# Introduction to Intermodulation in Non-Linear System

Intermodulation is the most important drawback of a non-linear system. It is similar to the desensitization effect discussed in previous sections. In this case, instead of one signal, we have two unwanted signals with high amplitude than the desired signal, and they are called interferer.

There are two conditions to note in intermodulation:

*w*_{1}and*w*_{2}are close to each other*w*_{1,}and*w*_{2}are close to the desired channel.

The figure assumes that the desired channel is 1GHz with *w*_{1} at 1.9GHz and *w*_{2} at 2.1GHz. These two signals are close to each other, and they are also close to the desired channel.

In the desensitization section, *w*_{1} and *w*_{2} were the input signals to the system where *w*_{1} was the desired signal and *w*_{2} was the unwanted signal; however, in this case *w*_{1} and *w*_{2} both are the unwanted signals with amplitude A_{1} and A_{2}.

The output for this non-linear system can be expressed in the same way as we did in desensitization section:

Observing the outputs from the non-linear system, we see that the first term represented in green, the output is similar to that in the linear system. The desired signal can be achieved by using a filter. If the selected channel ranges from 1.2GHz to 1.8GHz with *w*_{1} and *w*_{2} around 1.9GHz and 2.1GHz, respectively, then with the center frequency of 1.5GHz, the desired signal can be filtered using a high-end bandpass filter.

In the 2^{nd} term non-linearity, we get four different frequencies values, having DC values, 2*w*_{1}, 2*w*_{2}, *w*_{1}+*w*_{2}, and *w*_{2}–*w*_{1}. The DC part can be filtered using a filter. The frequencies 2*w*_{1}, 2*w*_{2}, and *w*_{1}+*w*_{2} can be ignored as they are higher values. The *w*_{2}–*w*_{1 }is a lower value with 0.2GHz and can also be filtered. Plotting these four frequencies, we see *w*_{1} can be filtered using a bandpass filter to get the desired signal.

There are have ten different frequency components in 3^{rd} order non-linearity. The linear system has only two components, but in non-linearity, we get 16 different frequencies in total. Out of these 16 different frequencies, most of them can be removed using filters. The components 1, 2, 3, 4, 5, 7, 8 & 10 can be removed as they are quite far from *w*_{1} and can be attenuated using a filter.

As we can see that frequency 9 falls within the desired signal channel range (1.2-1.8GHz). This signal is called the blocker signal that falls within the desired band.

The above figure shows the spectrum of these frequency components. When all the components are represented, we get the this spectrum representing the different frequency components. Using a filter, all other components can be attenuated. However, the blocker remains in the desired band. The blocker decreases the gain or blocks our system’s signal which causes the compression in gain.

In summary, if we have a channel that is close to two interferer signals coming from another application with higher frequency and amplitudes, we get a blocker within the desired channel. One of the 16 frequencies in the spectrum acts as a blocker to the desired channel with amplitude A_{1} and A_{2} (for simplification, we can write A_{1}=A_{2}=A). Therefore, when two interferer signals with frequencies close to each other and close to the desired channel are captured by a non-linear system, intermodulation occurs.