When measuring the distortion of dual tone intermodulation, two pure sine waves in the frequency spectrum should be applied to the ADC at frequencies f1 and f2, which are generally relatively close in distance. Set the amplitude of each tone to be lower than the full range, slightly exceeding 6dB, so that when the phase of the two tones increases, the ADC will not experience clipping. The positions of the second-order and third-order products are shown in Figure 1. Please note that the second-order product is at a frequency position that can be eliminated by a digital filter. However, the third-order products 2f2-f1 and 2f1-f2 are closer to the original signal, making filtering more difficult. Unless otherwise specified, double tone intermodulation distortion refers to these "close range" third-order products. The cross tone distortion product is generally measured in dBc, relative to the value of one of the two original tones, rather than the sum of the two.

    However, please note that if two tones are close to fs/4, the aliased third harmonic of the fundamental wave may make it exceptionally difficult to identify the true product of 2f2-f1 and 2f1-f2. The reason is that the third harmonic of fs/4 is 3fs/4, and aliasing occurs at the frequency of fs-3fs/4=fs/4. Similarly, if two tones are close to fs/3, aliasing second harmonic may interfere with the measurement. The principle is the same as above, the second harmonic of fs/3 is 2fs/3, and aliasing occurs at fs-2fs/3=fs/3.

    Second and third order intermodulation cutoff points (IP2, IP3), 1-dB compression point

    The product of third-order intermodulation distortion is particularly troublesome in multi-channel communication systems, where channel isolation remains unchanged throughout the entire frequency band. The third-order intermodulation distortion product may mask small signals in the presence of large signals.

    In amplifiers, mixers, and other RF components, the third-order intermodulation distortion product is generally represented by the third-order intermodulation cutoff (IP3), as shown in Figure 2. Two pure frequencies of sound are applied to the system. The output signal power of a single tone (in dBm) and the relative amplitude of the third-order product (based on a single tone) are expressed as functions of the input signal power. The fundamental wave is represented as the slope=1 curve in the graph. If the nonlinearity of the system is approximated through power series expansion, for every 1dB increase in the signal, the amplitude of the second-order IMD (IMD2) will increase by 2dB, as shown by the slope=2 curve in the figure.

    Similarly, for every 1dB increase in the signal, the amplitude of the third-order IMD (IMD3) increases by 3dB, as shown by the slope=3 curve in the figure.

    Under a low-level dual tone input signal and two data points, second-order and third-order intermodulation distortion lines can be drawn, as shown in Figure 2 (the principle is that a point and a slope define a straight line).

    However, once the input signal reaches a certain level, the output signal will begin to be soft limited or compressed. One relevant parameter here is the 1dB compression point. This is the point where the output signal is compressed by 1dB from an ideal input/output transfer function. In Figure 2, this point is located in the area between the ideal slope=1 line becoming a dashed line and the actual response showing signs of compression (solid line).

    However, both second-order and third-order intermodulation cross-sections can be extended to intersect with the extension line (dashed line) of the ideal output signal line. These intersection points are called second-order and third-order intermodulation cutoff points, respectively, represented as IP2 and IP3. These power level values are usually based on the output power of the device conducted to a matching load (usually but not necessarily 50), represented as dBm

    It should be noted that IP2, IP3, and 1dB compression points are all functions of frequency, and as expected, the higher the frequency, the more severe the distortion.

    For a given frequency, the approximate level value of the third-order IMD product can be calculated as a function of the output signal level, given the known third-order intermodulation cutoff point.

    The concept of second-order and third-order intermodulation cutoff points is invalid for ADC because in this case, the change in distortion product is unpredictable (as a function of signal amplitude). ADC does not gradually start compressing signals approaching full scale (there is no 1dB compression point); Once the signal exceeds the input range of the ADC, the ADC will act as a hard limiter, causing a sudden and significant amount of distortion due to clipping. On the other hand, for signals far below full scale, the distortion bottom remains relatively stable and is not affected by the signal level, as shown in Figure 3.