How to work an amplitude problem
Identify the reference first. Put the compared echo in the numerator and the reference echo in the denominator. Divide matching units before taking the base-10 logarithm, then multiply by 20. A ratio greater than one gives a positive result. To reverse the calculation, divide the signed dB value by 20 and raise 10 to that power.
For positive amplitude magnitudes A1 and A2 in matching units, use:
- ΔdB = 20 × log10(A2 / A1).
- Amplitude ratio A2 / A1 = 10^(ΔdB / 20).
The amplitude equation is published in Olympus, Ultrasonic Flaw Detection Tutorial (2021), “Decibel,” printed p. 72. Positive ΔdB means A2 is higher; negative means lower. This tool compares amplitudes, not acoustic power. The factor for a power ratio would be 10.
Screen-height conversions
On a calibrated linear A-scan, substitute height for amplitude. Evident, 3.5 Display Formats describes the A-scan's amplitude axis. The following are algebraic applications of the amplitude formula:
- Signal relative to reference: ΔdB = 20 × log10(Hsignal / Href).
- Height after a signed change: Hnew = Href × 10^(ΔdB / 20).
- Gain from current X% to target Y%: G = 20 × log10(Y / X).
Use heights in percent FSH throughout. A signal's difference from a reference and the gain needed to bring it to that reference have opposite signs. Zero height has no finite logarithmic result; a clipped echo is not a valid amplitude reading.
Worked example: 20% signal, 80% reference
At unchanged gain, a 20% FSH echo relative to an 80% FSH reference is 20 × log10(20 / 80) = −12.0412 dB. To raise that same echo from 20% to 80%, add 20 × log10(80 / 20) = +12.0412 dB, a fourfold amplitude change.
Doubling amplitude is 6.0206 dB; exactly +6 dB gives a ratio of 1.995262. Starting from 80% FSH, that predicts 159.621% FSH, above a conventional 100% display. Reduce gain and remeasure rather than use a clipped peak. These are fictional calculation examples, not exam items.
Second example: 50% signal, then a −6 dB change
To bring a 50% FSH echo up to an 80% FSH target, add 20 × log10(80 / 50) = +4.0824 dB. Separately, starting from 90% FSH and lowering gain by 6 dB gives 90 × 10^(−6 / 20) = 45.1069% FSH. These numbers are invented for practice. The same formulas are on the UT and MT formula sheet.
Calculated dB reference table
This original table is generated from the equations above using an 80% FSH reference. Values are rounded for display.
| ΔdB | A2 / A1 | Height (% FSH) |
|---|---|---|
| -20 | 0.1000 | 8.000 |
| -12 | 0.2512 | 20.095 |
| -6 | 0.5012 | 40.095 |
| 0 | 1.0000 | 80.000 |
| +6 | 1.9953 | 159.621 (off scale) |
| +12 | 3.9811 | 318.486 (off scale) |
| +20 | 10.0000 | 800.000 (off scale) |
Assumptions and use limits
Compare echoes at the same gain, scale and receiver settings. Gain predictions assume a linear, unsaturated response and unchanged coupling. They do not correct beam spread, attenuation, transfer losses or reflector geometry. An amplitude ratio alone does not establish flaw size or acceptability. The 80% reference is an example, not a required procedure setting.
Related UT tools
Calculate refraction and critical angles with Snell's law, then calculate skip distance and beam travel.