IMPACT OF POWER VARIATION ON 3RD ORDER PASSIVE INTERMODULATION OF
COAXIAL RF-CABLES AND THEIR CONNECTORS
Hartmut Gohdes
RFS kabelmetal, Division of kabelmetal electro GmbH, D-30179 Hannover, Germany
Abstract
Aim of the work was to find out the relationship between the 3rd order intermodulation-signal generated by
cable assemblies and the stimulating power level. The theoretical relationship will be described, and
statistically evaluated results of measurements of different types of cable assemblies will be presented and
discussed. Possible reasons and proposals for further investigations will be given.
Introduction
During the last years, wireless telecommunication has increased significantly. Therefore the available
frequency-spectrum has to be used efficiently. Beside the increase of information rate by using digital
information transfer and multiplex-modulation, smaller band- and channel-spacings are possibilities to reach
this aim. This bears problems to solve.
One of those problems is distortion caused by 3rd order intermodulation products of passive devices (IM3products).
For that reason, 3rd order intermodulation is a topic of growing interest. Manufacturers and customers are
discussing IM3 values, which are determined by different test-methods, at different frequencies, and at
different power levels of the stimulating signals.
Generation of passive intermodulation
IM-products are generated in non-linear devices at all possible sum- and difference-frequencies of two or
more signals. They are disturbing, if they fall into the band of operation. Often this is the case with IMproducts of odd order. 3rd-order IM-products are generated at the frequencies fim3 = 2 ⋅f1 ± f2 , and are
generally of higher level than those of 5th and higher orders.
If fim3 falls into a receiving-channel, this signal is disturbing transfer of information.
IM-products can be generated by active components (amplifiers etc.) and passive components like filters,
duplexer, RF-cables, waveguides and antennas.
Sensitivity to unwanted signals is very high in passive components, if they are used for transmission and
reception at the same time. Unwanted signals caused by the high power transmitters can disturb low level
received signals.
1
If we assume two signals:
u (t ) = U1 * cos(ω 1t ) + U 2 * cos(ω 2 * t + ϕ ) (1)
and a characteristic of the device:
i (t ) = a1 * u (t ) + a2 * u 2 (t ) + a3 * u 3 (t ) (2)
intermodulation of 3rd order is generated among signals of other frequencies:
i 3 (t ) = c12 * U1 * U 2 * cos(2ω 2 − ω 21 )t + 2ϕ )
2
+ c21 * U 2 * U1 * cos(2ω 1 − ω 2 )t − 2ϕ )
2
(3)
If the power series is expanded to powers higher than 3, it can be observed, that coefficients of higher
power also contribute to the 3rd order IM-level, because they also produce signals of 2ω 2 − ω 1 and
2ω 1 − ω 2 [1].
The amplitude of the IM3-signal is depending on the amplitudes of the input signals. If c12 and c21 are
considered as constants and contribution of coefficients of higher power is neglected, equal variation of the
signal-power of both signals causes three times the power variation of the IM3-signal. This relationship can
be displayed as a straight line with a constant gradient of 3 in logarithmic scale. If there is any contribution
of IM from higher power coefficients, the gradient will deviate from this value.
Sources of intermodulation are considered as point sources inside the device under test. Hence, the IM3signal is propagating in both directions of a two-port device.
Measurement
Measurement of passive IM3 is a comparatively new challenge to the industry, so standardization of
techniques and procedures is in process actually in IEC TC 46 WG 6. RFS kabelmetal is contributing to
these international standardization efforts.
IM3-products of passive components are usually of much smaller level than those of active components.
IM3 products of cable assemblies are typically in the range of -150 dBc to -160 dBc. Hardware for the test
set-up must be selected carefully or built by oneself to achieve lowest self-intermodulation.
The measurements were performed with two different set-ups. One for the 900 MHz range (GSM) and one
for the 1800 MHz range (DCS 1800). In both cases reflected intermodulation was measured. To prevent
high intermodulation generation, like it is the case with lumped terminations, the DUT was terminated by
approximately 120 m of 1/4" cable with a soldered connector. The filters and duplexers are selected from
standard GSM- and DCS 1800 hardware. The block-diagrams are shown in figure 1 and 2.
Synthesizer-sources are locked to the frequency reference of the spectrum-analyzer to perform accurate
zero-span measurements. Each signal is amplified by a 100 W power-amplifier to the desired level.
Combination of the two signals is done in the 900 MHz-set-up by two filters and tuned lines, in the 1800
MHz set-up by a 3 dB-hybrid. Therefore the 900 MHz-set-up works only with a particular pair of frequencies,
while the 1800 MHz-set-up can be run with different pairs. The task of the duplexer is to separate the lowlevel IM3-signal from the high-level stimulating signals. It is one of the most critical parts of the set-up. It
must provide only the lowest and the most stable IM3-products. The duplexer is supplying the stimulating
signals to the DUT, which is connected to the other critical component, the cable-load. It must also be of
very low intermodulation. The portion of the IM3-signal, which is travelling back into the duplexer, is
separated, filtered and amplified before it is displayed on the screen of the spectrum-analyzer. The IM3frequency is 914 MHz, or 1760 MHz, respectively. The LNA allows a fast and low noise signal detection.
Spikes of a short risetime can still be detected with those set-ups.
2
Figure 1: 900-MHz IM3-set-up
Figure 2: 1800 MHz IM3-set-up
Calibration of the set-up is done in two steps: The gain of the IM3-path is measured with a calibrated source
connected to the testport, and the level of the stimulating signals is adjusted with a calibrated powermeter
connected to the testport.
Once the set-up is calibrated, IM3-level of the system itself without a DUT must be measured. The selfintermodulation limits the dynamic range of the measurement system. In table 1, the level of selfintermodulation for every input-level is noted.
900 MHz [dBm]
System IM3 [dBm]:
1800 MHz [dBm]
System IM3 [dBm]:
37
-134
37
-136
40
-128
40
-134
43
-123
43
-128
46
-113
46
-122
48
-107
-
Table 1: power level of each signal and level of system-IM3
Self-intermodulation and measurement error introduce measurement uncertainties into the measurement. In
this case, measuring intermodulation of 10 dB more than the system-intermodulation at 43 dBm input levels
causes a measurement error of approximately ± 5,5 dB. If relative measurements are done, the
measurement error is reduced to about ± 2 dB, because system IM3-level is subtracted nearly completely
from the results. Noise of the spectrum-analyzer and level uncertainty of the sources remain.
To minimize the influence of measurement error and piece-to-piece deviation, a number of 20 - 30
assemblies of each type was tested. It was noted, that intermodulation-level changed by some dB, if the
same DUT was connected and measured several times. For that reason, all power levels were adjusted and
stored into the memory of the synthesizers, before the measurements were started. Measurements were
done by connecting the DUT to the set-up once and measure it at every stored power-level.
First measurements were taken with 0,5 dB steps. Due to the measurement uncertainty, the changes of
intermodulation were too small to give reliable results. Since 0,5 dB steps gave no further information, 3 dBsteps respectively 2 dB steps were used instead. The power levels are shown in table 1.
The different types of assemblies are shown in table 2.
3
Only devices with 7-16 connectors were tested, because IM3-performance of this connector-type is
substantially better than of other connector types. For low-intermodulation applications, this connector will
be chosen in most cases.
Type
Length
1 High flexible jumper 1/2"
2 High flexible jumper 1/2"
3
jumper 1/2"
4 High flexible jumper 1/2"
5
jumper 1/2"
6
cable 7/8"
2m
2m
2m
1,5 m
1,5 m
1,5 m
I.C.
material
copper clad alumi-nium wire
silver coated copper strand
copper wire
copper clad alumi-nium wire
copper wire
copper tube
O.C.
material
Copper
Copper
Copper
Copper
Copper
Copper
I.C.
contact
Soldered
Soldered
Soldered
Spring Finger
Spring Finger
Spring Finger
O.C.
contact
Soldered
Soldered
Soldered
Flared
Collet
Collet
Table 2: Tested cable assemblies
Measurement results and evaluation
The evaluation procedure for assembly type 1 will be described in great detail. The results of the other types
were evaluated similarly.
Thirty samples were tested. Mean value and standard deviation were calculated for each power-level.
Figure 3 shows the results of the 900 MHz measurements in a diagram, figure 4 those of the 1800 MHz
measurements. Mean values and standard deviation of the measurements are presented by the triangles
and the whiskers. A linear regression line is calculated from all the mean values. It is plotted as "linear
(Assembly Type 1)". This allows a visual check of the correspondence between measured values and
regression line. Assuming that the relationship between change of stimulating levels and change of IM3level is constant, this relationship is characterized by the gradient of the regression line.
R2 is a measure of certainty, which also gives information about the correspondence between data and
regression line.
Intermodulation of Assembly Type 1 (900 MHz)
-110,00
IM level [dBm]
-115,00
-120,00
Assembly Type 1
-125,00
Linear (Assembly Type 1)
-130,00
y = 1,721x - 198,88
R 2 = 0,9927
-135,00
-140,00
37
39
41
43
45
47
Input level [dBm]
Figure 3: Intermodulation 900 MHz of Assembly type 1
Intermodulation of Assembly Type 1 (1800 MHz)
-110,00
-115,00
IM level [dBm]
-120,00
-125,00
Assembly Type 1
-130,00
Linear (Assembly Type 1)
-135,00
-140,00
y = 1,3711x - 185,88
R2 = 0,9096
-145,00
-150,00
37
39
41
43
45
47
Input level [dBm]
Figure 4: Intermodulation 1800 MHz of Assembly type 1
Because assembly 1 is a specially IM3-optimized product, IM-values appear very low and stable. They are
very close to the system dynamic. Standard deviation of the measurements with one power level is higher
at 1800 MHz than at 900 MHz.
4
Assembly 4 is made of the same cable-type as Assembly 1, but with non-soldered connectors. The contact
zone of the helically corrugated outer conductor is not so well defined as it is for the soldered assembly type
1. Also the inner conductor spring finger contact causes more IM3 as its soldered counterpart. This type of
assembly shows the highest level of IM3 and the maximum standard deviation of all tested types. For that
reason, we can achieve the best measurement accuracy with this type.
Like for assembly type 1, standard deviation for 1800 MHz is higher than for 900 MHz.
Figure 5 and Figure 6 show the results of the measurements and the regression line.
Intermodulation of Assembly 4 (900 MHz)
-80,00
37
39
41
43
45
47
IM level [dBm]
-90,00
-100,00
Assembly Type 4
-110,00
Linear (Assembly Type 4)
-120,00
-130,00
y = 2,6843x - 226,04
R2 = 0,9999
-140,00
Input level [dBm]
Figure 5: Intermodulation 900 MHz of Assembly type 4
Intermodulation of Assembly Type 4 (1800 MHz)
-80,00
37
39
41
43
45
47
IM level [dBm]
-90,00
-100,00
Assembly Type 4
-110,00
Linear (Assembly Type 4)
-120,00
-130,00
y = 2,4217x - 212,41
R2 = 0,9996
-140,00
Input level [dBm]
Figure 6: Intermodulation 1800 MHz of Assembly type 4
Table 3 and Table 4 show the number n of tested devices, the gradient of the regression-line and R2 for all
tested types of assemblies:
Type
Type 1
Type 2
Type 3
Type 4
Type 5
Type 6
n
30
20
20
20
20
20
lin. reg.
1,72
2,0
1,48
2,68
2,17
1,79
2
R
0,99
1,0
0,99
1,0
1,0
1,0
Table 3: Regression gradient 900 MHz
Type
Type 1
Type 2
Type 3
Type 4
Type 5
Type 6
n
30
20
20
20
20
20
lin. reg.
1,37
2,27
1,36
2,42
1,96
0,83
2
R
0,91
1,0
1,0
1,0
0,98
0,94
Table 4: Regression gradient 1800 MHz
5
Discussion
The quality of approximation of the regression-line is indicated by the measure of certainty (R2).
For most types, R2 is very good and near to 1. Assembly type 1 has a worse R2 of 0,91 at 1800 MHz, and R2
of assembly type 6 at 1800 MHz is 0,94.
In both cases, the measured IM3 is very close to the noise-floor. Thus the measurement uncertainty for
37 dBm stimulating power is very high. If the IM3-values of 37 dBm are excluded from the data of these two
data sets, R2 is increasing.
Table 5 shows the results of the corrected 1800 MHz measurements.
Type
Type 1
Type 2
Type 3
Type 4
Type 5
Type 6
n
30
20
20
20
20
20
2
lin. reg.
1,86
2,27
1,36
2,42
1,96
1,08
R
0,98
1,0
1,0
1,0
0,98
0,99
Table 5: Corrected Regression gradients at 1800 MHz
Now the linear regression-line-model seems to describe the examined behaviour sufficiently well, but still
the calculated gradient is not constant.
Neglecting the contribution of coefficients of higher power than 3 at the frequency of the 3rd order, the
expected gradient is 3.0
Among the different types of assemblies and even between the two frequency-ranges, remarkable
differences can be observed. The gradient of the regression line varies from 1,08 up to 2,68.
There are several possible reasons:
1. The factors c12 and c21 are not constant and depending on the applied power of the stimulating signals.
In [2] a variety of mechanisms are given, which can be responsible for the generation of IM3-products.
These effects are different in their characteristic dependency on the stimulating power. It is most likely,
that for every stimulating power-level a different combination of those effects are dominant. Hence, c12
and c21 are a result of the actual combination of effects.
2. Contribution of the higher power terms at third order frequencies is not negligible.
Expansion of the power series to an odd power higher than 3 shows, that the terms of higher odd power
also produce mixing signals at third order IM-frequencies. The IM3-signal will be influenced by each of
the different contributors of the higher powers. Figure 5 shows an example for the superposition of a
positive 3rd power coefficient (Pout1) and a negative 5th power coefficient (Pout2). The result is plotted
as 'Poutges'. An extreme value can be observed at the point of intersection of 'Pout1' and 'Pout2'. Left of
it the gradient is less, and right of it more than 3.
0
0
10
20
Pout1( x )
30
Pout2( x )
40
Poutges( x )
50
60
70
70
10 9
10
8
7
6
5
4
3
2
1 0
1
20. log( x )
2
3
4
5
6
7
8
9 10
10
Figure 7: Influence of negative higher order coefficient
6
3. IM3-level is depending on the duration of RF-penetration.
The devices were tested with consecutively increased power-levels. It might be possible, that the IM3level changes during the test due to heating- or 'burn in'-effects. However, this is most unlikely, because
some tests with consecutively decreased power-levels gave the same results as with increased powerlevels.
Conclusion
6 Types of cable assemblies of different construction and IM3-behaviour were selected. 20 to 30 samples of
each type were measured. The relation between IM3-level and stimulating power-level was characterized.
Statistical evaluation of the result shows an individual behaviour of each type at each frequency-range.
Some possible reasons were given.
The conclusion of the experiment is, that only those IM3-values of similar stimulating signal-level can be
compared.
It is not allowed, to calculate IM3-levels for other stimulating signal-levels, in order to make measurements
at different power levels comparable.
It is highly recommended, to adjust the level of
measurement.
the stimulating signals very accurately for any
Some possible explanations have been given. To prove those theoretical considerations, further
examinations are necessary. Especially test-set-ups with higher dynamic ranges and higher power-levels
promise to give deeper understanding.
ACKNOWLEDGEMENTS
The author would like to thank Dr. Nagel and Mr. Fischer of RFS kabelmetal for encouragement to write this
paper and for the fruitful discussions.
Also Mr. Schumacher and Mr. Bernasch have to be mentioned, who made innumerable IM3-measurements.
References
[1]: "A Study Of Multipaction in Multicarrier RF Components", J.S. Petit, A.D. Rawlins, p. 41 ff.
[2]: "A Study Of Passive Intermodulation Interference in Space RF Hardware", A.P. Foord, A.D. Rawlins, p.
60 ff.
Author
Hartmut Gohdes
RFS kabelmetal
Kabelkamp 20
D-30173 Hannover
Germany
Hartmut Gohdes was born in 1963. He studied electronics at the Fachhochschule Hannover and obtained
his Dipl.-Ing. (FH) degree in 1991. In the same year he joined RFS kabelmetal as a development engineer,
where he is responsible for the design of transmission lines. He is engaged in the field of RF-measurement,
especially the measurement of passive intermodulation.
Remark
The above article is a reprint from the proceedings of the 46th International Wire and Cable Symposion,
Philadelphia, Pennsylvania, Nov. 17 – 20, 1997
7