What does the term “Spurious-free” mean in Spurious-free Dynamic Range (SFDR)?

In the term spurious-free dynamic range (SFDR), spurious-free means that non-linear distortion is below the noise floor for given input levels. The system is spurious when non-linear distortion is present above the noise floor. The system is spurious-free when non-linear distortion is below the noise floor. SFDR therefore is the range of output levels whereby the system is undisturbed by non-linear distortion or spurs.

 SFDR contrasts with compression dynamic range (or linear dynamic range (LDR)) which is the range of output levels whereby the fundamental tone is proportional to the input, irrespective of distortion tone levels. The fundamental tone is no longer considered to be linear beyond the 1dB compression point, after which the output fundamental tones do not increase at the same rate as the input fundamental tones.

Image credits (modified): Pozar, Microwave Engineering, 2nd Edition

Spurs are non-linear distortion tones generated by non-linearities of a system. The output of a non-linear system can be modeled as a Fourier series.

The first term a0 is a DC component generated by the non-linear system. The second term a1Vin is the fundamental tone with some level of gain a1. The third term a2Vin2 is a second order non-linear distortion tone. The fourth term a3Vin3 is the third-order non-linear distortion tone. Further expansion of the Fourier series generates more harmonic and distortion tones. Even order harmonic distortion tones are usually outside of the band of interest, unless the system is very wideband. Odd order distortion tones however are found much closer to the fundamental tone in the frequency domain. SFDR is usually taken with respect to the third order intermodulation distortion, however it may also occasionally be taken for the fifth order (or seventh).

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