Appendix A: Calculation Of Intermodulation Products - Shure Wireless Microphone Systems Operation Manual

R
E F E R E N C E
Appendix A
CALCULATION OF
INTERMODULATION PRODUCTS
The simplest IM products that can occur between any two
operating frequencies (f1 and f2) are the sum of the two
frequencies and the difference between the two frequencies:
f1 + f2 (sum)
f1 - f2 (difference)
If we choose f1 = 200 MHz and f2 = 195 MHz, then:
f1 + f2 = 200 + 195 = 395 MHz (sum)
f1 - f2 = 200 - 195 = 5 MHz (difference)
These IM products are sufficiently far away from the
original frequencies that they will generally not cause
problems to a third wireless microphone system in the
original frequency band.
However, as mentioned earlier, other products of
non-linear circuits are multiples of the original
frequency. That is, application of a single frequency to
a non-linear circuit will produce additional products
that are double, triple, quadruple, etc. the original
frequency. Fortunately, the strength of these products
decreases rapidly as the order (multiplication factor)
increases. The practical result is that only the products
at two times and three times the original frequency are
significant. Since these products then combine as
sums and differences with themselves and with
the original frequencies, the following additional
products can occur:
(2 x f1)
(2 x f2)
(3 x f1)
(3 x f2)
(2 x f1) ± f2
(2 x f2) ± f1
(3 x f1) ± f2
(3 x f2) ± f1
(2 x f1) ± (2 x f2)
(3 x f1) ± (2 x f2)
(3 x f2) ± (2 x f1)
(3 x f1) ± (3 x f2)
The "order" or type of IM product is identified by the
particular combination of frequencies that created it. The
order of an IM product is the sum of the multipliers
(coefficients) of the frequencies in the expressions above.
The complete group of possible frequencies (original
frequencies, intermodulation products and combinations)
that can exist when two systems (at 200 MHz and 195 MHz
for this example) are operated simultaneously is thus:
I
N F O R M A T I O N
Product
f1 (original frequency) 1
f2 (original frequency) 1
2 x f1
2 x f2
f1 + f2
f1 - f2
3 x f1
3 x f2
(2 x f1) + f2
(2 x f1) - f2
(2 x f2) + f1
(2 x f2) - f1
(3 x f1) + f2
(3 x f1) - f2
(3 x f2) + f1
(3 x f2) - f1
(2 x f1) + (2 x f2)
(2 x f1) - (2 x f2)
(3 x f1) + (2 x f2)
(3 x f1) - (2 x f2)
(3 x f2) + (2 x f1)
(3 x f2) - (2 x f1)
(3 x f1) + (3 x f2)
(3 x f1) - (3 x f2)
Though
combinations is lengthy, it can be seen that only the IM
products at 185, 190, 205 and 210 MHz are in the same
general band as the two original operating frequencies.
These products will not cause compatibility problems
between the two original systems but can interfere with
other systems that may be added in this band. In this
example, the operating frequency of a third system should
be chosen to avoid these four IM frequencies. In general,
only odd-order IM products are considered because
even-order products typically fall well away from the original
frequencies, as shown above. Furthermore, though higher
odd-order IM products may also fall near the original
frequencies, only 3rd order and 5th order IM products are
strong enough to be of concern.
If three or more systems are operated simultaneously,
the situation becomes somewhat more complicated but the
same principles apply. In addition to the IM products
calculated for each pair of frequencies, products due to
combinations of three transmitters must also be considered.
Two-Transmitter Intermodulation Calculation
Order Frequency
200
195
2 400
2 390
2 395
2 5
3 600
3 585
3 595
3 205
3 580
3 190
4 795
4 405
4 785
4 385
4 790
4 10
5 990
5 210
5 985
5 185
6 1185
6 15
this list of calculated
Significant
Yes
Yes
No
No
No
No
No
No
No
Yes
No
Yes
No
No
No
No
No
No
No
Yes
No
Yes
No
No
frequency
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