Passive intermodulation in printed lines: effects of trace dimensions and substrate

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Published in IET Microwaves, Antennas & PropagationReceived on 12th December 2007Revised on 1st June 2008doi: 10.1049/iet-map:20070314

ISSN 1751-8725

Passive intermodulation in printed lines:effects of trace dimensions and substrateA.P. Shitvov D.E. Zelenchuk A.G. Schuchinsky V.F. FuscoThe Institute of Electronics, Communications and Information Technology (ECIT), Northern Ireland Science Park,Queen’s University of Belfast, Queen’s Road, Queen’s Island, BT3 9DT Belfast, Northern Ireland, UKE-mail: [email protected]

Abstract: A comprehensive experimental study was performed to identify and discriminate mechanismscontributing to passive intermodulation (PIM) in microstrip transmission lines. The effects of strip length andwidth, and substrate materials on PIM performance of printed lines were investigated in the GSM900,DCS1800 and UMTS frequency bands. The major features of the experiment design, sample preparation andtest setup are discussed in detail. The measurement results have demonstrated that the PIM levelcumulatively grows on the longer microstrip lines and decreases on wider strips and, thus, indicated that thedistributed resistive nonlinearity of the printed traces represents the dominant mechanism of intermodulationgeneration in the printed lines on PTFE-based substrates.

1 IntroductionPrinted circuit boards (PCBs) constitute the backbone ofmost telecommunication equipment. The signal integrityand electromagnetic compatibility of the PCB-baseddevices impose increasingly stringent requirements toPCB performance and pose particular challenges in high-power applications such as printed antennas, filters andinterconnects [1].

Passive intermodulation (PIM) in printed circuits hasmajor detrimental effects leading to deleteriouselectromagnetic interference in wireless communicationssystems. Despite the growing demand for effective meansof mitigating PIM generation in PCBs, the mechanismsunderlying this phenomenon are still barely understood andare scarcely addressed in the technical literature.

Recent studies [2–5] have revealed some correlationbetween the properties of PCB materials and measuredPIM products. At the same time, they have alsodemonstrated that the PIM performance of printed traceswas extremely sensitive to the measurement techniques andfabrication processes. Moreover, the results of the PIMmeasurements presented in the literature were often

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inconsistent, for example, the correlation between carrierattenuation and the PIM level reported in [2] was notobserved in [3].

Nevertheless, certain interrelations between laminateconstruction and the PIM performance of processed PCBhave been empirically identified [5]. In particular, the effectof the copper cladding and the surface bonding layer onPIM performance has been observed along with the effectof walls of etched traces [2, 4]. However, the role of thetrace shape and laminate composition in PIM productionhas received no consistent interpretation so far, mostlybecause of lack of the pertinent experimental data on PIMgeneration in PCB materials.

To address these issues and gain insight into the origins ofPIM production in PCB materials, it is essential to performsystematic and repeatable PIM measurements on thecanonical printed structures, which are adequately describedby the predictive phenomenological models. Therefore theobjective of this study was to set up the targeted experiments,which could allow us to measure PIM products on themicrostrip lines and juxtapose the obtained experimental datawith the characteristics inferred from the nonlineartransmission line (NTL) model [6, 7].

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In this paper, we present the results of the firstcomprehensive experimental study of third-order PIM(PIM3) generation on microstrip lines specially designedand manufactured in order to identify and separate theindividual contributions of the material and geometricalparameters to PIM performance of PCB. The main featuresof the PIM characterisation of PCB materials, the test setupand data analysis are presented in Section 2. In Section 3,the results of the PIM measurements are discussed, and themain findings are summarised in the Conclusions. Theprincipal aspects of the NTL model used for interpretationof the PIM measurements are summarised in Appendix.

2 Design of experiments2.1 Measurement setup

The test setup is based on a commercial SummitekInstruments PIM analyser [8]. Three different models:SI-900B, SI-1800B and SI-2000B(E), have been used forthe measurements in the GSM900, DCS1800 and UMTSfrequency bands as detailed in Table 1. The analyser feeds atwo-tone signal (two continuous wave carriers) into thedevice under test (DUT), and monitors levels of the forwardPIM products at the DUT output port and the reverse PIMproducts at the DUT input port in the respective bands ofthe instrument receiver. Magnitude of the forward andreverse PIM3 products (PIM3) is measured either at a spotfrequency or in a frequency sweep of one tone at a time. Inthe latter case, the PIM3 frequency fIM3 ¼ 2f1 2 f2 ( f1 , f2)is swept in the bands specified in Table 1 as follows:

1. The carrier frequency f1 is fixed at its lowest value, and f2 isswept downward from its maximum value (referred to as‘DOWN’ sweep).

2. The carrier frequency f2 is fixed at its maximum value, andf1 is swept upward from its lowest value (referred to as ‘UP’sweep).

To ensure a meaningful comparison of test specimens, thefull test setup is first calibrated for the residual PIM3 levelwithout a DUT. This provides a reference PIM3 level of thetest instrument together with the cable assemblies. Themeasurement uncertainty has been assessed by repeating

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the tests after disconnecting and reconnecting the DUTthree to five times and then averaging the measurementresults over the swept frequency band and a series ofreconnections. This allows us to reduce the effect ofintrinsic noise in the test setup itself, which could becommensurate with the measured PIM3 level in high-quality (low PIM) PCB laminates. Therefore the meanvalues of the measured PIM3 are adopted in this paperas the representative quantities for characterisation ofspecimen performance. The viability of such an approach issupported by the following observations:

i. The PIM3 levels at spot frequencies demonstrated timevariations whereas their median consistently remainedwithin narrow margins.

ii. Frequency dependencies of PIM3 magnitude exhibitedrandom kinks, especially, the reverse PIM3 response. Thesecould be caused by occasional minor changes in the sampleassembly or drift of the instantaneous residual PIM3 level.Such adverse effects of the instrumental instabilities weregrossly eliminated by averaging.

Finally, it is important to note that the instrumentuncertainties strongly affect measurement data at the levelclose to the residual PIM level [8]. However, our extensivetests have shown that even near the analyser sensitivityfloor, where the instantaneous PIM3 level has greatervariations, the PIM3 median consistently demonstrates thedistinctive signatures of PIM products in the test specimens.

2.2 Sample design and preparation

The board layouts with the microstrip line specimens usedin the experiments are shown in Fig. 1, and the parametersof the respective PCB materials are listed in Table 2. Thetest samples were specially designed to explore the effectsof trace geometry and substrate material composition onPIM3 generation. To reduce sensitivity of the test results tomanufacturing factors and tolerances, two to three replicasof each board were fabricated simultaneously. Thefollowing microstrip line specimens were manufactured andtested:

Table 1 Frequency bands of carriers and PIM3 products

PIM analyser Frequency band Frequency sweep f1, MHz f2, MHz fIM3, MHz

SI-900B GSM900DOWN 935 960–955 910–915

UP 935–937.4 960 910–914.8

SI-1800B DCS1800DOWN 1832–1805 1880 1784–1730

UP 1805 1880–1825 1730–1785

SI-2000B(E) UMTSDOWN 2110 2170–2160 2050–2060

UP 2110–2115 2170 2050–2060

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i. Uniform straight and meandered 50 V lines of severallengths (Board 1 with the layout shown in Fig. 1a).

ii. Straight lines of different widths combined with the six-section Klopfenstein tapered transformers providing theimpedance matching between the central sections and 50 V

Figure 1 Plan view of the microstrip lines on the boardsspecified in Table 2

a Layout of Board 1 – uniform straight and meandered microstriplines of different lengths (width of all traces is 4.32 mm): 100 mm(TL1), 300 mm (TL2), 500 mm (TL3), 917 mm (TL4), 1828 mm (TL5),2736 mm (TL6); other dimensions: W1 ¼ 41.4 mm,W2 ¼ 82.7 mm, L1 ¼ 72.1 mm, L2 ¼ 318 mm, L3 ¼ 132.9 mm,L4 ¼ 45.7 mm, L5 ¼ 40.6 mmb Layout of Boards 2 and 3 with microstrip lines of differentwidths: W1 ¼ 2.29 mm, W2 ¼ 9.14 mm, W3 ¼ 13.46 mm,W4 ¼ 4.32 mm; length of the uniform central sections:LC ¼ 522 mm; lengths of the tapered sections: LT1 ¼ 164.8 mm,LT2 ¼ 169.6 mm, LT3 ¼ 186.7 mm; full length of the trace:L ¼ 914 mm; distance between traces: W5 ¼ 87 mm; distancefrom the edge: W6 ¼ 43.5 mmc Layout of Boards 4 – 9 with straight uniform 50 V microstriplines of length L ¼ 914 mm on different substrates; thesubstrate parameters and the respective strip widths W1 foreach material are given in Table 2; distance between traces:W2 ¼ 87 mm; distance from the edge: W3 ¼ 43.5 mm

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input/output ports (Boards 2 and 3 with the layout shownin Fig. 1b).

iii. Straight uniform 50 V microstrip lines on the substrateswith different laminate compositions (Boards 4–9 specifiedin Table 2 with the trace layouts shown in Fig. 1c).

Note that the Boards 1–3 are made of the same laminatematerial, see Table 2.

The PIM measurement data available from the PCBmanufacturers and end-users often showed significantvariations of PIM3 performance of printed lines despitetheir substrate materials having identical specifications,[4, 5]. To minimise uncertainties caused by the different rawmaterials in PCB laminates and fabrication techniques, ourspecimens were produced in strictly controlledmanufacturing processes. Namely, Boards 1–3 and 9 havethe same laminate composition and copper claddingbut different thickness. The same grade of low-profilereverse-treated copper foil of thickness 35 mm withmetallic zinc-free anti-tarnish coating was used for coppercladding of all laminates except Board 4. The foil used inBoard 4 had the same thickness but came from a differentsupplier. To prevent environmental contamination of theexposed copper surfaces, all conductors were coated by a1 mm thick immersion tin. According to [9], such aprotective layer provides low PIM finishing of the printedtraces. The specimens were manufactured by the samecommercial PCB processing house and produced in threeseparate batches: (i) Boards 1 (ii) Boards 2 and 3 and (iii)Boards 4–9.

2.3 Microstrip launchers

The low-PIM launchers represent the critical elements of thetest setup employed for evaluation of PIM performance ofPCB laminates. It was shown experimentally in [10] and iscorroborated experimentally in Section 3.4 below that input/output matching of the printed microstrip lines has asignificant impact on the measured PIM3 response of thetransmission lines. Therefore high-quality coaxial-to-microstrip transitions are required to reduce theinhomogeneity of the power distribution along the traces,which is caused by standing waves in the mismatched lines.The board launchers have been specially designed for ourexperiments to provide the reflection coefficient less than220 dB over a wide frequency range (broadband matching isnecessary for testing the same specimens in the differentfrequency bands).

To examine the effect of the launchers on the PIM3generation, the straight uniform microstrip lines on Boards4–7 were equipped with two types of coaxial-to-microstriptransitions shown in Fig. 2:

i. Cable launchers, Fig. 2a, were made from the PIM3certified connectorised cable assemblies, which comprised

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Table 2 Boards specifications and the material parameters

Boardnumber

Dielectric composition Thickness,mm

Relativepermittivity

Losstangent

Strip width of 50 V

line, mm

1–3 PTFE/woven glass 1.58 2.5a 0.0019a 4.32

4b Cured resin-impregnated woven glass 0.76 3.00a 0.0034a 1.9

5 PTFE/woven glass 0.76 3.00a 0.0030a 1.9

6 BT epoxy/ceramic/woven glass 0.76 3.00a 0.0026a 1.9

7 PTFE/ceramic/woven glass 0.76 3.00c 0.0014c 1.9

8 PTFE/woven glass 0.76 2.17a 0.0009a 2.3

9d PTFE/woven glassd 0.76 2.5d 0.0019d 2.11

aMeasured at 10 GHz bDifferent supplier of raw copper foil and laminate cMeasured at 1.9 GHz dBoards 1-3 and 9 havesimilar laminate composition

6.35 mm semi-rigid coaxial cable of length 250 mm andDIN 7/16 flange-mount connectors. The cable assemblieswere cut in the middle and each half was fitted at the PCBedges using the newly designed coaxial-to-microstripadaptors (see the encircled item in Fig. 2a).

ii. DIN 7/16 edge-mount connectors were attached directlyat the PCB edges; see Fig. 2b. The measurement results inFig. 2c demonstrate that the cable launchers exhibit aconsiderably lower reflection coefficient than the edge-mount connectors: less than 225 dB in the GSM900frequency band and 220 dB in the DCS1800 and UMTSbands.

Figure 2 Microstrip launchers

a Cable launcherb DIN 7/16 edge-mount connectorc Input reflection coefficient of the cable launchers andconnectors, measured on Board 6, and the original cableassembly used for making the cable launchers

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Finally, it is important to note that this study was carriedout on high-performance PCB materials certified bymanufacturers for low-PIM applications. Consequently,PIM characterisation of such materials poses an enormouschallenge because of the limited sensitivity of the availablePIM analysers (typically 2125 dBm over 90% of theintermodulation frequency band), and the difficulties inseparating PIM products generated by the printed tracesand the test fixture including launchers/connectors.Nonetheless, the results presented in Section 3 demonstratethat the experimental approach described here provides aconsistent and reliable means for evaluation of PIMperformance of a broad range of PCB materials.

3 Experimental results anddiscussionThe test specimens described in Section 2 have beendesigned for the targeted experiments, which are aimed atidentification of the PIM generation mechanisms inmicrostrip lines and discrimination of the effects of tracegeometry and the substrate material on PIM performanceof PCB laminates.

All measurements were performed in a screened anechoicchamber to exclude interference from external sources.After each reconnection of the specimen, the integrity ofthe whole assembly was checked by tapping the joints andthe board to ensure that there were no mechanical faults orloose connectors, which could alter PIM response of theDUT. Occasionally during the tests, we observed a drift ofcarrier(s) power that led the PIM3 magnitude of the DUTto fall below the initial residual level. Such instances weretreated as random errors of the instrument and wereincluded in the estimations of the measurement uncertainty.

3.1 Cumulative effect

Distributed weak nonlinearity of the printed traces has beenassumed as a primary source of PIM generation in microstrip

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lines on low-loss substrates. The NTL model [7] with thecurrent-driven nonlinear resistivity defined by (1) inAppendix predicted cumulative growth of the forward PIM3

with line length. To investigate this phenomenonexperimentally, PIM3 level on the uniform 50 V microstriplines of several different lengths was measured first.Magnitude of the forward PIM3 on the microstrip traces ofBoard 1 (Fig. 1a) is shown in Fig. 3 for the ‘DOWN’frequency sweep in the DCS1800 band. The plottedexperimental points represent mean values in the sweptfrequency band (1730–1784 MHz), and the error barsdelimit the maximum PIM3 deviations in the series ofreconnections.

Fig. 3 demonstrates that forward PIM3 monotonicallygrows on the longer traces, and the measurement resultscorrelate well with the NTL model prediction based on (2).The measurement results of the same lines for theGSM900 band were reported earlier in [11] and alsoexhibited a general trend of higher forward PIM3 on longertraces. In the ‘UP’ frequency sweep, Table 1, the forwardPIM3 level exhibits the same qualitative trend, although itsmagnitude differs slightly. This discrepancy is attributed todissimilar matching conditions in the ‘UP’ and ‘DOWN’sweeps of the respective carrier frequencies (Fig. 2c). It isnoteworthy that despite a steady increase of the forwardPIM3 with line length in Fig. 3, it does not growindefinitely. According to the NTL model, whenattenuation of the carriers on sufficiently long lines exceedsthe rate of PIM3 generation, forward PIM3 starts to decay(2). This phenomenon was also observed in the theory oftravelling-wave harmonic generators [12].

In contrast to the forward PIM3, the reverse PIM3 levelshowed no consistent increase on longer lines, and its levelremained below the forward PIM3. These observations areconsistent with the NTL model predictions and suggestthat the reverse PIM products are predominantly formed

Figure 3 Forward PIM3 against the line length measured onBoard 1 (squares) in the DCS1800 band (‘DOWN’ sweep) atcarriers’ power 2 � 43 dBm and the NTL model simulationsat 1730 MHz (triangles)

Error bars delimit the maximum PIM3 deviations in the series ofreconnections

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near the input port of the matched microstrip line.This effect can also be attributed to the phase matching ina nonlinear mixing process [13].

Thus, the presented results of PIM3 measurements onmicrostrip lines of different lengths provide conclusiveevidences of the cumulative growth of PIM3 products onprinted lines [2, 14] and support the phenomenology of theNTL model with distributed nonlinearity.

3.2 Effect of strip width

The effect of strip width on PIM3 product generation isdifficult to assess independently because it is accompaniedby the line mismatch, which is caused by the change of theline impedance. Two approaches have been used toinvestigate this effect:

i. Substrates with modified parameters to compensate for thestrip width variations and maintain the line impedance at the50 V [3].

ii. Impedance transformers integrated with lines of differentwidths on the same substrate to provide matching to 50 V

input and output ports (Fig. 1b).

The latter configuration has been adopted in this workbecause it allows the direct comparison of the lines ofseveral different widths on a single board (Fig. 1b) and,thus, excludes additional uncertainty incurred by dissimilarsubstrates. The shortcoming of this arrangement is that thematching transformers may also contribute to PIM3generation and somewhat obscure the effect of the linewidth as detailed below.

The results of forward PIM3 measurements in theGSM900 frequency band are shown in Fig. 4 for thematched microstrip lines of several widths fabricated on

Figure 4 Forward PIM3 against microstrip line widthmeasured on Boards 2 and 3 (squares) in the GSM900band (‘UP’ sweep) at carriers’ power 2 � 43 dBm, and theNTL model simulations at 910 MHz (triangles)

Error bars delimit the maximum PIM3 deviations within each groupof the specimens with the same strip width


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Boards 2 and 3 (see the layout in Fig. 1b). The data points inFig. 4 represent quantities averaged over the frequency band,the sample line triplets and a series of reconnections (theresidual forward PIM3 level was below 2120.4 dBm). Errorbars delimit the maximum PIM3 deviations within eachgroup of specimens with the same strip width.

The PIM3 magnitude in Fig. 4 exhibits a monotonicdecrease with strip width that can be attributed to lowercurrent density on wider traces with nonlinear resistivitydefined by (1). A similar effect was also observed in [3] formicrostrip lines with different substrates. Theseexperimental results are consistent with NTL modelpredictions and, hence, provide an independentconfirmation that the current-driven distributed nonlinearresistivity of printed traces represents the dominantmechanism of PIM3 generation in microstrip lines onPTFE/woven glass substrates.

It is noteworthy that the forward PIM3 magnitudemeasured on 917 mm long uniform microstrip lines onBoards 2 and 3 is higher than on Board 1, Figs. 3 and 4.The only difference between these two groups of specimensis that they were manufactured in separate batches. Thisfact demonstrates once again that PIM performance ofprinted lines is highly sensitive to the laminate materialsand fabrication process.

The reverse PIM3 level has shown little correlation with thestrip width. Apparently, this implies that weakly reflectingmatching transformers make a dominant contribution tothe reverse PIM3. This conclusion is consistent with theobservations in Section 3.1 that the reverse PIM3 level ispredominantly determined by the line section near theinput port of the matched microstrip line, and that evensmall reflections can noticeably affect the reverse PIM3 [11].This is why impedance matching transformers maycompletely disguise the effect of the trace width on thereverse PIM3 level.

It is necessary to note that PIM3 measurements on thetraces of different widths have shown higher sensitivity tofabrication tolerances and workmanship, which causehigher measurement uncertainties, Fig. 3. Nevertheless, theobtained experimental results consistently demonstrate thequalitative trend of a lower forward PIM3 on microstriplines with wider traces. These results provide furtherevidence of PIM generation on Boards 1–3 by the current-driven distributed nonlinearity of printed traces (Appendix).

3.3 Effect of dielectric substrate

The effect of the dielectric substrate on PIM3 generation inthe GSM900 frequency band had been first considered in[11]. In this section, the study is substantially extended toinclude other frequency bands and different materials andto investigate, particularly, the relationship between thedielectric substrate loss and PIM3 level.


To evaluate the effect of laminate composition on PIM3performance of PCB, straight uniform 50 V microstrip lineswere fabricated on Boards 4–9 (Fig. 1c), whose parametersare given in Table 2 (manufacturers’ specifications). Theinsertion loss in each line was measured first at frequencies910, 1730 and 2050 MHz and is plotted against thesubstrate loss tangent in Fig. 5a (zero loss tangentcorresponds to the typical cable assembly used for making thecable launchers). The results of forward PIM3 measurementsin the GSM900, DCS1800 and UMTS bands are shown inFig. 5b. The experimental points represent mean values inthe respective frequency bands averaged over the sampletriplets. The value at 0 loss tangent corresponds to theresidual forward PIM3 of the PIM analyser with the test fixture.

Although a general trend of increased PIM production onthe boards with higher permittivity and loss tangent can beinferred from Fig. 5, no consistent correlation between thePIM3 level and the substrate loss has been observed. Indeed,comparison of the linear insertion loss in Fig. 5a and PIM3

level in Fig. 5b shows that although insertion loss growswith loss tangent, PIM3 magnitude does not follow thesame trend. This implies that for tested laminates,dielectric loss represents a second-order effect on PIM3

Figure 5 Insertion loss and forward PIM3 against thesubstrate loss tangents specified in Table 2

a Insertion loss at fIM3 frequencies of 910 MHz (GSM900, circles),1730 MHz (DCS1800, squares) and 2050 MHz (UMTS, triangles)b Forward PIM3 at carriers’ power 2 � 43 dBm in GSM900(circles), DCS1800 (squares) and UMTS (triangles) frequency bands

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generation when compared with the nonlinear resistivity ofprinted traces. Apparently, various ingredients of thelaminate composition such as glass reinforcement, bondinglayers, impregnation and others affect the PIM3 levelthrough both nonlinearity of the substrate itself and thelinear attenuation of carriers caused by the dielectric loss(2). However, individual contributions of these twomechanisms can hardly be separated in our two-portmeasurements.

The results of PIM3 measurements at fIM3 ¼ 910 MHz onBoards 5, 8 and 9 with similar laminate composition(Table 2) are summarised in Table 3. In contrast to othersubstrates, these laminates are composed of PTFE andwoven glass only and do not contain any additives. Theirmain differences consist in the grade of glass reinforcementand bonding layers. However, despite the similarity of thelaminate construction and the constituent materials used,no explicit correlation between the forward PIM3 level andsubstrate permittivity or loss tangent has been observed.The level of the reverse PIM3 also remains practicallyunchanged (note that the reverse PIM3 level in Table 3 iscommensurate with the background PIM3 of the entire testsetup whose sensitivity floor is limited not only by thereverse residual PIM3 of the instrument itself (measuredat 2132 dBm) but also by the test fixture, cable launchers

Table 3 PIM3 against dielectric substrate parametersmeasured at fIM3 ¼ 910 MHz and carriers’ power 2 � 43 dBm

Boardnumber

Relativepermittivity

Losstangent

Forward‘UP’PIM3,dBm

Reverse‘UP’PIM3,dBm

8 2.17 0.0009 2104.8 2122.3

9 2.5 0.0019 2115.7 2126.2

5 3.0 0.0030 297.7 2126.5

Table 4 Forward and reverse PIM3 (dBm) on the Boards4–7 with the cable launchers and DIN 7/16 edge-mountconnectors; the measurement results for the UMTS bandat carriers’ power 2 � 43 dBm

Boardnumber

Cable launchers DIN 7/16 edge-mount connectors

ForwardPIM3

ReversePIM3

ForwardPIM3

ReversePIM3

4 283.2 298 282.1 286.1

5 291.8 2108.7 290.2 295

6 284.4 2104.4 285.8 299.1

7 294.8 2102.5 289.9 291.5

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and connectors). Then, taking into account that the samecopper cladding was used in all these specimens, we caninfer that the observed differences in PIM3 performance ofthe tested laminates are inflicted by the weak intrinsicnonlinearity of dielectric substrates. This phenomenonrequires further experimental and theoretical investigationsand will be addressed elsewhere.

3.4 Effect of impedance matching

The effect of impedance matching on PIM3 generation bymicrostrip lines has been evaluated with two types ofmicrostrip launchers shown in Fig. 2: cable launchers andedge-mount connectors. The results of PIM3 measurementsin the UMTS band are summarised in Table 4 anddemonstrate that regardless of the board type, thespecimens with edge-mount connectors typically exhibitreverse PIM3 of an order �5–10 dB higher than sampleswith cable launchers. The forward PIM3 remains nearly atthe same level for both types of launchers, being primarilydetermined by the properties of the substrate and traces.The observed effect of impedance mismatch on PIM3 isfully consistent with the simulation results [10] obtainedfrom the NTL with distributed nonlinear resistivity.

Indeed, according to [10], the load mismatch more stronglyaffects the reverse PIM3 level than the forward PIM3, whereasthe reverse PIM3 level remains always lower than the forwardPIM3. This is exactly what has been observed in all ourmeasurements, and it is also consistent with the measurementresults discussed in Section 2.3. Thus, we can infer fromthese experimental observations that high quality matching isa prerequisite for reliable and consistent evaluation of PIM3performance of printed circuits and PCB materials.

4 ConclusionsThe targeted experiments have been carried out to identify themechanisms of PIM generation on printed microstrip lines andto elucidate the effects of the trace geometry and materialparameters on PIM3 performance of PCB laminates. Toensure the integrity of the measurements, the microstrip lineswere thoroughly designed and fabricated using controlledmanufacturing processes. Special cable launchers with a lowreflection coefficient (less than 220 dB) over a broadfrequency band have been designed to provide the highquality impedance matching of the specimens with the testinstruments. In the measurement trials, the effects of striplength and width, substrate material and launchers on PIM3generation in microstrip lines have been explored. The mainfindings can be summarised as follows:

i. The magnitude of the forward PIM3 monotonically increaseswith line length, thus providing explicit evidences of thecumulative growth of the PIM3 products along the linecaused by the distributed nonlinearity of the printed traces.

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ii. The reverse PIM3 level is lower than the forward PIM3 onthe matched lines and shows no direct correlation with linelength; however, the reverse PIM3 is more strongly affectedby the impedance mismatch.

iii. The average magnitudes of the forward PIM3, measuredon Boards 2 and 3, exhibit a monotonic decrease with linewidth; this observation along with the cumulative growthof PIM products suggest that the current-driven distributednonlinearity of microstrip traces represents the dominantmechanism of PIM generation on printed lines.

iv. For tested PCB laminates, no obvious correlation hasbeen observed between the measured PIM3 level and thepermittivity, loss tangent and composition of the substrates;these results indicate that nonlinearity of the PTFE-basedsubstrates represents a second-order effect when comparedwith nonlinear resistivity of the printed traces.

v. Input/output matching significantly affects the generationof the reverse PIM3, namely, edge-mount connectors typicallyexhibit the reverse PIM3 level of �5–10 dB higher than cablelaunchers, whereas the level of forward PIM3 remains nearlythe same for both the types of launchers.

The study of PIM generation on printed lines presented inthe paper is based on measurements, which involved multiplesamples of different lengths and shapes. Alternatively, near-field probing can be employed to map PIM productdistributions on printed traces. This approach has recentlybeen implemented in [15] and has independently confirmedthe cumulative growth of the forward PIM3 level onmicrostrip lines. However, it is necessary to note that near-field probing on low-PIM laminates and short transmissionlines is constrained by the sensitivity floor of the PIManalysers and the requirement of a weak coupling of theprobe (typically less than 235 dB). Thus, the two-port PIMmeasurements used in this paper currently represent the onlypractical way for characterisation of the high performancePCB materials with low intrinsic nonlinearity.

5 AcknowledgmentThe authors are grateful to Taconic Advanced DielectricDivision Ltd., Trackwise Designs Ltd., Racal AntennasLtd., PCTEL Inc. and Castle Microwave Ltd. for theirgenerous help with the preparation of the test samples andproviding measurement facilities. Special thanks to Mr. JimFrancey for numerous discussions and support. The authorsappreciate the suggestions made by Dr. David Linton overthe period of this work.

6 References

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[2] SCHUCHINSKY A.G., FRANCEY J., FUSCO V.F.: ‘Distributedsources of passive intermodulation on printed lines’.Proc. 2005 IEEE Antennas and Propagation Society Int.Symp., Washington, DC, USA, July 2005, vol. 4B,pp. 447–450

[3] KUGA N., TAKAO T.: ‘Passive intermodulation evaluation ofprinted circuit board by using 50 V microstrip line’. Proc.Asia Pacific Microwave Conf. (APMC 2004), New Delhi,India, December 2004

[4] EL BANNA B.: ‘Passive intermodulation from printedcircuit boards’. Technical Report D1200002735,Powerwave Technologies, Inc., Sweden, June 2006

[5] FRANCEY J.: ‘Passive intermodulation study’ TechnicalReport, Taconic ADD, 2003, http://www.taconic-add.com,accessed April 2008

[6] SHITVOV A.P., ZELENCHUK D.E., SCHUCHINSKY A.G.: ‘Distributedmodel of passive intermodulation phenomena inprinted transmission lines’. Proc. 13th Int. StudentSeminar on Microwave Applications of NovelPhysical Phenomena, Rovaniemi, Finland, August 2006,pp. 61–63

[7] ZELENCHUK D.E., SHITVOV A.P., SCHUCHINSKY A.G., OLSSON T.:‘Passive intermodulation on microstrip lines’. Proc. 37thEuropean Microwave Conf. (EuMC’07), Munich, Germany,October 2007, pp. 396–399

[8] Passive intermodulation distortion analyzer:‘Operating and maintenance manual’. SummitekInstruments, Part Number 1902000, Rev. C, June 2004 edn.

[9] PEREZ J.V.S., ROMERO F.G., RONNOW D., SODERBARG A., OLSSON T.:‘A micro-strip passive inter-modulation test set-up;comparison of leaded and lead-free solders andconductor finishing’. Proc. 5th Int. Workshop onMultipactor, Corona and Passive Intermodulation in SpaceRF Hardware (MULCOPIM 2005), Noordwijk, TheNetherlands, 2005, pp. 215–222

[10] ZELENCHUK D.E., SHITVOV A.P., SCHUCHINSKY A.G.: ‘Effect ofmatching on passive intermodulation in transmission lineswith distributed nonlinear resistance’. Proc. Int. URSICommission B – Electromagnetic Theory Symp.(EMTS 2007), Ottawa, ON, Canada, July 2007, R19-39,EMTS171

[11] ZELENCHUK D.E., SHITVOV A.P., SCHUCHINSKY A.G.: ‘Effect oflaminate properties on passive intermodulationgeneration’. Proc. Loughborough Antennas and Prop.Conf. (LAPC 2007), Loughborough, UK, April 2007,pp. 169–172

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[12] AULD B.A., DIDOMENICO M. JR., PANTELL R.H.: ‘Traveling-waveharmonic generation along nonlinear transmission lines’,J. Appl. Phys., 1962, 33, (12), pp. 3537–3545

[13] SHITVOV A.P., ZELENCHUK D.E., SCHUCHINSKY A.G.: ‘Experimentalobservations of distributed nonlinearity in printed lines’.Proc. 14th Int. Student Seminar on Microwave andOptical Applications of Novel Physical Phenomena,Belfast, UK, 2007, pp. 70–73

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[16] SERON D., COLLADO C., MATEU J., O’CALLAGHAN J.M.: ‘Analysisand simulation of distributed nonlinearities inferroelectrics and superconductors for microwaveapplications’, IEEE Trans. Microw. Theory Tech., 2006, 54,(3), pp. 1154–1160

[17] DAHM T., SCALAPINO D.J.: ‘Theory of intermodulation insuperconducting microstrip resonator’, J. Appl. Phys.,1997, 81, (4), pp. 2002–2009

[18] ILYNSKY A.S., SLEPYAN G.Y., SLEPYAN A.Y.: ‘Propagation,scattering and dissipation of electromagnetic waves’(Peter Peregrinus Ltd., London, 1993)

7 AppendixA phenomenological model of PIM3 generation in printedtransmission lines with a weak distributed nonlinearity [6,7] is used to interpret the measurement results. Thecurrent-driven per-unit-length nonlinear resistance is

The Institution of Engineering and Technology 2009

defined similar to [16, 17]

R ¼ R 0 þ R2I 2¼ r0

ÐJ 2 dsÐ

J ds� �2

þ r2

ÐJ 4 dsÐ

J ds� �4

I 2;

R0 .. R2I 2 (1)

where R0 is the linear resistance and R2 the nonlinearresistance; J is the surface current density on theinfinitesimally thin imperfect conductors, [18]; r0 and r2

are the macroscopic linear and nonlinear resistivities,respectively. The macroscopic nonlinear resistivity r2 is themodel parameter, which is retrieved from the experimentaldata.

The solution of the nonlinear telegrapher’s equations forthe perfectly matched segment of the transmission line offinite length l gives the following expression for the currentdistribution along the line at the PIM3 frequency fIM3 [7]

IIM3(x) ¼ R2j [�(1þ n) exp (�gIM3x)þ exp (�(2g1 � g2)x)

þ n exp (�gIM3(2l � x)� 2al )] (2)

where g1,2,IM3 ¼ ib1,2,IM3þ a are the complex wavenumbersat the frequencies of carriers f1,2 and of the intermodulationproduct fIM3; j ¼ 3V 2

1 V2= 32nZ20 f1� �

Z0 f2� �

Z0 fIM3

� ��

�

gIM3 þ a� ��

, n ¼ a=gIM3 and V1,2 are the source voltages atthe frequencies f1,2 and Z0( f ) is the line characteristicimpedance. Then, forward PIM3 magnitude is calculated asfollows

PIM3 lð Þ ¼1

2Re IIM3 lð ÞUIM3 lð Þ��

(3)

where IIM3(l ) and UIM3(l ) are current and voltage at thetransmission line output (x ¼ l ); � stands for complexconjugation and Refg is the real part. Equations (1)–(3) areused for calculations of the PIM3 level on microstrip lineswith the dominant current-driven nonlinearity.


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Passive intermodulation in printed lines: effects of trace dimensions and substrate