In RF or microwave multi-carrier communication systems, IMD3 is an important indicator to measure linearity or distortion.

Before understanding IMD3, let’s first introduce what IMD is.

**IMD (Intermodulation Distortion)**

When two signal frequencies F1 and F2 or multiple signal frequencies pass through the same remote RF transmission system at the same time, nonlinear frequency components are generated between the fundamental frequency signals due to the nonlinear influence of the transmission system. This phenomenon is called intermodulation. The nonlinear frequency component is called intermodulation product. If these intermodulation products fall within the receiving frequency band and are strong enough, they will form interference with the fundamental signal frequency, which is called passive intermodulation interference or passive intermodulation distortion

The intermodulation product is represented by the following formula:

**f1m=mf1±nf2········**

In the formula:

f1, f2 are the input fundamental frequency

f1m is the intermodulation frequency or intermodulation product

m, n are positive integers including 1, m+n is the order of intermodulation

Example: When m+n=3, it is the third-order intermodulation

**Dynamic Third-Order Intermodulation: **Test third-order intermodulation of components at rest;

**Static third-order intermodulation: **Test the third-order intermodulation of components under shaking.

**How is the IMD3 defined?**

The original two frequency signals in the radio frequency device will arouse the interference signals of other frequencies, and the nonlinearity of the radio frequency device leads to the mutual influence of different frequency signals.

** **Generally, poor contact or aging of RF devices may cause nonlinearity of devices. Intermodulation is literally understood as mutual influence (two or more), and the intermodulation product is the product of mutual influence.

When two or more frequencies of radio waves propagate in non-linear radio frequency devices, or when they run into metal objects in the air, intermodulation interference signals of other frequencies may be generated, just like the transmission of panic. Panic spreads to a flock of goats (IMD3), but the degree of panic may decrease, and the flock’s panic spreads to the birds (fifth-order intermodulation: IMD5), and the degree of panic decreases again.

The intermodulation interference signal has third-order, fifth-order, seventh-order or more, but the third-order intermodulation component is the largest.

If the frequency difference of the sum of the two frequencies is , the frequency of the third-order intermodulation is generally at the position of the sumand,as shown in Figure 1.

Figure 1:IMD3

A graph of the main signal and intermodulation products displayed in the scanner is shown in Figure 2.

Figure 2: IMD3 testing gragh

The third-order intermodulation is an important indicator used to measure the nonlinearity of radio frequency devices. Its magnitude is expressed by the ratio of the intermodulation product to the main output signal, and the unit is **dBc.**

When selecting RF devices, the larger the absolute value of the third-order intermodulation index, the better. The larger the value, the smaller the intermodulation output to the main signal relatively, and the smaller the interference effect on the system.

The power ratio of the third-order intermodulation component to the fundamental frequency component is defined as IMD3, which is expressed by logarithm as

simplify further:

IMD3(dB)=2Pin+Res.

In the formula, the remainder Res. is expressed as follows

In the approximate linear region, the above remainder can be considered as a constant, which means that for every 1dB increase in the input power, the IMD3 will deteriorate by 2dB; conversely, for every 1dB decrease in the input power, the IMD3 will improve by 2dB. This relationship is not satisfied if the approximate linear region is exceeded.

**The difference between IP3 and IMD3:**

**IP3** (Third-order Intercept Point） ,

**IMD3 **(Third Order Intermodulation），

The difference between the two is mainly that IP3 is for power value, IMD3 is relative value,

Normally, in the device parameters, IP3 has input third-order intermodulation (IIP3), output third-order intermodulation (OIP3),

IMD3 mainly has the third-order intermodulation suppression degree

and the units of the two are dBm for IP3 and dBc for IMD3.

**How to test the third-order intermodulation distortion and the power of the intermodulation point?**

The test of IMD3 and IP3 is not difficult, but there are some points need to be cared about in the test. If they are not handled properly, the accuracy of the test results will be affected.

For the test of third-order intermodulation, it is required to feed equal amplitude dual tone signal to the tested part. The dual tone spacing shall be set according to the test requirements of the tested part. Generally, it is necessary to select the appropriate dual tone point and frequency spacing according to the actual use scene. For the test of IMD3, the two-tone amplitude can be large or small. However, if IP3 is to be tested, the amplitude should not be too large. It must be ensured that the part to be tested works in the approximate linear region.

Figure 3: Connection Diagram of using two signal sources to test third-order intermodulation distortion

During the test, two signal sources can be used to provide dual tone signals, which is the most commonly used method for third-order intermodulation test, and can provide relatively pure dual tone signals.

Or use a vector source to edit the waveform file through the baseband side, so that a single channel can output a dual tone signal. The signal generated by this method will have a certain degree of third-order intermodulation distortion. Therefore, this method is only used as an alternative when there are no two signal sources.

Figure 4: Connection diagram of using a single vector source to test third-order intermodulation distortion

Fig. 3 and Fig. 4 respectively show the schematic diagram of the third-order intermodulation test connection when two dual tone generation modes are adopted. The whole test is relatively simple. Use the spectrometer to test the spectrum output by the amplifier, set the appropriate reference level, center frequency, span and RBW, and display the spectrum of the fundamental frequency and the third-order intermodulation signal. Use the marker function to calibrate IMD3, and thus calculate the power value of IP3. At present, the medium and high-end spectrometers on the market basically have IMD3 and IP3 direct test functions, which makes the test more convenient.