devices. The alternate method uses absorptive diplexers to separate the harmonic response from the high power probe signal, thus increasing the system’s dynamic range. The method is also capable of measuring the reﬂected harmonic from devices. The method is relatively simple to implement and it is cost effective for measuring weak nonlinear responses of circuit elements. This paper has presented an implementation of this method with the capability of achieving 175-dBc dynamic range over a 22% bandwidth. The system is capable of producing over 10 W (+40 dBm) of probe signal power while measuring second harmonics generated by a DUT as low as −135 dBm, resulting in the 175 dBc dynamic range. This paper has outlined system requirements that dictate the dynamic range of the harmonic measurement system and provided guidance to achieve the required dynamic range. Results are presented on passive RF circuit elements that are not traditionally thought to exhibit nonlinearities, which require a high dynamic range, nonlinear measurement system.

Author Contributions: All authors equally conceived and designed the experiments; R.M.N. and K.A.G. performed the experiments; G.J.M. and A.F.M. provided the theoretical support; K.D.S. contributed the logistics and measurement facilities; all authors analyzed the data; R.M.N. wrote the first draft of the paper, and all authors contributed to its final form. Funding: This research was supported by U.S. Army Research Office (ARO) contract #W911NF-12-1-0305 through a subcontract from Delaware State University (DSU). Conflicts of Interest: The authors declare no conflict of interest. The funding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

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