Preprint. This is the submitted version of a paper published in Electronic environment.

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1 Preprint This is the submitted version o a paper published in Electronic environment. Citation or the original published paper (version o record): Stranneb, D. (0) A Primer on PIM. Electronic environment, (): 0- Access to the published version ma require subscription. N.B. When citing this work, cite the original published paper. Permanent link to this version:

2 A Primer on PIM Background PIM is an acronm or Passive InterModulation, an intererence problem in wireless sstems. The problem is not new, but has been known since long time back b designers o, or instance cell phone sstems, space probes, connectors, coaxial cables, antennas and ilters. The problem most requentl occurs, when dealing with high RF-currents in conined spaces. In this text, the basic theories behind PIM will be briel discussed. Intermodulation Intermodulation is a process where two or more signals, having requenc components,, etc, are mixed in such a wa, that new requenc components, not belonging to the initial set o requencies, are created. In some applications, or instance ampliiers, intermodulation causes distortion o the signal, and is not a desired propert. In mixers, modulators and demodulators however, intermodulation is used to shit signals rom one requenc band to another. In this case, it is a desired eature. For intermodulation to occur, two or more signals need to be multiplied. A common wa to achieve this is to add the signals, and to pass the sum through a nonlinear device. To illustrate the properties o a nonlinear device, let us start with the concept o linearit. Assume we have or instance an ampliier, with input signal ( a linear case, be expressed as: ( kx( x and output signal (. The relation between the two signals can, in =, where k is the gain, which is a constant. The linear ampliier is simpl a perect proportionalit, as shown in igure. A straight line, passing thru the origin, where k is the slope o the line. Figure, the transer curve o a linear device Now, assume the input signal x ( to the device consists o two ine unctions, with requenc and respectivel: ( = ( π + ( π x then, the output signal ( will be: ( = kx( = k ( π + k ( π

3 The output signal onl contains requencies Perect!,,, the same requencies as in the input signal. Now, or the nonlinear device, sa or example that the transer unction o the ampliier is: ( x ( igure. =, i.e. the output signal is the input signal raised to three. An example can be ound in Figure, example o transer curve o a nonlinear device This is certainl NOT a straight line, and is thereore a nonlinear transer unction. The ormal requirements o a linear transer unction are: d = k and = 0 at x = 0. dx I the same input signal as above is applied to this nonlinear device, the output signal will be: ( = x ( = ( ( π + ( π ) = ( π + ( π ( π + ( π ( π + ( π The our terms can be rewritten as: ( π = ( ( π + ( π ) ( π ( π = ( π + ( π ( ) + ( π ( + ) ( π ( π = ( π + ( π ( ) + ( π ( + ) ( π = ( ( π + ( π ) Here it is obvious that a number o new requenc components have been created. I we examine the expression above, we ind:, are the original requenc components, no problem. The requenc components +, +,, are quite high requencies, compared to the desired ones, and can oten be iltered out easil. But and pose problems, since the are close to the desired requencies, and cannot be removed using ilters.

4 In this case, the nonlinearit had the exponent, and the requenc o the problematic intermodulation products were and. I the exponent had been 5, the problematic requencies would have been and. For exponent 7, and would be created. In the general case, this group o intermodulation products, can be expressed as IM = m n, where m and n are integers. The order o the intermodulation products are obtained as m + n. So ar, onl odd exponents, i.e. intermodulation orders have been studied. It is an interesting act, that even numbered orders never produce requenc components close to the desired, original requencies, and thereore, in most cases do not present a problem. Nonlinearities The nonlinear mechanisms considered in this context are passive. Passive means that the device does not have a power suppl. Examples: connectors, cables, antennas etc. It ma even suggest that mechanical, non-electric parts, e.g. cable clamps, handles and bolts can act as passive nonlinearities. Nonlinearit oten gets more pronounced at higher signal levels, i.e. strong RF-currents. There are basicall two situations, where a part ma carr strong RF-currents. The irst case is conducted current. Current originating rom e.g. a strong radio transmitter. A tpical situation is RF-current lowing in cables, connectors, cable joints and antennas. I, or instance, a connector act nonlinearl, intermodulation products ma be created. The second case is current induced b radiation. Metallic parts in the vicinit o a transmitter antenna, will pick up RF-power rom the electromagnetic ield and convert it into a RF-current in the part. I the part has a nonlinear behavior, intermodulation products ma occur, which will then be reradiated as wireless intererence. But wh do metallic parts have nonlinear current behavior? There are mainl two mechanisms involved. The irst one is the properties o the conducting material itsel. For example, some magnetic materials ma exhibit a nonlinear perormance, due to the act that the current causes magnetic ields, and that magnetization curves are nonlinear or strong currents. In other cases, the nonlinearit o a material ma be caused b polarization issues. The second mechanism is caused b surace eects in the interace between two materials. For example, oxidation on a contact surace ma contribute a MIM-diode. MIM stands or Metal- Insulator-Metal. This is a nonlinear quantum eect. MIM-diodes suer rom poor mechanical stabilit, but the can operate at ver high requencies, above 0 THz. The have also been considered or solar energ conversion. So, to avoid PIM problems, select materials careull, and keep our connector suraces clean rom oxide and dirt. PIM in practice We will use a tpical GSM base station to illustrate the practical problems with PIM. The GSM sstem is a ull duplex sstem, which implies that all transmitters and receivers will operate simultaneousl. To avoid intererence, dierent requencies are used. In or instance the P-GSM-900 band, an uplink band is deined between MHz, and a downlink band between MHz. The uplink is rom the handset to the base station, and the downlink the other wa round.

5 Tpicall, we will ind a number o prett strong radio transmitters transmitting in the downlink band, while a number o sensitive radio receivers operate in the uplink band. Obviousl, we do not want an signals rom the downlink to interere with the delicate signals in the uplink. As long as everbod stas on their allocated requenc, all will work ine. However, intermodulation has the nast eect o creating new requencies that are not expected... The downlink band harbors channels. I we transmit on p channels, there ma occur p ( p ) problematic intermodulation products. This means that in worst-case, 55 intermodulation products will be generated. This is a simpliied example, in realit there are man more requenc components to take into account (due to the modulation o the signals). Oten, the intermodulation products ma not be experienced as discrete requencies, but rather as a general increase in the noise loor. Where in the requenc band ma the intermodulation products show up then? Doing some calculations, varing the transmitting requencies and rom the lower to the upper limit o the downlink, we can ind the location o the intermodulation products. For third order products the requenc o the intermodulation products are given b and, or the ith order b and and or the seventh order b and. As can be seen in igure, the intermodulation products occur pair wise and smmetricall round the downlink band. Yellow is the downlink. Purple is the third order, blue ith order and pink seventh order intermodulation products. (Onl intermodulation products outside the downlink band shown). Figure, requenc ranges o uplink, downlink and intermodulation products outside the downlink The green band in igure is the uplink. It is clear that the requenc range o the intermodulation products overlap considerabl, and that the risk or intererence is imminent. Raising the noise loor, in the sensitive uplink, degrades the perormance o the radio links and the base station, thus reducing the revenue. So, at last, a word o wisdom: Sta linear! Dag Stranneb Dag is perorming PIM studies at Campus Alred Nobel, Örebro Universit, in collaboration with Nolato AB in Hallsberg, Sweden. More inormation can be ound at: