SFDR is frequently written in the units of dBHz^(2/3), particularly for fiber optic links. Fiber optic links can often have such high bandwidth, that assuming a bandwidth in SFDR is unhelpful or misleading. Normalizing to 1Hz therefore became a standard practice. The units of SFDR for a real system with a bandwidth are dB.

Now consider that the real system has a specific bandwidth. The real SFDR can be calculated using the following formulas: SFDR_real = SFDR_1Hz – (2/3)*10*log10(BW)

RF Photonic links (also called Microwave Photonic Links) are systems that transport radiofrequency signals over optical fiber. The essential components of an RF photonic link are the laser as a continuous-wave (CW) carrier, a modulator as a transmitter and the photodetector as a receiver. A low-noise amplifier is often used before the modulator.

Optical fiber boasts much lower loss over longer distances compared to coaxial cable, and this flexibility of optical fiber is one advantage over conventional microwave links. Another advantage of RF photonic links are their immunity to electromagnetic interference, which plays a more significant role in electronic warfare (EW) applications. RF Photonic links are employed in telecommunications, electronic warfare, and quantum information processing applications, although the performance requirement in each of these situations vary. In telecommunications, a high bandwidth is required, while in EW applications having high spurious-free dynamic range (SFDR) and a low noise figure (NF) is critical. In quantum information processing applications, a low insertion loss is critical.

In EW scenarios, unlike in telecommunications, the expected signal frequency and signal power is unknown. This is because typically, an RF photonic link is found as a radar receiver. In a system with high SFDR and low NF, distortion is minimized, the radar has stronger reliability and range, and smaller signals can be registered. Here is a demonstration of two scenarios with different SFDR and NF:

In general, the third order distortion tones are understood to exist as in-band distortion at frequencies 2ω_{2}-ω_{1} and 2ω_{1}-ω_{2} in a two tone intermodulation test. Third order distortion also exists at frequencies ω_{1} and ω_{2}. Second order distortion tones are found outside of a narrowband system at 2ω_{2}, 2ω_{1}, and ω_{1}+ω_{2}.

Consider the two-tone input of a non-linear system with frequencies ω_{1} and ω_{2}:

V_{in} = A[cos(ω_{1}t)+cos(ω_{2}t)]

The second order and third order distortion tones are calculated on the following page. In summary, the tones are shown in the table below. This shows that third order distortion tones are found not only in the positions mentioned above, but also contribute to the fundamental tone frequencies. In a spurious-free system, all third order tones will be below the noise floor. This is verified in MATLAB with ω_{1}, ω_{2} at 500kHz, 501kHz.

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.

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 a_{0} is a DC component generated by the non-linear system. The second term a_{1}V_{in} is the fundamental tone with some level of gain a_{1}. The third term a_{2}V_{in}^{2} is a second order non-linear distortion tone. The fourth term a_{3}V_{in}^{3} 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).

The units of spurious-free dynamic range (SFDR) are dB·Hz^(2/3). The units can be a source of confusion. The short answer is that it is a product of ratios between power levels (dBm) and noise power spectral density (dBm/Hz). The units of dBHz^(2/3) are for SFDR normalized to a 1Hz bandwidth. For the real SFDR of a system, the units are in dB.

If we look at a plot of the equivalent input noise (EIN), the fundamental tone, OIP3 (output intercept point of the third order distortion), and IMD3 (intermodulation distortion of the third order), a ratio of 2/3 exists between OIP3 and SFDR. This can be recognized from the basic geometry, given that the slop of the fundamental is 1 and the slope of IMD3 is 3.

Now, we need to look at the units of both OIP3 and EIN. The units of OIP3 are dBm and the units of the equivalent input noise (a noise power spectral density) are dBm/Hz.

SFDR = (2/3)*(OIP3 – EIN)

[SFDR] = (2/3) * ( [dBm] – [dBm/Hz] )

Now, remember that in logarithmic operations, division is equal to subtracting the denominator from the numerator. and therefore:

[dBm/Hz] = [dBm] – 10*log_10([Hz])

Note that the [Hz] term is still in logarithmic scale. We can use dBHz to denote the logarithmic scale in Hertz.

[dBm/Hz] = [dBm] – [dBHz]

Substituting this into the SFDR unit calculation:

[SFDR] = (2/3) * ( [dBm] – ( [dBm] – [dBHz] )

This simplifies to:

[SFDR] = (2/3) * ( [dBm] – [dBm] + [dBHz] )

Remember that the difference between two power levels is [dB].

[SFDR] = (2/3) * ( [dB] + [dBHz] )_

The units of [dB] + [dBHz] is [dBHz], as we know from the same logarithmic relation used above for [dBm] and [dB].

[SFDR] = (2/3) * [dBHz]

Now, remember that this is a lkogarithmic operation, and a number multiplying a logarithm can be taken as an exponent in the inside of the logarithm.Therefore, we can express Hz again explicitly in logarithm scale, and move the (2/3) into the logarithm.