Technical Note · Measurement and Specifications
Reading Dynamic Range Specifications
Four different measurements are all called "dynamic range," and they can differ by 50 dB on the same channel. What each one measures, where the physical limits are, and how to compare vibration controller specifications on equal terms.
Key takeaways
- A dynamic range figure means nothing without its conditions: which measurement, which input range, and what bandwidth.
- Broadband, spurious-free (SFDR), two-tone and control dynamic range measure different things. Only control dynamic range is what a test actually gets.
- An ideal 24-bit converter is limited to about 146 dB. A single-range figure above that is not physically possible.
- Reading noise in one FFT line instead of across the band adds about 10·log10(lines): 38 dB at 6,400 lines, 50 dB at 100,000.
- Panther publishes >110 dB system dynamic range and 128 dB SFDR, each under its own name.
Why "dynamic range" needs a qualifier
Dynamic range is the ratio between the largest signal a system can handle and the smallest it can distinguish. Both ends of that ratio need a definition. The top is usually a full-scale sine on one input range. The bottom is where the definitions diverge: it can be the total broadband noise, the largest distortion spur, the noise in one FFT line, or the lowest level a controller can hold on a real shaker.
Each choice is legitimate for its purpose. The problem comes when a figure measured one way is compared with a figure measured another way, or when a specification gives the number without saying which it is. This note sets out the four measurements, the physics that bounds them, and the questions that put two specifications on equal terms. For converter and noise-floor fundamentals and system optimization, see Dynamic Range Considerations in Vibration Testing.
The four measurements
Broadband dynamic range
Full scale compared with the total noise across the measurement bandwidth, on a single fixed input range, with the input terminated or shorted. This is the measure an analog engineer means by signal-to-noise ratio. It answers the practical question: while the channel is set up for my largest signal, how small a broadband signal can it still measure?
Spurious-free dynamic range (SFDR)
A near-full-scale tone compared with the largest spurious tone or harmonic anywhere in the band. SFDR describes linearity and distortion, not noise: it answers could a small real tone be confused with a distortion product? Because spurs are discrete tones and the noise is spread across the band, SFDR is normally larger than broadband dynamic range on the same channel. It is a standard converter metric with defined test methods (IEEE Std 1241).
Two-tone (tone detectability)
A large tone and a much smaller tone are applied together, and the result is the largest ratio at which the small tone can still be seen above the noise in an FFT. It is a useful demonstration of how cleanly a channel separates a small tone from a large one. But the small tone only has to rise above the noise in its own spectral line, so the result depends on the FFT resolution, as the next sections show.
Control dynamic range
The spread between the highest and lowest levels in a test profile that the controller can hold within tolerance on a real system: a profile with a deep notch, a steep roll-off, or a wide peak-to-valley span. It depends on the whole control loop, not just the input channel, and it is the number that decides whether a difficult test can be run.
| Measurement | Top of the ratio | Bottom of the ratio | What it tells you |
|---|---|---|---|
| Broadband | Full-scale sine, one range | Total noise across the bandwidth | Smallest broadband signal measurable at a given range setting |
| SFDR | Near-full-scale tone | Largest spur or harmonic | Linearity; freedom from false tones |
| Two-tone | Large tone | Smallest visible tone in one FFT line | Tone detectability at a given resolution |
| Control | Highest profile level held | Lowest profile level held in tolerance | What a real test can achieve |
A related figure is output (drive) dynamic range: full scale compared with the noise on the drive signal. It limits how deep a notch the controller can drive, and it is set by the DAC, reconstruction filter and output stage together.
The hard ceiling: converter physics
An ideal N-bit converter, with nothing but quantization noise, has a signal-to-noise ratio of:
For 24 bits that is 146.2 dB. No 24-bit converter reaches it: thermal noise in the converter and its reference, and the analog front end ahead of it, add to the quantization noise. Working backward, every dynamic range figure implies an effective number of bits (ENOB):
| Dynamic range | Implied ENOB | Comment |
|---|---|---|
| 108 dB | 17.6 bits | Typical rating of a current wideband 24-bit measurement ADC at full bandwidth |
| 110 dB | 18.0 bits | Achievable as a complete-system figure with careful front-end design |
| 122 dB | 20.0 bits | Ideal limit of a 20-bit DAC |
| 130 dB | 21.3 bits | At the edge of the best narrow-bandwidth converters, before any front end |
| 146 dB | 24.0 bits | Theoretical limit of a perfect 24-bit converter |
| 160 dB | 26.3 bits | More bits than a 24-bit converter has: not possible on one range |
Thermal noise sets a second, independent limit. Every resistor and amplifier input generates noise, and the whole input chain (attenuators, protection, buffer amplifiers and converter) must be quieter than the target. Table 3 shows the noise budget, referred to the input, for a ±10 V peak range over a 50 kHz bandwidth, and the resistance whose own thermal noise would use up that budget at room temperature.
| Dynamic range | Total noise (rms) | Noise density | Equivalent resistor |
|---|---|---|---|
| 110 dB | 22 µV | 100 nV/√Hz | ~600 kΩ |
| 120 dB | 7.1 µV | 32 nV/√Hz | ~60 kΩ |
| 130 dB | 2.2 µV | 10 nV/√Hz | ~6 kΩ |
| 146 dB | 0.35 µV | 1.6 nV/√Hz | ~150 Ω |
| 160 dB | 0.07 µV | 0.32 nV/√Hz | ~6 Ω |
A 160 dB channel would need its entire input chain to be as quiet as a 6 Ω resistor across 50 kHz. A practical vibration controller input, with a 1 MΩ input impedance and protection against tens of volts, is nowhere near that.
Bandwidth matters. Sigma-delta converters improve as their bandwidth is reduced by digital decimation: halving the bandwidth halves the noise power and gains 3 dB. That is legitimate engineering, and it is exactly why a dynamic range figure must state its bandwidth.
FFT processing gain: why one line looks quieter than the channel
An FFT divides the measurement bandwidth into spectral lines. Broadband noise is spread across all of them, so each line holds only a fraction of the total. A tone, by contrast, stays concentrated in one line. The noise in a single line is lower than the total by approximately:
This is what drives two-tone and per-line "noise floor" figures. Nothing about the hardware changes as the line count rises; the noise is simply divided more finely.
| Spectral lines | Processing gain | Apparent dynamic range |
|---|---|---|
| 400 | +26 dB | 126 dB |
| 1,600 | +32 dB | 132 dB |
| 6,400 | +38 dB | 138 dB |
| 25,600 | +44 dB | 144 dB |
| 102,400 | +50 dB | 150 dB |
Per-line measurements are valuable for analysis: they show how small a discrete tone a channel can detect at a given resolution. They are not the dynamic range of the channel, and they cannot be compared with a broadband figure.
Two more ways a number grows
Adding input ranges together
Auto-ranging inputs switch gain so that small and large signals both land near full scale. Some specifications add the span of the ranges to the dynamic range of one range. Panther's inputs run from ±0.5 V to ±12 V in eight steps, a span of 27.6 dB; by that arithmetic a 110 dB channel could be described as 138 dB. At any instant, though, a test runs on one range, and the noise floor of that range is what the test sees.
Quoting a component instead of the system
"24-bit" and "32-bit" describe the width of a data word, not the performance of the channel. A converter's data sheet rating, measured by its manufacturer with an ideal source and a shorted input, does not include the attenuators, protection, filters, grounding and cabling of a real controller. A system specification should be measured at the connector, on production hardware.
Control dynamic range: the number a test actually gets
A closed-loop test runs through the accelerometer and its conditioning, the input channel, the control algorithm, the drive output, the power amplifier, and the shaker with its fixture. The test can be no cleaner than the noisiest of these. In practice, accelerometer noise and amplifier noise typically hold a real system to around 100 to 110 dB regardless of the converters behind them, and a controller's own published control dynamic range is usually 90 to 100 dB.
That is also why output word length matters less than it appears. A controller can only correct what its inputs can measure, and the reconstruction filter, output stage and amplifier set the drive's real floor. Panther's 20-bit DAC has an ideal range of about 122 dB, matched to what the complete drive path delivers.
Make the most of the range you have. Choose accelerometer sensitivity so the test's largest level uses most of the input range, and check the lowest point of the profile against the channel's noise floor before the test (see Transducer Sensitivity Selection). Lines out of tolerance at the ends of a sloped profile are often a noise-floor problem (see Why Did My Random Vibration Test Abort?).
Comparing specifications on equal terms
Before putting two dynamic range figures side by side, ask the same questions of both:
- Is it broadband, SFDR, two-tone, input, output or control dynamic range?
- Is it for a single, fixed input range, or does it include the span of several ranges?
- What measurement bandwidth and sample rate apply?
- Is the noise integrated across the band, or read from one FFT line? If per line, at how many lines?
- Was it measured at the connector of a production system, or taken from a converter data sheet?
- Was any weighting or narrow-band filtering applied?
- What is the published control dynamic range, and will it be demonstrated on your shaker, with your fixture and accelerometers?
| Misconception | Reality |
|---|---|
| "24 bits means 144 dB." | 24 bits is the word length. The ideal limit is 146 dB, and real converters with their front ends are far below it. |
| "A bigger dynamic range number is always better." | Only if the numbers measure the same thing under the same conditions. A per-line or range-stacked figure can exceed a broadband figure by 30 to 50 dB on identical hardware. |
| "SFDR and dynamic range are the same." | SFDR measures the largest spur; broadband dynamic range measures total noise. SFDR is normally the larger. |
| "A 32-bit DAC gives cleaner drive." | The output stage, filter and power amplifier set the drive's floor long before word length does. |
| "Input dynamic range is what my test gets." | The test gets control dynamic range, which the whole loop limits. |
Panther's figures and their conditions
Panther publishes both of the input figures that matter, each under its own name, measured at the BNC connector on the complete Panther signal path.
| Specification | Value | Conditions |
|---|---|---|
| System dynamic range | >110 dB | Broadband, single fixed input range, complete signal path; no per-line noise floor, no range stacking |
| Spurious-free dynamic range (SFDR) | 128 dB | Full-scale tone to the largest spur or harmonic |
| Amplitude linearity | ±0.05 dB to −70 dB; ±0.20 dB to −110 dB | Referred to full scale of each range |
| Analog anti-aliasing | >105 dB alias attenuation | Fixed at 524 kHz |
| ADC resolution | 24-bit | 262,144 samples/s, simultaneous on all channels |
| Drive output dynamic range | >110 dB | 20-bit DAC, complete output path |
| Drive output harmonic distortion | < −100 dB | Complete output path |
| Crosstalk | < −100 dB | Between outputs |
How Panther helps
- Specifications you can reproduce: system figures measured at the connector on production hardware, with each dynamic range figure named for what it measures.
- Eight input ranges with auto-ranging: ±0.5 V to ±12 V, so the largest level of the test lands near full scale and the full dynamic range of one range is available to it.
- Linearity to −110 dB: amplitude linearity is specified down to −110 dB below full scale, so low-level profile segments are measured accurately, not merely detected.
- Matched drive path: a 20-bit DAC with greater than 110 dB output dynamic range and harmonic distortion below −100 dB, sized to what the amplifier and shaker can use.
- Demonstrated, not just specified: ask for a demonstration on your own test, with a profile that has a deep notch or a wide peak-to-valley span, and see the achieved control spectrum against tolerance.
Frequently asked questions
Can a 24-bit system have 160 dB dynamic range?
No. The theoretical limit of an ideal 24-bit converter is about 146 dB (6.02 × 24 + 1.76). Real converters, front ends and analog circuits are lower. A figure of 160 dB can only come from reading noise in a single FFT line, adding the span of several input ranges together, or leaving the measurement conditions unstated.
What is the maximum dynamic range of a 24-bit ADC?
About 146 dB in theory, from the quantization limit 6.02N + 1.76 dB with N = 24. Current wideband 24-bit measurement converters are rated at roughly 108 to 120 dB at their full bandwidth, and a complete measurement channel is lower than the converter alone.
What is the difference between dynamic range and SFDR?
Broadband dynamic range compares full scale with the total noise across the measurement bandwidth on one input range. Spurious-free dynamic range (SFDR) compares a full-scale tone with the largest spur or harmonic. SFDR describes distortion, not the noise floor, so it is usually the larger number.
What is a two-tone dynamic range test?
A large tone and a much smaller tone are applied together, and the result is the largest ratio at which the small tone can still be seen in an FFT. Because each FFT line holds only a fraction of the total noise, the result grows with the number of spectral lines. It measures tone detectability, not broadband dynamic range.
What is FFT processing gain?
When broadband noise is spread across N spectral lines, each line holds about 1/N of it, so the noise in one line is about 10·log10(N) dB below the total. At 6,400 lines that is about 38 dB; at 25,600 lines about 44 dB. A noise floor read from one line is therefore not the channel's dynamic range.
What is control dynamic range?
The spread between the highest and lowest levels in a test profile that the controller can hold within tolerance on a real system. It is limited by the whole control loop, including the accelerometer, the power amplifier and the shaker, and is always lower than the input channel's dynamic range.
What dynamic range does Panther have?
Panther publishes greater than 110 dB system dynamic range, measured broadband on a single input range with the complete signal path in place, and 128 dB spurious-free dynamic range. Neither figure uses a per-line noise floor or adds input ranges together.
References and further reading
- IEEE Std 1241, IEEE Standard for Terminology and Test Methods for Analog-to-Digital Converters.
- W. Kester, "Taking the Mystery out of the Infamous Formula, SNR = 6.02N + 1.76 dB," Analog Devices Tutorial MT-001.
- W. Kester, "Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR so You Don't Get Lost in the Noise Floor," Analog Devices Tutorial MT-003.
- J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures, 4th ed., Wiley.
- Spectral Dynamics Technical Library: Dynamic Range Considerations in Vibration Testing; Transducer Sensitivity Selection; Why Did My Random Vibration Test Abort?
