A Method for Measuring the Maximum Measurable Gain of a Passive Intermodulation Chamber

electronics

Article A Method for Measuring the Maximum Measurable Gain of a Passive Intermodulation Chamber

Zhanghua Cai 1, Yantao Zhou 1, Lie Liu 2, Francesco de Paulis 3 , Yihong Qi 4 and Antonio Orlandi 3,*

1 Department of Electrical and Information Engineering, Hunan University, Changsha 410082, China; [email protected] (Z.C.); [email protected] (Y.Z.) 2 General Test Systems, Shenzhen 518102, China; [email protected] 3 UAq EMC Laboratory, Department of Industrial and Information Engineering and Economics, University of L’Aquila, 64100 L’Aquila, Italy; [email protected] 4 Peng Cheng Laboratory, Shenzhen 518066, China; [email protected] * Correspondence: [email protected]; Tel.: +39-0862-434432

Abstract: This paper presents an approximate method that allows the calculation of the maximum measurable gain (MMG) in an anechoic chamber. This method is realized by using a low passive intermodulation (PIM) medium-gain directional antenna. By reducing the distance between the antenna and the wall of the chamber to reduce path loss, the purpose of replacing a high-gain antenna with a medium-gain antenna is achieved. The speciﬁc relationship between distance and equivalent gain is given in this paper. The measurement interval is determined by the 3 dB beamwidth of the measurement antenna to scan the whole chamber. A set of corresponding data for the residual PIM level and the MMG of the chamber can be obtained by the method of measurement outlined herein. The feasibility of this method was veriﬁed by measurements in two PIM measurement chambers. Keywords: anechoic chamber; antenna measurement; passive intermodulation measurement Citation: Cai, Z.; Zhou, Y.; Liu, L.; de Paulis, F.; Qi, Y.; Orlandi, A. A Method for Measuring the Maximum Measurable Gain of a Passive 1. Introduction Intermodulation Chamber. Electronics Passive intermodulation (PIM) has an important impact on wireless communication 2021, 10, 770. https://doi.org/ systems [1–3]. The PIM source is generated by non-linear factors in radio frequency (RF) 10.3390/electronics10070770 systems. It mainly includes contact non-linearity [4,5] and material non-linearity [6,7]. When signals of multiple frequencies are mixed into non-linear passive components, cor- Academic Editor: Rocco Guerriero responding PIM signals are generated. If the frequencies of the PIM signals are in the operating frequency band of the receiver, it will create interference in the system. The Received: 27 February 2021 sensitivity and channel capacity of the system will thereby be reduced. Therefore, for Accepted: 20 March 2021 Published: 24 March 2021 satellite [8], base station [9], indoor-distributed antennas, and other wireless systems, PIM is an important technical indicator. With the development of 5G and autonomous vehicles,

Publisher’s Note: MDPI stays neutral achieving the highest possible sensitivity has become extremely important. Hence, the with regard to jurisdictional claims in importance of PIM cannot be ignored. published maps and institutional affil- The antenna is one of the most important components in wireless communication iations. systems, and is also one of the components that could most easily be a source of PIM [10–13]. The design of antennas is highly related to the structure, and therefore structural design and processing technology are the key to controlling the PIM levels of antennas. The purpose of structural design is to minimize PIM levels, such as avoiding direct metal-metal contact and reducing solder joints. The actual PIM level is directly related to the processing Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. technology. The same products may have different PIM levels owing to small differences in This article is an open access article processing. For example, the tightness of contact between metals [5] or a lack of uniformity distributed under the terms and in solder joints [14] will result in different PIM levels. Therefore, it is difficult to predict conditions of the Creative Commons whether a product is qualified or not from a theoretical perspective. For antennas with Attribution (CC BY) license (https:// tight PIM specifications, measurement is the most effective means of evaluation. creativecommons.org/licenses/by/ As PIM levels are very low compared to the power of carrier, the test results are prone 4.0/). to interferences from external signal sources. Therefore, it is necessary to ensure that there

Electronics 2021, 10, 770. https://doi.org/10.3390/electronics10070770 https://www.mdpi.com/journal/electronics Electronics 2021, 10, 770 2 of 15

are no interfering signals in the environment during measurement. In reality, it is difficult to guarantee a completely interference-free environment. Hence, the device under test (DUT) is usually measured in a shielded anechoic chamber. The anechoic chamber shields the interference from external signals and reduces the space reflection, which is widely used in microwave measurements [15–20]. The use of an anechoic chamber can also greatly improve the accuracy of the PIM measurement, especially for radiating components such as antennas. In addition, the shielding enclosure and absorber of the chamber could also generate PIM signals [7]. The shielding enclosure of the PIM measurement chamber is made of several metal plates, and the connections of the metal plates can be fixed by welding, screws, etc. However, no matter which method is used, contact non-linearity will inevitably occur at the connections and will become a potential source of PIM. The absorber generally consists of polyurethane foam (commonly referred to as sponge) and carbon black or graphite powder. The shaped absorber is obtained by mixing, soaking, and drying the materials, which can lead to the uneven distribution of materials. In addition, there may be incomplete contact between large-sized carbon particles, which form loose clusters. Therefore, the absorber is another potential source of PIM, while the part in contact with the shielding enclosure may also create PIM products. The antenna under test (AUT) radiates electromagnetic waves during measurement. When electromagnetic waves are transmitted to the absorbers, the absorbers may generate PIM. At the same time, a portion of the energy will produce another PIM product on the shielding enclosure. These PIM products can be received by the AUT and increase with increases in the gain of the antenna, which could artificially inflate the measured PIM of the AUT. In this situation, some antenna products that originally meet the PIM performance indicators will be mistakenly regarded as substandard products, resulting in a reduction in the efficiency of industrial production and a waste of resources. Currently, the manufacturers of PIM measurement chambers only provide a single residual PIM index. This indicator is not a problem in the measurement of non-radiating devices; however, it is not appropriate for antennas, as the increase in the gain of the AUT could cause an increase in the residual PIM level of the chamber. Therefore, for antennas, a reasonable residual PIM level of the chamber should be accompanied by some sort of index related to AUT gain. We thus propose an index denoted the maximum measurable gain (MMG). The AUT should not produce a PIM value higher than the residual PIM index in the PIM test chamber. The MMG can then be defined as the maximum antenna gain that satisfies this condition. The novel concept of MMG proposed in this paper is critical for the evaluation of the PIM performance of a chamber for antenna PIM measurements. However, according to our knowledge, the recent research on PIM is mainly focused on analyses of PIM models [21–23] and PIM test devices [24–27]. At present, no one has proposed a similar idea of defining the MMG of the PIM measurement chamber, and thus there is no corresponding method of estimating the MMG. The direct method of evaluating the MMG of a PIM measurement chamber is to measure corresponding high-gain, low-PIM antennas. However, this is not a simple task. First, designing high-gain antennas with low PIM is difficult, as high-gain antennas often have complex metal structures and feeding networks. Solder joints, metal connections, and substrates can cause non-linearity, and generate more PIM products. Secondly, high- gain antennas typically have a more narrowly radiated main lobe. It would be extremely laborious to scan the entire chamber with a high-gain antenna. Finally, the size of a high-gain antenna is large, which is not convenient for measurement. Hence, we present here a method for evaluating the MMG of a shielded anechoic chamber with a single low-PIM medium-gain directional antenna. The medium-gain directional antenna has three advantages. First, the gain of a medium-gain antenna is generally around 10 dBi, which can be achieved by a smaller unit. Low PIM levels can be achieved owing to its simple structure. Secondly, the beam of a medium-gain antenna has a certain directivity, and its side lobes and back lobes are small, which can clearly detect the differences in Electronics 2021, 10, x FOR PEER REVIEW 3 of 15

Electronics 2021, 10, 770 3 of 15 be achieved by a smaller unit. Low PIM levels can be achieved owing to its simple structure. Secondly, the beam of a medium-gain antenna has a certain directivity, and its side lobes and back lobes are small, which can clearly detect the differences in performance in differentperformance positions in different within the positions anechoic within chamber. the anechoic Thirdly, chamber.the results Thirdly, of the measurements the results of ofthe the measurements medium-gain of antenna the medium-gain can be directly antenna used can to judge be directly whether used the to chamber judge whether can be usedthe chamber to measure can an be antenna used to measurewith a smaller an antenna gain, which with a reduces smaller gain,the workload. which reduces Finally, the a mediumworkload.-gain Finally, antenna a medium-gain can be equivalent antenna to a canhigh be-gain equivalent antenna toby achanging high-gain the antenna measure- by mentchanging distance. the measurement Therefore, the distance. present Therefore,paper proposes the present a method paper to proposes compensate a method for gain to basedcompensate on the forpath gain loss. based In addition, on the path a scanning loss. In addition,method for a scanning evaluating method the chamber for evaluating based onthe the chamber main lobe based of on the the anten mainna lobe is also of theprovided. antenna Using is also this provided. method, Using the residual this method, PIM levelthe residual of the system PIM level from of themeasuring system fromantennas measuring with different antennas gains with can different be also gains measured can be andalso the measured MMG at and the the required MMG atnoise the floor required can noisebe evaluated. ﬂoor can be evaluated. ThisThis paper paper is is organized organized as asfollows. follows. In Section In Section 2, a2 PIM, a PIM measurement measurement system system is intro- is duced.introduced. The method The method for determining for determining the MMG the MMG is proposed is proposed in Section in Section 3. In3 .Section In Section 4, ex-4, periments,experiments, performed performed using using two two chambers, chambers, are are presented presented to to verify verify the the proposed proposed method. method. Lastly,Lastly, conclusions are provided. 2. PIM Measurement System 2. PIM Measurement System As previously mentioned, PIM is caused by the non-linearity of components. Consid- As previously mentioned, PIM is caused by the non-linearity of components. Con- ering a mixed signal with two frequencies, the possible frequencies of the PIM products sidering a mixed signal with two frequencies, the possible frequencies of the PIM products are determined by the following formula: are determined by the following formula: = ± · ± · fIMfIM = m m f1 f1 n  ff 22 ((1)1)

inin which mmand andn aren positiveare positive integers. integers. When When it is anit is even an even number, number, the frequency the frequency of fIM ofis

usuallyf IM is usually so far from so far the from operating the operating frequency frequency band of band the system of the thatsystem it can that be it ignored. can be ig- Of nored.the odd Of PIM the signals,odd PIM the signals, amplitude the amplitude of the third-order of the third PIM-order is the PIM largest. is the Therefore, largest. There- PIM fore,measurement PIM measurement usually detects usually the detects magnitude the magnitude of the third-order of the third PIM,-order and thePIM, measured and the measuredresults are results used to are estimate used to the estimate value of the the value higher-order of the highe PIM.r- Theorder system PIM. architectureThe system ar- for chitecturemeasuring for the measuring level of PIM the is level shown of PIM in Figure is shown1. in Figure 1.

Signal Power PIM test Filter generator amplifier Chamber AUT

TX RX ∑

Combiner Duplexer

Spectrum Analyzer Low-noise amplifier FigureFigure 1. 1. PassivePassive intermodulation intermodulation ( (PIM)PIM) measurement measurement architecture.

TwoTwo single single-frequency-frequency carrier carrier signals, signals, ff11 andand f2,f are2 , are combined combined into into one one channel channel after af- terbeing being amplified amplified and and filtered. filtered. The The mixed mixed signal signal can can be transmittedbe transmitted to the to the AUT AUT through through the theduplexer. duplexer. A signal A signal with with two two frequencies frequencies will will generate generate PIM PIM signals signals on the on AUT.the AUT. The PIMThe PIMproducts products can becan received be received by the by test theinstrument test instrument via the via duplexer. the duplexer. After After processing processing by filter, by low-noise amplifier, and other components, the level of the received PIM signal fIM can be filter, low-noise amplifier, and other components, the level of the received PIM signal fIM detected by the spectrum analyzer. The PIM level of each component in the system must can be detected by the spectrum analyzer. The PIM level of each component in the system be very low. must be very low. The PIM signals that may be generated during the PIM test is shown in Figure2. f1 The PIM signals that may be generated during the PIM test is shown in Figure 2. f1 and f2, are the frequencies of two working signals. SIM_Ai is the PIM signal generated by and f 2 , are the frequencies of two working signals. SIM_ Ai is the PIM signal generated the AUT as a result of the mixed transmitting signals S f1 and S f2 ; SIM_Ar is also generated by the AUT but is a result of the receiving signals S0 and S0 ; S0 is the reflected f1 f2 IM_Ai signal of SIM_Ai; SIM_AM and SIM_SE are the PIM products generated by the absorbing material and chamber wall, respectively; S is the signal from the outside owing to the IM_EX Electronics 2021, 10, x FOR PEER REVIEW 4 of 15

by the AUT as a result of the mixed transmitting signals S and S ; S is also gen- f1 f2 IM_ Ar S ' S ' S ' erated by the AUT but is a result of the receiving signals f1 and f2 ; IM_ Ai is the re- Electronics 2021, 10, 770 4 of 15 flected signal of SIM_ Ai ; SIM_ AM and SIM_ SE are the PIM products generated by the ab-

sorbing material and chamber wall, respectively; SIMEX_ is the signal from the outside

owing to the ineffective shielding of the anechoic chamber; and SIM_ SYS is the PIM signal fromineffective the test shielding instrument of the owing anechoic to non chamber;-linear devices and SIM, _suchSYS is as the amplifier, PIM signal filter, from dup thelexer, test cable,instrument and so owing on. to non-linear devices, such as ampliﬁer, ﬁlter, duplexer, cable, and so on.

Sheilding enclosure

Absorbing material AUT

PIM test instrument Cable

Anechoic chamber

Figure 2. PIM products during PIM test.

According to Figure 2 2,, thethe PIMPIM levellevel actuallyactually measuredmeasured byby thethe instrumentinstrument isis thethe sumsum of all of the aforementioned PIM signals: = + 0 ' + + PIM_totalPPPPPIM_ totalPIM_Ai IM _ A iP IM IM_Ai _ Ai P IM __ ArAr  IMPIM _ EX_EX +PIM_AM + PIM_SE + PIM_SYS (2) PPPIM___ AM  IM SE  IM SYS (2) = PIM_Ai + PIM_SYS + PIM_CH PPPIM_ A i  IM _ SYS  IM _ CH where where P = P0 + P + P IM_CH IM_Ai IM_Ar IM_EX (3) +PIM_AM' + PIM_SE PPPPIM____ CH IM Ai  IM Ar  IM EX The symbols in Equation (2) indicate the power level of the corresponding subscripted(3) PPIM__ AM  IM SE PIM signals in Figure2. Of the seven PIM signals in Equation (2), PIM_Ai is the actual PIM valueThe of AUT, symbols while in the Equation others are (2) the indicate sources the of error.power The level value of oftheP IM corresponding_SYS is decided sub- by the performance of the PIM test instrument and test cable. The level of the remaining five scripted PIM signals in Figure 2. Of the seven PIM signals in Equation (2), PIM_ Ai is the signals depends on the performance of the PIM measurement chamber. All the PIM signals actual PIM value of AUT, while the others are the sources of error. The value of P in Equation (2) will be included in the measurement results. IM_ SYS is decided by the performance of the PIM test instrument and test cable. The level of the remaining3. The Method five sign for Evaluatingals depends the on MMG the performance of a PIM Measurement of the PIM measurement Chamber chamber. All theAs PIM analyzed signals previously in Equation during (2) will the be PIMincluded measurement, in the measurement there are fiveresults. interference signals in the PIM anechoic chamber, which will increase with increases in the gain of the AUT.3. The Therefore, Method for it isEvaluating necessary the to defineMMG theof A MMG PIM Measurement under the corresponding Chamber noise floor. The mostAs analyzed ideal way previously to evaluate during the performancethe PIM measurem of a largeent, PIMthere measurement are five interference chamber sig- is nalsto place in the a low-PIM,PIM anechoic high-gain chamber, antenna which in thewill quietincrease zone, with rotate increases the antenna in the togain scan of the wholeAUT. Therefore, sphere, and it measureis necessary the PIMto define value the at eachMMG location. under the However, corresponding in reality, noise high-gain floor. Theantennas most usuallyideal way have to complexevaluate structuresthe performance and feeding of a large systems. PIM Theymeasurement will introduce chamber more is non-linear factors, such as more solder joints and metal connections, creating even more sources of PIM. It is difficult to achieve a low PIM for a high-gain antenna. Thus, a low-PIM, medium-gain directional antenna can be considered as an alternative. The PIM level that the antenna can receive depends on the received power of the AUT. As shown in Figure3, the reflection of the absorbers is small. It is usually ignored when analyzing the reflection level of an anechoic chamber [7,28]. Thus, the absorbers can be Electronics 2021, 10, 770 5 of 15

seen just as a loss constant. In addition, the metal wall of the chamber can be approximated Electronics 2021, 10, x FOR PEER REVIEW 6 of 15 as a total reﬂection surface. It has a mirror effect. For example, for the antenna A0, its effect 0 can be equivalent to placing an antenna A0 that is the same as A0 at a symmetrical position of the metal wall and removing the metal wall at the same time [29]. At this time, the Friis 2 formula can be used:   2  2 PPGRr1 t 1 λ  AM (7) P = P G G 4 2d (4) r t t r 4π1d 

whereLettingPt is the PPr transmitting0 r 1 , we can power get: of the antenna, Pr is the received power of the virtual antenna, which is equal to the reﬂected power received by the AUT when there is a d G G 0 metal plane, t and r are the gain of theGG transmitting0 1 antenna and the receiving antenna,(8) d respectively, λ is the wavelength in free space, and d 1is the distance between the transmitting and receiving antennas. In the PIM measurement chamber, both the transmitting and Equation (8) can be written in dB units as: receiving antennas are the AUT itself. In other words, Gr = Gt. The absorption loss of the

absorbing material needs to beG considered.0 dB  G 1 Then, dB 10 Equation lg d 0 / d(4) 1  can be modiﬁed as: (9)

Obviously G dB G dB , but the received2 power of the two antennas in the two 0  1   2 λ Pr = PtGt RAM (5) states are the same. The measured result of 4Aπ1d at P1 can be equivalent to the measured result of A0 at P0. The purpose of replacing the high-gain antenna with a medium-gain in which RAM represents the reﬂection ratio of the absorbing material. For the same type antenna can be achieved. In this case, the received power of the PIM signals S IMSE_ and of absorber, RAM can be considered to be a ﬁxed value [7,30]. Thus, it can be multiplied S for a high-gain antenna is also can be replaced by a medium-gain antenna due to byIMAM Equation_ (4) as a constant. According to Equation (5), there are three factors affecting thethe receivedreduced path power loss. of theWe antenna:can also use the E transmittingquations (6)– power,(9) approximately. the gain of theRegardless antenna, of and the theloading distance effect of of the the transmitting absorbers, the and minimum receiving value antennas. of d1 Changesis the height in power of the willabsorbers. cause changesTherefore, in the the heating highest effect gain of thatthe antenna, can be and compensated changes in temperature can be approximated will affect the as

PIM10 lg level.d0 / h Therefore,ab  , where thehab transmitting is the height power of the andabsorbers. antenna gain exert different effects on PIM.Since A high-gain there are antenna no complicated cannot be created devices simply such as by probes increasing and turntablesthe power. in Thus, the PIMit is necessarymeasurement to reduce chamber, the distance replacingd to the compensate antenna does for the not received introduce power. other In variables Equation that (5), 2 whencould keepingaffect results the transmitting in the process power of moving constant, the antenna only (G texcept/d) is the a variable. change in As the long reflec- as 2 (tionGt/ dlevel) stays owing the to same, distance an equal change. amount of power can be received.

A0' A1' A1 A0

P1 P0

Anechoic chamber FigureFigure 3.3. DifferentDifferent measurementmeasurement positionspositions ofof directionaldirectional antennas.antennas.

AsSince shown the Friis in Figure formula3, the can position only be usedP0 is theunder center the far of the-field PIM conditio measurementns, it is inaccurate chamber. Inusing reality, the theFriis antenna formula is usuallywhen placed at this position for measurement in order to achieve minimal reﬂection. It is assumed that the PIM of a directional antenna A0 with a gain of 2d 2 D2 /  G0 is measured at position P0, and that the1 PIM of a directional antenna A1’ with a gain of 2 (10) G1 is measured at position P1. The main radiation d1  D /  directions of both antennas are toward the −x direction. Since most of the energy of a directional antenna is concentrated in the mainwhere, radiationD is the direction, maximum only physical the reﬂection size of fromthe antenna. the −x plane needs to be considered, and When the distance is short, simulation results can be used to assist the calculation. The simulator used in this paper is the High Frequency Structure Simulator (HFSS). Figure 4 shows the received power obtained by simulation and calculated by the Friis formula. The horizontal axis is the distance from the transmitting antenna to the receiving antenna. Antennas used in Section 4 are calculated with a gain of 10.5 dBi at 0.9 GHz and 8 dBi at 1.73 GHz. The transmitted power is set to 0 dBw. Thus, the Friis formula is consistent with

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the reﬂection from other surfaces can be ignored. Then, Equation (5) can be used in this situation. The following two formulas can be obtained:

2 2 λ Pr0 = PtG0 RAM (6) 4π2d0

2 2 λ Pr1 = PtG1 RAM (7) 4π2d1

Letting Pr0 = Pr1, we can get: d0 G0 = G1 (8) d1 Equation (8) can be written in dB units as:

G0(dB) = G1(dB) + 10lg(d0/d1) (9)

Obviously G0(dB) > G1(dB), but the received power of the two antennas in the two states are the same. The measured result of A1 at P1 can be equivalent to the measured result of A0 at P0. The purpose of replacing the high-gain antenna with a medium-gain antenna can be achieved. In this case, the received power of the PIM signals SIM_SE and SIM_AM for a high-gain antenna is also can be replaced by a medium-gain antenna due to the reduced path loss. We can also use Equations (6)–(9) approximately. Regardless of the loading effect of the absorbers, the minimum value of d1 is the height of the absorbers. Therefore, the highest gain that can be compensated can be approximated as 10lg(d0/hab), where hab is the height of the absorbers. Since there are no complicated devices such as probes and turntables in the PIM measurement chamber, replacing the antenna does not introduce other variables that could affect results in the process of moving the antenna except the change in the reflection level owing to distance change. Since the Friis formula can only be used under the far-field conditions, it is inaccurate using the Friis formula when 2 2d1 ≤ 2D /λ 2 (10) d1 ≤ D /λ where, D is the maximum physical size of the antenna. When the distance is short, simulation results can be used to assist the calculation. The simulator used in this paper is the High Frequency Structure Simulator (HFSS). Figure4 shows the received power obtained by simulation and calculated by the Friis formula. The horizontal axis is the distance from the transmitting antenna to the receiving antenna. Antennas used in Section4 are calculated with a gain of 10.5 dBi at 0.9 GHz and 8 dBi at 1.73 GHz. The transmitted power is set to 0 dBw. Thus, the Friis formula is consistent with the simulation when the distance is long. The Friis formula is less accurate when the distance is short, and the simulated received power can be used to calculate the correct measurement distance d1 using Equations (6) and (7). The method of compensating for gain is discussed above, but no method is given to evaluate the residual PIM of the whole chamber. As the placement of the AUT is uncertain during the actual measurements, the direction of radiation is random. The PIM value is closely related to the structure, and small changes in the structure will result in changes in the PIM level. The structural consistency of the absorbers and the shielding enclosures of the chamber at various locations is difficult to ensure. Therefore, the entire anechoic chamber needs to be scanned. In short, the measured results of a single location cannot be used to define the noise floor of a PIM measurement chamber. Electronics 2021, 10, x FOR PEER REVIEW 7 of 15

Electronics 2021, 10, 770 the simulation when the distance is long. The Friis formula is less accurate when the7 of dis- 15 tance is short, and the simulated received power can be used to calculate the correct meas-

urement distance d1 using Equations (6) and (7).

20 Simulated at 0.9 GHz Calculated at 0.9 GHz 10 Simulated at 1.73 GHz Calculated at 1.73 GHz 0

-10

-20 Received power (dBw) power Received

-30

0.5 1.0 1.5 2.0 2.5 Distance (m) FigureFigure 4. 4.Received Received power power obtained obtained by by simulation simulation and and calculated calculated by by the the Friis Friis formula. formula.

OwingThe method to the of peculiarity compensating of PIM for measurements,gain is discussed it isabove, impossible but no tomethod use mechanical is given to rotatingevaluate devices the residual in the PIM PIM of measurement the whole chamber. chamber As (newthe placement sources of of PIM the AUT would is uncertain be introduced).during the Only actual discrete measurements, scanning can the be direction achieved. of radiation Here, a methodis random. is proposed The PIM tovalue scan is variousclosely positionsrelated to of the the structure, PIM measurement and small chamberchanges in based the structure on the main will lobe result of ain low-PIM changes directionalin the PIM antenna.level. The Sincestructural most consistency energy from of athe directional absorbers antennaand the shielding is contained enclosu in theres 3-dBof the main chamber beamwidth, at various it can locations be considered is difficult that theto ensure. PIM generated Therefore, by thethe otherentire radiation anechoic directionschamber needs of the to antenna be scanned. will be In muchshort, smallerthe measured than the results PIM of generated a single location by the main cannot lobe be radiation.used to define In this the way, noise the floor worst of a casePIM ofmeasurement each position chamber. in the anechoic chamber can be reflectedOwing without to the major peculiarity deviations of PIM by main measurement lobe scanning.s, it is impossible to use mechanical rotatingThe selectiondevices in of the specific PIM measurement locations for measurementchamber (new issources shown of in PIM Figure would5. Suppose be intro- thereduced). is a Only low-PIM discrete directional scanning antenna can be withachieved. a known Here, gain, a method and the is chamber proposed residual to scan PIM var- levelious whenpositions the AUTof the gain PIM is measurementGx needs to be chamber defined. Thebased equivalent on the main measurement lobe of a distancelow-PIM ddirectionalx can be obtained antenna. according Since most to Equation energy from (9), or a simulationdirectional results.antennad xisis contained the distance in fromthe 3- thedB antennamain beamwidth, to one wall it ofcan the be chamber. considered Taking that thethe −PIMx plane generated as an example,by the other the radiation antenna needsdirections to be of placed the antennadx away will from be themuch−x smallerplane, andthanthe the main PIM radiationgenerated directionby the main should lobe beradiation. towards In the this−x way,plane. the The worst projection case of of each the mainposition lobe in of the the anechoic antenna inchamber the −x canplane be isreflected shown inwithout Figure major5a (marked deviations as S), by which main islobe approximately scanning. an ellipse. To simplify the actualThe measurement, selection of a specific rectangular locations area canfor bemeasurement used instead is ofshown an ellipse in Figure to represent 5. Suppose the mainthere beam is a low coverage-PIM directional of the antenna. antenna The with length a known and width gain, ofand the the rectangle chamber are residual calculated PIM by the horizontal and vertical 3 dB beamwidth of the antenna, respectively. As shown in level when the AUT gain is G needs to be defined. The equivalent measurement dis- Figure5b, the horizontal-plane beamwidthx of antenna is θ . According to the geometric d h d relationships,tance x can thebe followingobtained according formula can to Equation be obtained: (9), or simulation results. x is the distance from the antenna to one wall of the chamber. Taking the  x plane as an example,

the antenna needs to be placed dxL haway= 2d fromx tan (theθh/2 )x plane, and the main radiation(11) direction should be towards the  x plane. The projection of the main lobe of the antenna L where,in the hxcan plane be seenis shown as the in coverage Figure 5a range (marked in the as horizontalS), which is plane. approximately The measurement an ellipse. intervalTo simplify of the the horizontal actual measurement, direction should a rectangular not be lessarea thancan be this used length. instead Similarly, of an ellipse the measurement interval in the vertical direction should not be less than the following value: to represent the main beam coverage of the antenna. The length and width of the rectangle are calculated by the horizontal and vertical 3 dB beamwidth of the antenna, respectively. Lv = 2dx tan(θv/2) (12) As shown in Figure 5b, the horizontal-plane beamwidth of antenna is h . According to wherethe geometricθv is the relationships, beamwidth in the the following vertical plane. formula Finally, can be the obtained: position to be measured for the −x plane is shown in Figure5c. The measurement method of the remaining ﬁve walls L 2 d tan / 2 is the same as that of the −x plane. h x h  (11)

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where, Lh can be seen as the coverage range in the horizontal plane. The measurement interval of the horizontal direction should not be less than this length. Similarly, the measurement interval in the vertical direction should not be less than the following value:

Lv 2 d x tan v / 2 (12)

Electronics 2021, 10, 770 wherev is the beamwidth in the vertical plane. Finally, the position to be measured8 offor 15 the  x plane is shown in Figure 5c. The measurement method of the remaining five walls is the same as that of the  x plane.

P1 S

Anechoic chamber

(a) (b)

Anechoic chamber

(c)

FigureFigure 5. 5. SelectionSelection method method of of measurement measurement positions positions for for the the−xx plane. ( a) Main lobe lobe projection projection of of thethe antenna. antenna. ( (bb)) Sectional Sectional view view of of the the xoyxoyplane, plane, and and (c ()c sectional) sectional view view of of the theyoz yozplane. plane.

TheThe method method for for determining determining the the MMG MMG in in the the PIM PIM measurement measurement chamber chamber is is summa- summa- rizedrized as as follows: follows: (1)(1) FirstFirst determine determine the the PIM PIM noise noise floor floor target target of of the the chamber. chamber. For For example, example, if if the the required required rresidualesidual PIM PIM level level is is lower lower than than −160−160 dBc dBc at at 43 43 dBm, dBm, the the directional directional antenna antenna used used for for measurementmeasurement must must have have a a PIM PIM below below −160−160 dBc. dBc. During During the the test, test, if if a a measurement higherhigher than than −160−160 dBc dBc appears, appears, it itis isconsidered considered not not to to meet meet the the requirement. requirement. (2)(2) DetermineDetermine the the gai gainn to to be be measured. measured. The The maximum maximum gain gain to be to measured be measured can canbe di- be rectlydirectly determined determined according according to tothe the actual actual application. application. Generally, Generally, a a stepping stepping method method cancan be be used used to to determine determine the the MMG. MMG. First First determine determine an anappropriate appropriate gain, gain, and andif the if measurementthe measurement results results meet meetthe requirements, the requirements, increase increase the measurement the measurement gain appro- gain priatelyappropriately until a untillevel a higher level higher than the than target the target noise noisefloor flooris detected. is detected. Otherwise, Otherwise, de- creasedecrease the themeasurement measurement gain gainuntil until the measurement the measurement results results are lower are lowerthan the than target the noisetarget floor. noise floor. (3)(3) CalculateCalculate the the measurement measurement di distancestance according according to to the the gain gain to to be be measured, measured, which which can can be determined according to Equation (9) or simulation results. be determined according to Equation (9) or simulation results. (4) Determine the measurement positions according to the beamwidth and measurement distance of the antenna. The specific method is described above. (5) If a result higher than the target noise floor appears during the measurement, it is not necessary to continue measuring the remaining positions. It can also be assumed that the results of measurements with an antenna with this gain will be unreliable. Otherwise, the six planes should be measured completely. In conclusion, a reasonable PIM measurement chamber floor noise index should include the following information: measurement power, measurement frequency, MMG, and a value for the level of PIM. Electronics 2021, 10, 770 9 of 15

The phase effect on PIM with multiple PIM sources is not considered here, because the positions of the PIM sources are uncertain. However, if we can get enough results by scanning the entire chamber, we can approximately obtain the highest PIM level of the chamber. Finally, in order to improve the reliability of the above measurement method, the antenna used should include the following two features in addition to low-PIM and medium-gain. The antenna should have a symmetrical main beam, which can reduce the measurement uncertainty and make the scanning process more convenient. The antenna cannot have a large side-lobe level and back-lobe level, which will cause the antenna to have a large reﬂection on all sides of chamber, resulting in errors in the gain equivalent method. Generally, the side-lobe and back-lobe should be about 10 dB lower than the main direction level.

4. Experimental Validation Three experiments are outlined in this section to verify the feasibility of the proposed method. The PIM test instruments used in the experiments are NTPIMD-900DA and NTPIMD-1800DA, which were used for measurements of low frequency (transmitting frequency range from 925 MHz to 960 MHz, and receiving frequency range from 880 MHz to 915 MHz) and high frequency (transmitting frequency range from 1805 MHz to 1880 MHz, and receiving frequency range from 1710 MHz to 1785 MHz), respectively. Correspond- ingly, two low-PIM antennas were used for testing. The low-frequency antenna can cover 880–960 MHz with a gain of approximately 10.5 dBi and a beamwidth of approximately 55 degrees. The high-frequency antenna can cover 1710–1880 MHz with a gain of approximately 8 dBi and a beamwidth of approximately 70 degrees. They were originally designed as base station units with a PIM lower than −165 dBc at 43 dBm. Measurements were performed in two PIM measurement chambers with different performances to reflect the effectiveness of the evaluation method. Since the measurement settings can substantially influence the results of measuring PIM, the test process needs to be strictly controlled. First, the placement of the cable could affect the measurement results. During the experiment, it is imperative that the cable is maintained in a straight state without unnecessary bending. Secondly, the tightness of the joint connection also affects the measurements. This uncertainty can be avoided by taking multiple measurements. Reconnect the connector before each measurement, and try to ensure that the connector is sufficiently tight (a torque wrench can be used). Finally, a prolonged measurement will cause the antenna to heat up, which will affect the PIM value. Thus, avoid continuous measurement for more than 5 min. During multiple measurements, you can cool the antenna for approximately 5 min. It is worth noting that the experiments in this paper are only used to verify the feasibility of the proposed method, and did not follow the steps in Section3 to perform a complete scan of the chamber. Complete measurements are very laborious and involve many repetitive tasks. A custom support frame and low PIM cable of the appropriate length are also required to ensure measurement reliability. The first experiment was used to verify the feasibility of the method of changing the distance to achieve an equivalently high gain. This experiment was performed mainly in the PIM chamber A illustrated in Figure6a. As the residual PIM level is relatively large in chamber A, the measured results will more clearly reflect the change. As shown in Figure7, six points at different distances from one side of chamber A were selected for measurement. The six points are at the same height, and only the position in the x direction is different. The environment within the chamber is shown in Figure6b. Each position was measured for PIM values at three different powers. Prior to the measurement, a low PIM load without radiation was measured in the chamber to show the noise level from the test instrument and cables. The low-frequency and high-frequency measurement results are shown in Tables1 and2, respectively. The equivalent gain is obtained by using Equation (10). It can be seen that, regardless of the frequency of the antenna, the PIM values increase as Electronics 2021, 10, x FOR PEER REVIEW 10 of 15

the PIM chamber A illustrated in Figure 6a. As the residual PIM level is relatively large in chamber A, the measured results will more clearly reflect the change. As shown in Figure 7, six points at different distances from one side of chamber A were selected for measurement. The six points are at the same height, and only the position in the x direction is different. The environment within the chamber is shown in Figure 6b. Each position was measured for PIM values at three different powers. Prior to the measurement, a low PIM load without radiation was measured in the chamber to show the noise level from the test Electronics 2021, 10, 770 instrument and cables. The low-frequency and high-frequency measurement results are10 of 15 shown in Tables 1 and 2, respectively. The equivalent gain is obtained by using Equation (10). It can be seen that, regardless of the frequency of the antenna, the PIM values increase as the measurement distance decreases. When the measurement distance is changed from 1.6 mthe to 0.65 measurement m, the PIM distance level of decreases.the antenna When increases the measurementby approximately distance 10 dB is at changed 43 dBm from (low-1.6frequency m to 0.65 increases m, the PIM by 9.98 level dB, ofthe high antenna-frequency increases increases by approximately by 11.85 dB),10 which dB at is 43 a dBm large(low-frequency deviation. In the increases case of bylow 9.98 power, dB, high-frequency the reflected signal increases is very by 11.85 weak dB),. For which example, is a large it maydeviation. be less than In the −130 case dBm, of low which power, is the the measurable reﬂected signal minimum is very of weak. the PIM For example,test instru- it may ment.be This less small than − level130 dBm,will not which affect is the the measurable measurement minimum results of. Thus, the PIM thetest change instrument. caused This by thesmall distance level is will not not obvious. affect the Thes measuremente results are results. consistent Thus, with the changethe analysis caused in bySection the distance 3. That isis, not when obvious. the distance These is results reduced, are consistentthe received with power the analysisof the antenna in Section increases,3. That and is, whena higherthe PIM distance level isis reduced,received. theIt can received be seen power from of the the results antenna of increases,the measurements and a higher that PIM chamberlevel A is may received. result It i cann errors be seen when from measuring the results a ofhigh the-gain measurements antenna. For that example, chamber an A may antennaresult with in errorsa gain whenof 13 dBi measuring at 900 MHz a high-gain needs to antenna. be measured For example, at 43 dBm, an antenna while the with PIM a gain of 13 dBi at 900 MHz needs to be measured at 43 dBm, while the PIM index requirement index requirement is lower than −160 dBc. Any antenna that meets the index does there- is lower than −160 dBc. Any antenna that meets the index does therefore not meet the fore not meet the requirements, as the noise of the chamber itself is greater than −160 dBc requirements, as the noise of the chamber itself is greater than −160 dBc in this situation. in this situation.

PIM test chamber

PIM test instrument

Operating computer

(a) (b) Electronics 2021, 10, x FOR PEERFigure REVIEW 6. A photograph of chamber A. (a) Appearance of the PIM measurement chamber A, (b) 11 of 15 Figure 6. A photograph of chamber A. (a) Appearance of the PIM measurement chamber A, (b) mea- measurementsurement arrangement arrangement in in PIM PIM measurement measurement chamber chamber A. A.

0.85 m 0.95 m 1.05 m 1.6 m P6 P5 P4 P3 P2 P1 0.75 m 0.65 m

Anechoic chamber

FigureFigure 7.7. MeasurementMeasurement positionspositions inin PIMPIM measurementmeasurement chamberchamber A.A.

TableThe 1. Measured second experiment results of chamber was performed A at 900 MHz in the. PIM measurement chamber B (Figure8) , mainly for comparison and auxiliary veriﬁcation. The six points shown in Figure9 are se- Measurement Equivalent Measured PIM (dBc) lectedPosition for measurement. The six points are at the same height. Three different distances can be chosen to compareDistance with (m) the resultsGain of(dBi) chamber 33 A. dBm The PIM values40 dBm at different 43 positions dBm at the sameP1 distance were1.6 measured10.5 for auxiliary veriﬁcation.−169.0 The−166.8 measurement −160.3 intervals 0.7 m andP2 0.5 m at the1.05 corresponding 12.3 distances meet−168.5 the requirements −164.6 of Equation −158.4 (12). The P3 0.95 12.7 −168.6 −164.4 −156.3 P4 0.85 13.2 −168.2 −164.4 −155.7 P5 0.75 13.8 −168.0 −164.1 −154.8 P6 0.65 14.4 −164.5 −160.2 −150.3 Low PIM load - - −172.5 −171.1 −170.6

Table 2. Measured results of chamber A at 1730 MHz.

Measurement Equivalent Measured PIM (dBc) Position Distance (m) Gain (dBi) 33 dBm 40 dBm 43 dBm P1 1.6 8 −169.0 −167.6 −166.2 P2 1.05 9.8 −168.9 −166.4 −161.4 P3 0.95 10.3 −168.8 −166.6 −162.2 P4 0.85 10.7 −168.6 −166.4 −162.2 P5 0.75 11.3 −168.3 −166.2 −161.3 P6 0.65 11.9 −166.7 −163.6 −154.3 Low PIM load - - −170.5 −169.9 −169.1

The second experiment was performed in the PIM measurement chamber B (Figure 8), mainly for comparison and auxiliary verification. The six points shown in Figure 9 are selected for measurement. The six points are at the same height. Three different distances can be chosen to compare with the results of chamber A. The PIM values at different positions at the same distance were measured for auxiliary verification. The measurement intervals 0.7 m and 0.5 m at the corresponding distances meet the requirements of Equa- tion (12). The measurement setup is shown in Figure 8b, while the results of measurements are shown in Tables 3 and 4. Owing to the low PIM design of the shielding enclosure and the absorber [7], the residual PIM level in chamber B is very small. It is evident that the measured PIM values of the six positions exhibit only small differences (less than 1.5 dB) and do not show the distance effect. These small differences can be considered as measurement error. It can thus be considered that chamber B provides more accurate measurements than chamber A when measuring antennas with high gain, such as 14 dBi.

Electronics 2021, 10, 770 11 of 15

measurement setup is shown in Figure8b, while the results of measurements are shown in Tables3 and4. Owing to the low PIM design of the shielding enclosure and the absorber [ 7], the residual PIM level in chamber B is very small. It is evident that the measured PIM values of the six positions exhibit only small differences (less than 1.5 dB) and do not show the distance effect. These small differences can be considered as measurement error. It can thus be considered that chamber B provides more accurate measurements than chamber A when measuring antennas with high gain, such as 14 dBi.

Table 1. Measured results of chamber A at 900 MHz.

Measurement Equivalent Measured PIM (dBc) Position Distance (m) Gain (dBi) 33 dBm 40 dBm 43 dBm P1 1.6 10.5 −169.0 −166.8 −160.3 P2 1.05 12.3 −168.5 −164.6 −158.4 P3 0.95 12.7 −168.6 −164.4 −156.3 P4 0.85 13.2 −168.2 −164.4 −155.7 P5 0.75 13.8 −168.0 −164.1 −154.8 P6 0.65 14.4 −164.5 −160.2 −150.3 Low PIM load - - −172.5 −171.1 −170.6

Electronics 2021, 10, x FOR PEER REVIEW 12 of 15

Table 2. Measured results of chamber A at 1730 MHz.

Measurement Equivalent Measured PIM (dBc) It mayPosition be confusing that the measured results do not follow the typical relationship Distance (m) Gain (dBi) 33 dBm 40 dBm 43 dBm between the third-order PIM and the input power (with a slope of 2–3 dB/dB typically). The differencesP1 between the 1.6 average values of 8 the measurement−169.0 results−167.6 P1~P6 and−166.2 the − − − measurementP2 results of the 1.05 low PIM load are 9.8 listed in Tables168.9 3 and 4. It166.4 can be seen161.4 that P3 0.95 10.3 −168.8 −166.6 −162.2 all the valuesP4 are less than 2dB, 0.85 indicating that 10.7 the PIM value−168.6 of the antenna−166.4 used is− close162.2 to the low P5PIM load. The true 0.75 PIM value of antenna 11.3 is lower−168.3 than the −system166.2 noise− 161.3floor (for exampleP6 −135 dBm). Therefore, 0.65 the measured 11.9 data is dominated−166.7 by− 163.6the system− noise154.3 and theLow measurement PIM load error caused - by configuration. - In this−170.5 case, the typical−169.9 relationship−169.1 between PIM level and input power cannot be reflected in the measurement results.

(a) (b)

FigureFigure 8. A 8. photographA photograph of chamber of chamber B. ( B.a) (Appearancea) Appearance of the of the PIM PIM measurement measurement chamber chamber A, A, (b ()b ) mea- measurementsurement arrangement arrangement in in PIM PIM measurement measurement chamber chamber B. B.

It may be confusing that the measured results do not follow the typical relationship between the third-order PIM and the input power (with a slope of 2–3 dB/dB typically). The differences between the average values of the measurement results P1~P6 and the 0.65 m 0.3 m 0.65 m measurement results of the low PIM load are listed in Tables3 and4. It can be seen that P4 all the values areP less2 than 2dB, indicating that the PIM value of the antenna used is close to the low0 PIM.5 m load. The true PIM value of antenna is lower than the system noise ﬂoor P5 0.7 m P1

0.5 m P3 P6

Anechoic chamber Figure 9. Measurement positions in PIM measurement chamber B.

It can be seen from the two experiments that the method of measurement proposed herein can indeed obtain different PIM values at different distances. Furthermore, it can differentiate corresponding effects in chambers with different performances, which indi- cates that the method proposed here is effective. The last experiment measured a high-gain antenna, with a gain of 16 dBi, at positions P1 in the two PIM measurement chambers in order to verify the reliability of the measurement results. The measured power is 43 dBm, and the antenna works at approximately 900 MHz. According to the test results of the two experiments outlined above, it is evident that chamber A will yield errors when measuring the 16 dBi antenna. Although the performance of the 16 dBi antenna was not verified in chamber B, the results show that the measurement results will be superior to those of chamber A. The results of measurements from the third experiment are shown in Table 5. An outdoor measurement is used for

Electronics 2021, 10, x FOR PEER REVIEW 12 of 15

It may be confusing that the measured results do not follow the typical relationship between the third-order PIM and the input power (with a slope of 2–3 dB/dB typically). The differences between the average values of the measurement results P1~P6 and the measurement results of the low PIM load are listed in Tables 3 and 4. It can be seen that all the values are less than 2dB, indicating that the PIM value of the antenna used is close to the low PIM load. The true PIM value of antenna is lower than the system noise floor (for example −135 dBm). Therefore, the measured data is dominated by the system noise and the measurement error caused by configuration. In this case, the typical relationship between PIM level and input power cannot be reflected in the measurement results.

Electronics 2021, 10, 770 12 of 15

(for example −135 dBm).(a) Therefore, the measured data is dominated(b by) the system noise andFigure the 8. measurement A photograph errorof chamber caused B. ( bya) Appearance conﬁguration. of the In PIM this measurement case, the typical chamber relationship A, (b) betweenmeasurement PIM arrangement level and input in PIM power measurement cannot be chamber reﬂected B. in the measurement results.

0.65 m 0.3 m 0.65 m P4 P2 0.5 m P5 0.7 m P1

0.5 m P3 P6

Anechoic chamber FigureFigure 9.9.Measurement Measurement positionspositions inin PIMPIM measurementmeasurement chamber chamber B. B.

TableIt 3. canMeasured be seen results from of the chamber two experiments B at 900 MHz. that the method of measurement proposed herein can indeed obtain different PIM values at different distances. Furthermore, it can differentiate correspondMeasurementing effects in chambersEquivalent with differentMeasured performances, PIM (dBc) which indi- Position cates that the method proposedDistance (m)here is Gaineffective. (dBi) 33 dBm 40 dBm 43 dBm The lastP1 experiment measured 1.6 a high- 10.5gain antenna,− 167.9with a gain− of167.2 16 dBi, at− positions166.8 P1 in the two PIM measurement chambers in order to verify the reliability of the meas- P2 −168.2 −167.2 −165.8 0.95 12.7 urement results.P3 The measured power is 43 dBm, and the−168.0 antenna works−167.9 at approximately−166.3 900 MHz. According to the test results of the two experiments outlined above, it is evident P4 −168.4 −167.2 −166.5 that chamber A will yield errors when measuring the 16 dBi antenna. Although the per- P5 0.65 14.4 −168.7 −167.5 −167.2 formanceP6 of the 16 dBi antenna was not verified in chamber−168.2 B, the− results167.2 show−166.4 that the measurement results will be superior to those of chamber A. The results of measurements Low PIM load - - −169.5 −168.9 −168.5 from the third experiment are shown in Table 5. An outdoor measurement is used for Average(P1~P6)-Low - - 1.3 1.5 2.0 PIM load

Table 4. Measured results of chamber B at 1730 MHz.

Measurement Equivalent Measured PIM (dBc) Position Distance (m) Gain (dBi) 33 dBm 40 dBm 43 dBm P1 1.6 8 −167.6 −166.5 −165.8 P2 −167.9 −167.1 −165.5 0.95 10.3 P3 −167.7 −167.0 −166.0 P4 −168.0 −167.7 −166.7 P5 0.65 11.9 −168.0 −167.4 −166.0 P6 −168.3 −167.5 −166.3 Low PIM load - - −168.6 −168.2 −167.1 Average(P1~P6)-Low - - 0.7 1.0 1.1 PIM load

The last experiment measured a high-gain antenna, with a gain of 16 dBi, at positions P1 in the two PIM measurement chambers in order to verify the reliability of the measurement results. The measured power is 43 dBm, and the antenna works at approximately 900 MHz. According to the test results of the two experiments outlined above, it is evident that chamber A will yield errors when measuring the 16 dBi antenna. Although the performance of the 16 dBi antenna was not verified in chamber B, the results show that the measurement results will be superior to those of chamber A. The results of measurements from the third experiment are shown in Table5. An outdoor measurement is used for comparison. It is evident that the measured level of PIM in chamber B is significantly lower than that of chamber A (by approx. 10 dB). The fluctuation error of the instrument is not considered for PIM measurements, and the result would only increase as a result of interference. Thus, a lower PIM measurement is definitely more accurate. The last experiment demonstrates that chamber A results in a larger error when measuring a high-gain antenna, as was expected. This indirectly illustrates the effectiveness of our proposed method for the equivalent estimation of measurable gain.

Table 5. Measured results of a high-gain antenna in two chambers.

PIM Measurement Measured PIM at Position Gain (dBi) Measurement Chamber Distance (m) 900 MHz (dBc) A P1 1.6 16 −152.1 B P1 1.6 16 −161.5 Outside the chamber - - 16 −134.8

Finally, we believe that the accuracy of the proposed measurement method for MMG is close to the accuracy of the single antenna method, which is approximate ± 0.5 dB [31], since the proposed method is derived from the single antenna method. Further study of the accuracy will be conducted in future work.

5. Conclusions While it is necessary to define the MMG of PIM measurement chambers, precise measurements can be tedious and time consuming. Hence, the present paper proposes a method for estimating the MMG of PIM measurement chambers. Medium-gain, low- PIM directional antennas were used for the measurement. By reducing the distance between the main radiation direction of the antenna and the chamber wall during the measurement to reduce the path loss, the purpose of an equivalent high-gain antenna is achieved. The difficulties in designing high-gain and low-PIM antennas are avoided in using this method. The 3-dB main lobe of the antenna is used to determine the specific measurement positions and measurement intervals, in order to scan the entire chamber. Two different PIM measurement chambers were used for testing in the present study, and the results verified the effectiveness of the equivalent gain method, which can distinguish differences in performance between chambers. Thus, our proposed method is a feasible method for evaluating measurable gain in PIM measurement chambers.

Author Contributions: Conceptualization, Y.Q., L.L., A.O.; methodology, Y.Q., L.L., A.O., Z.C., Y.Z., F.d.P.; software, Z.C., Y.Z., F.d.P.; validation, Z.C., Y.Z.; writing—original draft preparation, Y.Q., L.L., A.O.; writing—review and editing Y.Q., L.L., A.O. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the National Natural Science Foundation of China under Grant 61671203. Conﬂicts of Interest: The authors declare no conﬂict of interest. Electronics 2021, 10, 770 14 of 15

References 1. Miao, X.; Tian, L. Digital cancellation scheme and hardware implementation for high-order passive intermodulation interference based on Hammerstein model. China Commun. 2019, 16, 165–176. [CrossRef] 2. Jin, Q.; Gao, J.; Huang, H.; Bi, L. Mitigation Methods for Passive Intermodulation Distortion in Circuit Systems Using Signal Compensation. IEEE Microw. Wirel. Compon. Lett. 2020, 30, 205–208. [CrossRef] 3. Audoin, C.; Candelier, V.; Diamarcq, N. A limit to the frequency stability of passive frequency standards due to an intermodulation effect. IEEE Trans. Instrum. Meas. 1991, 40, 121–125. [CrossRef] 4. Chen, X.; He, Y.; Yu, M.; Pommerenke, D.J.; Fan, J. Empirical Modeling of Contact Intermodulation Effect on Coaxial Connectors. IEEE Trans. Instrum. Meas. 2020, 69, 5091–5099. [CrossRef] 5. Yang, H.; Wen, H. TDR Prediction Method for PIM Distortion in Loose Contact Coaxial Connectors. IEEE Trans. Instrum. Meas. 2019, 68, 4689–4693. [CrossRef] 6. Jin, Q.; Gao, J.; Flowers, G.T.; Wu, Y.; Xie, G.; Bi, L. Modeling of Passive Intermodulation in Connectors with Coating Material and Iron Content in Base Brass. Ieee Trans. Microw. Theory Tech. 2019, 67, 1346–1356. [CrossRef] 7. Cai, Z.; Zhou, Y.; Liu, L.; Qi, Y.; Yu, W.; Fan, J.; Yu, M.; Luo, Q. Small Anechoic Chamber Design Method for On-Line and On-Site Passive Intermodulation Measurement. IEEE Trans. Instrum. Meas. 2020, 69, 3377–3387. [CrossRef] 8. Smacchia, D.; Soto, P.; Boria, V.E.; Guglielmi, M.; Carceller, C.; Garnica, J.R.; Galdeano, J.; Raboso, D. Advanced Compact Setups for Passive Intermodulation Measurements of Satellite Hardware. IEEE Trans. Microw. Theory Tech. 2018, 66, 700–710. [CrossRef] 9. Passive Intermodulation (PIM) handling for Base Stations, 3GPP TR 37.808. Available online: https://portal.3gpp.org/ desktopmodules/Specifications/SpecificationDetails.aspx?specificationId=2615 (accessed on 23 March 2021). 10. Wang, M.; Kilgore, I.M.; Steer, M.B.; Adams, J.J. Characterization of Intermodulation Distortion in Reconfigurable Liquid Metal Antennas. IEEE Antennas Wirel. Propag. Lett. 2018, 17, 279–282. [CrossRef] 11. Ng, K.J.; Islam, M.T.; Alevy, A.; Fais Mansor, M.; Su, C.C. Azimuth Null-Reduced Radiation Pattern, Ultralow Profile, Dual- Wideband and Low Passive Intermodulation Ceiling Mount Antenna for Long Term Evolution Application. IEEE Access 2019, 7, 114761–114777. [CrossRef] 12. Wu, D.; Xie, Y.; Kuang, Y.; Niu, L. Prediction of Passive Intermodulation on Mesh Reflector Antenna Using Collaborative Simulation: Multiscale Equivalent Method and Nonlinear Model. IEEE Trans. Antennas Propag. 2018, 66, 1516–1521. [CrossRef] 13. Towfiq, M.A.; Khalat, A.; Blanch, S.; Romeu, J.; Jofre, L.; Cetiner, B.A. Error Vector Magnitude, Intermodulation, and Radiation Characteristics of a Bandwidth- and Pattern-Reconfigurable Antenna. IEEE Antennas Wirel. Propag. Lett. 2019, 18, 1956–1960. [CrossRef] 14. Ansuinelli, P.; Schuchinsky, A.G.; Frezza, F.; Steer, M.B. Passive Intermodulation Due to Conductor Surface Roughness. IEEE Trans. Microw. Theory Tech. 2018, 66, 688–699. [CrossRef] 15. Pinho, P.; Santos, H.; Salgado, H. Design of an Anechoic Chamber for W-Band and mmWave. Electronics 2020, 9, 804. [CrossRef] 16. Zhao, F.; Liu, X.; Xu, Z.; Liu, Y.; Ai, X. Micro-Motion Feature Extraction of a Rotating Target Based on Interrupted Transmitting and Receiving Pulse Signal in an Anechoic Chamber. Electronics 2019, 8, 1028. [CrossRef] 17. Yousaf, J.; Lee, D.; Han, J.; Lee, H.; Faisal, M.; Kim, J.; Nah, W. Near-Field Immunity Test Method for Fast Radiated Immunity Test Debugging of Automotive Electronics. Electronics 2019, 8, 797. [CrossRef] 18. Zheng, Y.; Weng, Z.; Qi, Y.; Fan, J.; Li, F.; Yang, Z.; Drewniak, J.L. Calibration Loop Antenna for Multiple Probe Antennas Measurement System. IEEE Trans. Instrum. Meas. 2020, 69, 5745–5754. [CrossRef] 19. Matsukawa, S.; Kurokawa, S.; Hirose, M. Uncertainty Analysis of Far-Field Gain Measurement of DRGH Using the Single-Antenna Method and Amplitude Center Distance. IEEE Trans. Instrum. Meas. 2019, 68, 1756–1764. [CrossRef] 20. Zheng, J.; Ala-Laurinaho, J.; Räisänen, A.V. On the One-Antenna Gain Measurement Method in Probe Station Environment at mm-Wave Frequencies. IEEE Trans. Instrum. Meas. 2019, 68, 4510–4517. [CrossRef] 21. Zhang, L.; Wang, H.; He, S.; Wei, H.; Li, Y.; Liu, C. A Segmented Polynomial Model to Evaluate Passive Intermodulation Products From Low-Order PIM Measurements. IEEE Microw. Wirel. Compon. Lett. 2019, 29, 14–16. [CrossRef] 22. Shitvov, A.P.; Kozlov, D.S.; Schuchinsky, A.G. Nonlinear Characterization for Microstrip Circuits with Low Passive Intermodula- tion. IEEE Trans. Microw. Theory Tech. 2018, 66, 865–874. [CrossRef] 23. Wen, H.; Yang, H.; Kuang, H.; Qin, X.; Cai, G. Global Threshold Prediction of Multicarrier Multipactor With Time Distribution and Material Coefficients. IEEE Trans. Electromagn. Compat. 2018, 60, 1163–1170. [CrossRef] 24. Smacchia, D.; Soto, P.; Guglielmi, M.; Morro, J.V.; Boria, V.; Raboso, D. Implementation of Waveguide Terminations with Low-Passive Intermodulation for Conducted Test Beds in Backward Configuration. IEEE Microw. Wirel. Compon. Lett. 2019, 29, 659–661. [CrossRef] 25. Chen, X.; He, Y.; Yang, S.; Huang, A.; Zhang, Y.; Pommerenke, D.J.; Fan, J. Coplanar Intermodulation Reference Generator Using Substrate Integrated Waveguide with Integrated Artificial Nonlinear Dipole. IEEE Trans. Electromagn. Compat. 2019, 61, 969–972. [CrossRef] 26. Chen, X.; Yang, S.; Pommerenke, D.J.; He, Y.; Yu, M.; Fan, J. Compact Intermodulation Modulator for Phase Reference in Passive Intermodulation Measurements. IEEE Trans. Instrum. Meas. 2019, 68, 4612–4614. [CrossRef] 27. White, R.A.; Yell, R.W. Precise Differential-Phase Generator. IEEE Trans. Instrum. Meas. 1980, 29, 373–375. [CrossRef] 28. Hemming, L.H. Electromagnetic Anechoic Chambers; IEEE Press: Piscataway, NJ, USA, 2002; pp. 61–66. Electronics 2021, 10, 770 15 of 15

29. Silver, S. Microwave Antenna Theory and Design; Peregrinus: London, UK, 1984; pp. 585–586. 30. Zhang, Y.; Luo, Q.; Zhu, Y.; Liu, L. Development of conductive expended polypropylene rigid foam for OTA test chamber. Saf. EMC 2017, 16, 59–62. 31. Glimm, J.; Harms, R.; Munter, K.; Spitzer, M.; Pape, R. A single-antenna method for traceable antenna gain measurement. IEEE Trans. Electromagn. Compat. 1999, 41, 436–439. [CrossRef]