Spurious-Free Dynamic Range

Spurious-free dynamic range, usually abbreviated SFDR, is the range between the relevant noise floor and the largest signal level that can be processed before distortion spurs become unacceptable. In RF receivers and mixed-signal chains, the governing spur is often a third-order intermodulation product from two nearby tones.

The metric is useful because weak-signal sensitivity and large-signal linearity are not separate release questions. A receiver can have a low noise floor but poor blocker tolerance. Another receiver can have high intercept point but lose practical dynamic range because its bandwidth or noise figure is too large. SFDR puts both boundaries in one calculation.

Noise and Intermodulation Boundaries

For a receiver with noise figure NF and noise bandwidth B, the integrated input-referred noise floor can be screened as:

where N_B is in dBm when B is in hertz. For two equal input tones with power P_{in}, a third-order intermodulation product can be estimated from input third-order intercept point:

The two-tone SFDR boundary is found by setting the intermodulation product equal to the noise floor:

so the range above the noise floor is:

or:

This is a screening relationship. It assumes the receiver remains in the region where the third-order law is meaningful and that the reference plane, gain state and bandwidth match the measurement.

Worked Example

An RF receiver has input third-order intercept point:

Its input noise figure is:

and the decision bandwidth is:

The bandwidth term is:

so the input-referred noise floor is:

The maximum equal-tone input at the SFDR boundary is:

and the spurious-free dynamic range is:

If two equal blockers are measured at:

the third-order product estimate is:

With a 3 dB release allowance, the spur margin against the noise floor is:

The case passes narrowly. A small gain-state change, bandwidth change or blocker uncertainty could consume the remaining margin.

Boundary With Dynamic Range and IP3

SFDR is not the same as general dynamic range. Dynamic range may be limited by clipping, saturation, ADC full scale, display resolution, recovery time or application-specific detection rules. SFDR is narrower: it asks when spurious components, usually nonlinear products, rise above an allowed floor.

SFDR is also not the same as third-order intercept point. IIP3 is an extrapolated linearity metric. SFDR combines that linearity metric with the actual integrated noise floor. A high IIP3 does not guarantee high SFDR if the receiver bandwidth is wide or the noise figure is poor.

Bandwidth and Reference Plane

SFDR changes with bandwidth because integrated noise changes with bandwidth. Quoting SFDR without a noise bandwidth is incomplete. It also changes with gain distribution, filter placement and reference plane. A preselector may reduce blocker level before the nonlinear stage but add insertion loss that raises the effective noise figure.

For converters, the same idea applies with a different measurement convention. The spur limit may be expressed relative to full scale, a carrier, or a spectral bin. Engineers should state whether the reported range is input-referred, output-referred, per hertz, integrated over a band, or measured with an FFT configuration.

Validation Evidence

A defensible SFDR statement includes noise bandwidth, noise figure or measured noise floor, reference plane, gain state, tone spacing, tone powers, IIP3 source, measured spur levels, compression check, averaging settings, FFT window if used, temperature, uncertainty allowance and pass/fail threshold.

Two-tone validation is useful, but real environments may contain more than two signals. Multi-tone and field tests are often needed when spectrum occupancy, adjacent-channel leakage, reciprocal mixing, AGC behavior or time-varying blockers are credible.

Common Mistakes

Common mistakes include quoting SFDR without bandwidth, mixing input-referred IIP3 with output-referred noise, using a data-sheet intercept point from the wrong gain state, treating SFDR as a compression limit, ignoring reciprocal mixing, checking one tone when two-tone products are the risk, and reporting FFT spurs without calibration or window details.

The practical rule is to use SFDR as a release margin, not as a marketing number. It should tell whether the wanted operating range remains free of harmful spurs under the blocker, bandwidth and uncertainty conditions that the system will actually see.