1、 Rep. ITU-R SM.2021 1 REPORT ITU-R SM.2021 PRODUCTION AND MITIGATION OF INTERMODULATION PRODUCTS IN THE TRANSMITTER (Question ITU-R 211/1) (2000) Rep. ITU-R SM.2021 TABLE OF CONTENTS Page 1 Introduction 2 2 Generation of intermodulation 2 2.1 Intermodulation products due to discrete frequencies. 2 2
2、.2 Intermodulation noise due to continuous frequency spectrum 5 3 Mitigation techniques . 7 3.1 Suppression at transmitters 8 3.1.1 Transmitter architecture. 8 3.1.2 Filtering . 9 3.1.3 Linearization 12 3.2 Site-shielding for inter transmitter intermodulation 17 3.2.1 Antenna spacing 18 3.2.2 Antenn
3、a pattern . 19 3.3 Other mitigation measures 19 3.3.1 Reduction of intermodulation products in receivers 19 3.3.2 Frequency arrangements 19 3.4 Examples of intermodulation products generated on a radio site with FM and public mobile radio (PMR) . 20 3.4.1 Intermodulation between FM transmitters. 21
4、3.4.2 Intermodulation between PMR base station transmitters 23 3.4.3 Intermodulation at the input of the PMR base station . 23 3.4.4 Intermodulation between FM and PMR transmitters 24 References and Bibliography. 25 Annex 1 Mathematical description of the generation of intermodulation noise in the t
5、ransmitter . 26 2 Rep. ITU-R SM.2021 1 Introduction There are various types of intermodulation that can be found. In radio systems, these are manifested in a number of ways and defined as the following five types in Rec. ITU-R SM.1446: Type 1: Single channel intermodulation: where the wanted signal
6、is distorted by virtue of non-linearities in the transmitter. Type 2: Multichannel intermodulation: where the wanted signals of multi channels are distorted by virtue of non-linearities in the same transmitter. Type 3: Inter transmitter intermodulation: where one or more transmitters on a site inter
7、modulate, either within the transmitters themselves or within a non-linear component on site to produce intermodulation products. Type 4: Intermodulation due to active antennas: the multicarrier operating mode of an active antenna, along with the non-linearity of amplifiers, originates spurious emis
8、sions under the form of intermodulation signals. Type 5: Intermodulation due to passive circuits: where transmitters share the same radiating element and intermodulation occurs due to non-linearities of passive circuits. The generation and mitigation of these intermodulation products are described i
9、n the following sections in more detail. Some examples of intermodulation products generated at radio sites are given. Measurement techniques are referred in Rec. ITU-R SM.1446. A comprehensive list of useful literature is attached at the end of the Report including references for the measurement of
10、 intermodulation Types 1 to 3 ETSI, 1997; Shahid et al., 1996; Bhargava et al., 1981; ITU-R Handbook on satellite communications fixed-satellite service (Appendix 2-1, 5); Heathman, 1989; Bond et Meyer, 1970; Shimbo, 1971; Saleh, 1982; Wassermann et al., 1983; Tondryk, 1991; Kaeadar, 1986; IESS, 199
11、6; ETSI, 1995. Instead of intermodulation products the expression intermodulation noise is also used in order to reflect digital modulation formats. 2 Generation of intermodulation Intermodulation has classically been a major determinant of transmitter performance for amplitude modulated services, s
12、uch as single sideband (SSB) or independent sideband (ISB). Theoretically, it does not apply to any constant envelope transmission, although in practice, practical implementation limitations lead to some of such modulation techniques not providing absolutely constant envelope modulation, and thus re
13、quiring linear amplification if spectral regrowth is to be avoided. 2.1 Intermodulation products due to discrete frequencies The following approach Chadwick, 1986 is classical and a complete analysis for input signal which can be represented by discrete frequencies like all analogue signals in the t
14、ime domain. It may be also helpful for the basic understanding of the generation of intermodulation products. An amplifier can be characterized by a Taylor series of the generalized transfer function Chadwick, 1986 .5544332210+INININININekekekekeki where i0is the quiescent output current, k1, k2, et
15、c. are coefficients and eINrepresents the input signal. When two sinusoidal frequencies 1= 2 f1and 2= 2 f2of the amplitude a1and a2are applied to the input of the amplifier, the input signal is: tataeIN 2211coscos += and the output iOUTmay be shown to be the sum of the DC components: ()()42214142221
16、20312382aaakaakiiOUT+= Rep. ITU-R SM.2021 3 fundamental components,: taakaakakaakakak1421522315515221331311cos815415852343Gf7Gf8Gf6Ge7Ge8Ge6+ taakaakakaakakak2241532215525221332321cos815415852343Gf7Gf8Gf6Ge7Ge8Ge6+ 2nd order components: taakakak1222144132122cos232121Gf7Gf8Gf6Ge7Ge8Ge6+ taakakak22221
17、44232222cos232121Gf7Gf8Gf6Ge7Ge8Ge6+ ()taakaakaak2132142314212cos2323Gf7Gf8Gf6Ge7Ge8Ge6+3rd order components: taakakak1223155153133cos4516541Gf7Gf8Gf6Ge7Ge8Ge6+ taakakak2322155253233cos4516541Gf7Gf8Gf6Ge7Ge8Ge6+ ()taakaakaak2132215241522132cos8154543Gf7Gf8Gf6Ge7Ge8Ge6+ ()taakaakaak1222315421522132co
18、s8154543Gf7Gf8Gf6Ge7Ge8Ge6+ 4th order components: taktak242414144cos814cos81+ () () ()taaktaaktaak21321421222142123143cos2122cos433cos21+ and 5th order components: taktak252515155cos1615cos161+ () ()taaktaak212231521241523cos854cos165+ () ()taaktaak21421521322154cos16532cos85+ 4 Rep. ITU-R SM.2021 T
19、he series may be expanded further for terms in 66 INek etc. if desired. The relationships between the different products are shown in Fig. 1. It can be seen from this Figure and the equations that all the even order terms produce outputs at harmonics of the input signal and that the sum and differen
20、ce products are well removed in frequency far from the input signal. The odd order products, however, produce signals near the input frequencies f1 2f2et f2 2f1. Therefore, the odd order intermodulation products cannot be removed by filtering, only by improvement in linearity. Rap 2021-01f1f2f2 f1f1
21、+ f22 f12 f2IM3, 2 f2 f1IM5, 3 f2 2 f1IM7, 4 f2 3 f1IM3, 2 f1 f2IM5, 3 f1 2 f2IM7, 4 f1 3 f2Level(unscaled)FrequencyFIGURE 1Unscaled intermodulation (IM) products (bold lines)related to the fundamentals (bold dashed lines)FIGURE 1.Rap.2021-01 Assuming class A operation, a1= a2and k4, k5are very smal
22、l. The 3rd order intermodulation product IM3becomes proportional to a3. That means that the cube of the input amplitude and the graph of the intermodulation products will have a slope of 3 in logarithmic scale while the wanted signal will have the slope of 1 (see Fig. 2). Secondorder products IM2can
23、 be similarly calculated, and the graph for these has a slope of two. The points where these graphs cross are called 3rd order intercept point IP3and 2nd order intercept point IP2, respectively. IP3is the point where the intermodulation product is equal to the fundamental signal. This is a purely th
24、eoretical consideration, but gives a very convenient method of comparing devices. For example, a device with intermodulation products of 40 dBm at 0 dBm input power is to be compared with one having intermodulation products of 70 dBm for 10 dBm input. By reference to the intercept point, it can be s
25、een that the two devices are equal. As the level of the input signal increases, a point is eventually reached at which the output cannot increase, dB for dB, with the input. This is gain compression, and is important in defining the dynamic range of the device. For example, assuming an amplifier wit
26、h 20 dBm intercept point and at 0 dBm input to obtain a 40 dB intermodulation ratio, but because the devices input/output characteristics are not linear at this input level, the expected intermodulation ratio is not obtained. If, however, the compression point is a few dB higher, then the intermodul
27、ation ratio of 40 dB could be obtained. In the case of class AB operation different characteristics may occur as plotted in Fig. 2, especially at lower input signals. Rep. ITU-R SM.2021 5 Rap 2021-02Input (dBm)Output(dBm)Gain compressionIP2IP3IM2IM3FIGURE 2Examples of 2nd and 3rd order IM products,g
28、ain compression in class A operationFundamentalFIGURE 2.Rap.2021-02 2.2 Intermodulation noise due to continuous frequency spectrum The classical description of intermodulation at analogue radio systems deals with a two-frequency input model to a memoryless non-linear device. This non-linear characte
29、ristic can be described by a function f(x), which yields the input-output relation of the element device. The function, f, is usually expanded in a Taylor-series and thus produces the harmonics and as well the linear combinations of the input frequencies. This classical model is well suited to analo
30、gue modulation schemes with dedicated frequency lines at the carrier frequencies. The system performance of analogue systems is usually measured in terms of signal-to-noise (S/N) ratio, and the distorting intermodulation signal can adequately be described by a reduction of S/N. With digital modulati
31、on methods the situation is changed completely. Most digital modulation schemes have a continuous signal spectrum without preferred lines at the carrier frequencies. The system degradation due to intermodulation is measured in terms of bit error ratio (BER) and depends on a variety of system paramet
32、ers, e.g. the special modulation scheme which is employed. For estimation of the system performance in terms of BER a rigorous analysis of non-linear systems is required. There are two classical methods for the analysis and synthesis of non-linear systems: the first one carries out the expansion of
33、the signal in a Volterra series Schetzen, 1980. The second due to Wiener uses special base functionals for the expansion. Both methods lead to a description of the non-linear system by higher order transfer functions having n input variables depending on the order of the non-linearity. A more detail
34、ed description and two examples are given in Annex 1. The block diagram of example 1 is shown in Fig. 3. The two data signals x1(t) and x2(t) are linearly filtered by the devices with the impulse responses ha(t) and hb(t) in adjacent frequency bands. The composite summed signal y is hereafter distor
35、ted by an imperfect square-law device which might model a transmit-amplifier. The input-output relation of the non-linear device is given by: )()()(2taytytz += 6 Rep. ITU-R SM.2021 The input signals x1(t) and x2(t) are originated from a single signal x(t), because of the spectral separation by the f
36、ilters ha(t) and hb(t). Rap 2021-03ha(t)hb(t)x2(t)x1(t)x(t)y1y2yzImperfectsquare-lawdeviceFIGURE 3Signals y1(t) and y2(t) in adjacent channels subjected toan imperfect square-law deviceFIGURE 3.Rap.2021-03 The output signal z (t) including the intermodulation noise is plotted in Fig. 4. For RF-modul
37、ated signals the intermodulation distortion in the proper frequency band is caused by non-linearities of third order. For this reason the imperfect square-law device in Fig. 3 is now replaced by an imperfect cubic device with the input-output relation: )()()(3taytytz += Rap 2021-04f0 1/T f0f0 + 1/T
38、0 f0 1/Tf0f0 + 1/TPbPaPaPb1a2/32 f0 2/T 2 f002 f0 + 2/T 2 f0 2/T 2 f02 f0 + 2/T2 Pa* PbPb* PbPa* Paf FIGURE 4Upper part: power spectra of the signals y1(Pa) and y2(Pb) according to Fig. 3,lower part: spectral contributions of the intermodulating second-order termFIGURE 4.Rap.2021-04 Rep. ITU-R SM.20
39、21 7 there are several contributions of the intermodulation noise falling into the used channels near f0. The different parts Pa Pa Pa. Pb Pb Pbare plotted in Fig. 5. The thick line shows the sum of the distortions. Rap 2021-05af0f0+ 3/TPa* Pa* Pa+ 2Pb* Pa* PbPb* Pa* Pa2 Pa* Pa* Pb+ Pb* Pb* PbPb* Pb
40、* Paf f0 3/TIn-bandOut-of-bandFIGURE 5Intermodulation noise in the used frequency bands f0 1/T , the isolation, L, is given by the free space equation: () ( )222111,MHzlog20mlog205.27 += GGfdL dB () ( )2221110, = GGLL dB where d is the spatial separation of the antenna (m), f is the frequency (MHz)
41、and G1, G2are the antenna gains referred to isotropic antennas and depending on incident angles. For isotropic and very small antennas, the isolation can be approximated by the basic free space loss: L L0. Regarding real antenna patterns in elevation and azimuth the actual isolation will be larger.
42、Examples for VHF/UHF broadcasting transmitters are given in Fig. 15 Pye Telecom, 1978. The graphs based on vertical antenna polarization indicate which attenuations are possible in the VHF/UHF bands for horizontal and vertical separation. It is shown that maximum attenuation is always easier to obta
43、in when antennas are separated vertically. Rap 2021-15110102252510203040506070FIGURE 15Isolation versus separation of vertically polarized antennas450 MHz 150 MHz 80 MHz 40 MHz150 MHz80 MHz40 MHzSeparation betweeen antennas (m)Isolation (dB)Vertical separationHorizontal separation450 MHzFIGURE 15 Ra
44、p.2021-15 Rep. ITU-R SM.2021 19 It is to consider that for lower frequencies or huge and closely located antenna arrays, the far field condition is not valid which yields to smaller values of isolation. If obstacles like buildings, the mast or even the antenna hardware itself are located in the main
45、 lobes of the antennas, reflections are likely to occur and the isolation is also reduced. 3.2.2 Antenna pattern The isolation is also influenced by the antenna patterns deployed at the radio site, e.g., using notches in the pattern can increase significantly the isolation. For illustration, in Fig.
46、 16 the isolation gained by an dipole and 8 element Yagi antenna are plotted versus the normalized wavelength RA, 1987. The diagrams indicate that a minimum isolation is achieved for parallel spacing of the antennas and the isolation of an omnidirectional dipole is about 10 dB worse than for the 8 e
47、lement Yagi antenna having a directional pattern. About 8 to 10 dB larger isolation is obtained by collinear installation. The difference between dipole and Yagi is about 2 dB, but the large value is gained by the dipole due to larger attenuation at 90 elevation. Rap 2021-161101022525102030405060FIG
48、URE 16Typical isolations between antennas8-element Yagiantenna with co-linearelementsSpacing normalized to wavelengthIsolation (dB)8-element Yagiantenna with parallelelementsParallel dipolesCo-linear dipolesCo-linearelementsParallelelementsFIGURE 16 Rap.2021-16 3.3 Other mitigation measures 3.3.1 Re
49、duction of intermodulation products in receivers Filtering should be used at the front-end of receivers to reject adjacent-band energy. Similar techniques as described for transmitters in 3.1 may be applied. If the input level of the wanted signal is high enough, an additional, variable RF attenuator should be inserted between the antenna feeder and receiver input. It permits the reduction of the
