# What are the sources of passive intermodulation? How to solve passive intermodulation?

In our conventional understanding, RF passive components are all linear components. The coupling degree of the coupler, the loss and attenuation of the filter, the gain of the antenna, etc., we only need to add or subtract these components in the dBm format of the power. The corresponding dB value is sufficient.

In a time division duplex TDD system, transmission and reception are separated by time, and the intermodulation of the transmit link is not as concerned as in the past in frequency division duplex FDD.

I have been at ease for so long that I gradually forget the pain I once suffered. Especially those suffering from passive intermodulation in the production of FDD filters are so painful that they can only use metaphysics to explain the source of these PIMs, so that some people who are not so firm in their atheism have the idea of burning incense and praying to Buddha for help.

Today's RF engineers are indeed much happier than before.

The following are examples of failures caused by PIM products in satellite communications:

US Fleet Communications Satellite FLTSTCOM**Level 3**the American maritime satellite MARISAR**Level 13**European Intelsat V IS-V**Level 27**and even the European Maritime Satellite MARECS**Level 43** The PIM products fell into the receiving passband and caused interference, which once affected the development progress and use of some foreign satellite systems.

The impact of levels 3, 5, and 7 is relatively large, and it is easier for us to understand. Is it a bit too much to consider both levels 27 and 43?

Therefore, in RF design, being cautious at any time may cause unexpected losses.

So what are the sources of passive intermodulation? How to solve it? Let’s discuss it together today.

** **** **** Mathematical explanation of intermodulation products**

When we study the book "Signals and Systems", there is a relatively important concept - linear time-invariant system LTI.

A linear time-invariant system requires that when a signal passes through the system, it can be amplified, reduced, and delayed, but the basic characteristics of the signal remain unchanged. Mathematically, it must satisfy homogeneity, superposition, and time invariance. The following figure shows the comparison. Vivid explanation.

This forms the mathematical basis of our communication, and is also the effect that all communicators dream of achieving - all information can be transmitted without distortion.

To put it simply, the output y of this system is a linear function of the input x. To explain it in advanced mathematics, the first derivative of the function is a constant.

On the stage of the assumption of linear time-invariance, we dance wildly, forgetting that everything is as illusory as Jia Baoyu's Taixu illusion.**nonlinear**This is the normal state of this world.

Any change is uncertain, and the relationship between quantities is not a simple linear relationship.

Come on, it’s time to make up your math homework!

The transfer function of a nonlinear system can be expressed by an n-order Taylor series polynomial:

Of course, the transfer function of a linear system can be expressed as the first order of the Taylor series:

So in terms of transfer functions, linearity is just a special form of nonlinearity. Although we all like this simple equation, the reality is cruel. The Taylor series above with infinite polynomials is the reality.

Come on, put in the signal and see what comes out?

Let's be lazy and remove all the rest of this nonlinear system, leaving only the first three items:

At the same time, assume that the input signal is the simplest linear combination of two cosine signals of different frequencies.

So what is the output?

Continuing to expand trigonometric functions, have you suddenly discovered that trigonometric functions were born to solve communication problems?We use the sum-difference-product formula of trigonometric functions to expand it to get

It's simply terrible. Two signals of two frequencies come in, and a bunch of signals come out, and they are still a simplified version of nonlinearity. If it were standard nonlinearity, wouldn't it produce more results?

After calming down a bit, let’s take a look at what this product has to offer?

1. Frequency close to DC: w1-w2, DC

2. Frequencies close to the input signal: w1, w2, 2w1-w2, 2w2-w1,

3. Frequency of second-order harmonic: 2w1, 2w2

4. Frequencies near third-order harmonics: 3w1, 3w2, 2w1+w2, 2w2+w1

Put it in the frequency domain as shown below:

Normally, the two intermodulation signals 2w1-w2 and 2w2-w1 are close to the main signal, which will cause adjacent channel interference in the band. They are items that are often noticed in radio frequency design. The other items are far away from the main signal. For the intermodulation products produced by the active part, a filter can be added at the back end to filter out, but if it is the intermodulation product produced by the passive filter and the antenna, there is nothing you can do.

** **** **** **Physical mechanism of intermodulation products

For the active circuit part, the nonlinear explanation is relatively sufficient and the research is relatively thorough. For example, the mixer itself uses the nonlinearity of the circuit to complete the function of mixing the modulated signal and the carrier signal; as for the power amplifier, in order to pursue higher efficiency, it often works in the saturation region of the transistor, and the gain caused by the nonlinearity is A little bit of compression leads to a non-linear relationship between the output signal and the input signal.

The nonlinearity of passive devices is even more wonderful, so that sometimes, people can only turn to metaphysics. However, as people's research deepens, the physical mechanism of passive nonlinearity gradually appears before our eyes.The nonlinearity of passive devices can be mainly divided into**Material nonlinearity and contact nonlinearity**.

The nonlinear phenomena of materials include the following aspects:

1. Electron tunneling effect of dielectric thin layer: For example, the thin layer of aluminum oxide on the surface of aluminum material has this electron tunneling effect.

2. Ferromagnetic effect: Ferromagnetic materials have high magnetic permeability and change nonlinearly with the magnetic field, resulting in hysteresis effect; common ferromagnetic materials include iron, magnetic steel, cobalt, nickel, etc. Should be avoided in the design of RF passive components;

3. Electrostriction, that is, nonlinear changes in the electric field. For example, electrostriction produced in PTFE dielectric will contribute to PIM in coaxial cables;

4. Magnetoresistance, a change in the resistance of a metal conductor caused by a magnetic field;

5. Micro-discharge effect, due to the multiplication of secondary electrons due to the ion gas generated by a strong electric field, such as micro-discharge between micro-slits and across blisters in metal;

6. Dielectric breakdown, etc.

Of course, there are also space charge effects, ion conductivity, thermionic emission effects, internal Schottky effects, etc., which will cause nonlinearity of passive devices, thereby producing intermodulation signals.

** **** **** **contact nonlinearity

Contact nonlinearity mainly includes nonlinearity caused by material structure and aging.

1. The nonlinearity caused by the material structure mainly includes: the installation of different parts, such as resonators, connectors, tuning screws, etc., as well as micro cracks caused by bending of the material structure. The generation mechanism mainly includes mechanical effects and electronic effects caused by poor contact on the contact surface.

2. Nonlinearity caused by aging mainly means that as time increases, loosening or sliding of the contact surface will cause poor contact. In addition, the production of metal oxides will lead to more nonlinearity.

** **Summarize

In radio frequency design, nonlinearity is the norm. How to deal with the problems caused by nonlinearity is a final question that examines the design skills of radio frequency engineers. But normality does not mean that there will definitely be an impact. What we should do is to reduce its impact as much as possible.

If there is an effect, there must be a cause. When you encounter a problem, first try to find the root of the problem, and then the solution will emerge.

Review Editor: Huang Fei

#sources #passive #intermodulation #solve #passive #intermodulation

latest Update

- New audio design services launched
- Analysis of electrostatic surge protection scheme for NB-IoT device antennas
- New product launch | Xianji Semiconductor joins hands with VeriSilicon to break through multimedia MCU performance and create a new generation of digital instruments
- Innovative expanded beam fibre optic connector technology
- Key Trends in Gas and Particulate Sensor Technology
- What is the pipeline of a superscalar processor? What are the characteristics of superscalar processors?
- Current situation and development under accelerated increase in N-type penetration rate
- How to solve the frame loss phenomenon of industrial cameras?
- New MOSFET product family for automotive and industrial solutions
- The integration of generative artificial intelligence and the real economy promotes the development of new productivity