1 Overview
Intermodulation (IM, InterModulaTIon) refers to the radio frequency signal generated when two or more frequency signals pass through a device with nonlinear characteristics and has a relationship with the original signal, also known as intermodulation products, intermodulation or intermodulation products . In order to improve the system capacity, the phenomenon of using multiple carriers (frequency points) simultaneously in a communication system is very common, and the carrier power also tends to increase gradually; considering that the actual circuit usually has nonlinear characteristics, intermodulation and intermodulation interference become Common phenomena are found in cellular mobile communication systems, microwave communication systems, cluster mobile communication systems, satellite communication systems, ship communication systems, civil aviation communication systems, cable TV systems, etc. and attract wide attention.
Intermodulation is generally divided into active intermodulation and passive intermodulation. In view of the severity of the intermodulation products produced, people have traditionally focused on active intermodulation, but with the application of larger power transmitters and the continuous improvement of receiver sensitivity, system interference due to passive intermodulation is becoming more and more serious, so More and more attention is being paid by operators, system manufacturers and device manufacturers. Literature [1] compares the characteristics of active intermodulation and passive intermodulation:
The characteristics of active intermodulation: (1) the nonlinearity of the active circuit is relatively fixed and does not change with time; (2) the analysis theory is relatively mature; the indicators are clear and the specifications can give clear requirements for the indicators; (3) the transmission direction is relatively Stable; (3) It can be suppressed by adding bandpass / bandstop filters or improving filter performance, and high-order intermodulation interference is almost ignored.
The characteristics of passive intermodulation: (1) changes with power. The experiment of American Amphenol Company confirmed that every time the input power increases by 1 dBm, PIM produces a level change of about 3 dBm; (2) changes with time. The surface oxidation of the material, the contact pressure at the connection, and the degree of cable bending will change with time, which will affect the degree of nonlinearity. (3) Research theory lags behind, there is no substantial breakthrough in simulation research methods, and there is still a considerable distance from engineering. (4) There are many links and the transmission direction is not single, which is difficult to suppress. (5) There is high-order intermodulation.
Funding Information: This article is funded by the national "New Generation Broadband Wireless Mobile Communication Network" major special project "TD-LTE Network Optimization Tool Development" (2010ZX03002-008)
2 2 Generation mechanism of intermodulation [1] [2]
2.1 Harmonic generation mechanism
Assuming that there is only one single frequency signal input in the network, the relationship between the output signal and the input signal is as follows:
(1)
In the above formula, it is the DC term, the linear amplification term, and when the coefficients of the equal power order are non-zero, the output signal will have a nonlinear increase in distortion, that is, the so-called harmonic and intermodulation interference. After the single frequency signal is processed by the receiver, etc., the output signal is often accompanied by a signal of frequency N, which is called the Nth harmonic.
Suppose you input a single frequency sine wave,
Substituting into the Taylor expansion, the second power term on the right side of the expansion is:
(2)
In the above formula, there is a double-frequency signal (), which is usually called the second harmonic interference signal; similarly, the third power term on the right side of the expansion can get the third harmonic interference signal -----.
2.2 Generation mechanism of intermodulation
Assuming two single-frequency signal inputs in the network, then the interference generated at this time is intermodulation in addition to harmonics.
(3)
A. Derivation of 2nd order intermodulation
The 2nd power term after Taylor expansion is:
(4)
In the above formula, the mathematical transformation obtained by and is the second harmonic interference signal that has been introduced above, and after the triangular transformation, it is obtained:
(5)
The last two terms in this formula are the so-called second-order intermodulation terms, and the signal frequencies are: and.
B. Derivation of 3rd order intermodulation
The three power terms after the two standard sinusoidal signals are substituted into the Taylor expansion are:
(6)
In the above formula, the 3rd harmonic term caused by the mathematical transformation of and is obtained after the triangular transformation:
(7)
The last two terms in this formula are the so-called third-order intermodulation terms, and the signal frequencies are: 2f0-f1 and 2f0 + f1.
Similarly, two third-order intermodulation terms can also be obtained through triangle transformation, and the signal frequencies are: 2f1-f0 and 2f1 + f0, respectively.
Similarly, the 4th order intermodulation term, 5th order intermodulation term, and 6th order intermodulation term can be obtained.
General definition of BN order intermodulation
By extending the above analysis of dual-frequency signal intermodulation to multi-frequency, the general expression of intermodulation products in frequency can be obtained as,,, ---, is any integer value, that is, the order of intermodulation products.
Generally, the plus sign (such as f0 + f1, 2f0 + f1) in each pair of intermodulation products usually exceeds the working bandwidth, and only the minus sign (such as 2f0-f1, 3f0-2f1) may fall near the working bandwidth ; And for even-order intermodulation products, the minus sign terms (such as f0-f1, 2f0-2f1) are close to the DC term, and are usually outside the operating bandwidth. Therefore, the industry mainly focuses on the intermodulation of odd-order minus signs.
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