08 Ultrasound

Decibel intensity ratio

dB = 10 log₁₀(I/I₀) = 20 log₁₀(A/A₀). −3 dB is half intensity.

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Simulation

Decibel intensity ratio — Change the numbers; the scene follows.

Where it works

Ultrasound

Console

On the console — depth (13 µs/cm), PRF, frame rate, dynamic range, aliasing limit.

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Formula

\mathrm{dB}=10\log_{10}(I/I_0)=20\log_{10}(A/A_0)

Variables

I · Intensitya.u.I₀ · Reference intensitya.u.

Results

dB
Ratio
-10dB
A/A₀
Amplitude ratio
0.3162

Explanation

\mathrm{dB}=10\log_{10}(I/I_0)=20\log_{10}(A/A_0)

What it means

Decibels compress huge intensity ratios: dB = 10 log₁₀(I/I₀) = 20 log₁₀(A/A₀). −3 dB is half intensity; −6 dB is half amplitude; −20 dB is 1% intensity. Dynamic range of a scanner is quoted in dB. This is a working relation in Ultrasound.

Where it is used

Clinically it sits on the Ultrasound — Console. On the console — depth (13 µs/cm), PRF, frame rate, dynamic range, aliasing limit. Ultrasound equations sit on the probe face and along the beam: impedance, Snell, Doppler, MI and TI. They explain why gel matters, why aliasing appears, and why a mechanical index is on the screen.

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How to use it

Enter I and I₀. Attenuation in dB adds, which is why α in dB/cm/MHz is convenient. Never add ratios in percent across a long path — add dB then convert. Change one input and watch the curve and the simulation follow.

Symbols

IIntensity0.1 a.u.
I₀Reference intensity1 a.u.

Worked example

A typical case from the default values: I = 0.1 a.u. (Intensity); I₀ = 1 a.u. (Reference intensity). Substituting into the relation gives dB = -10 dB; A/A₀ = 0.3162. These are teaching numbers — align them with your machine.

Typical values give

dB = -10dB
A/A₀ = 0.3162

Where it comes from

The displayed formula is the working relation. dB = 10 log₁₀(I/I₀) = 20 log₁₀(A/A₀). −3 dB is half intensity. Usual reference: Edelman. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Edelman

Assumptions & limits

Log of a power ratio. 20 log is for amplitude (pressure), 10 log for intensity/power. Mixing them is a common error.

Pitfalls

Soft-tissue 1540 m/s is an assumption — not a measurement in that patient. Doppler angle 90° gives no shift. MI and TI are on-screen estimates, not absorbed dose. Log of a power ratio. 20 log is for amplitude (pressure), 10 log for intensity/power. Mixing them is a common error.

Keep this

Gel, angle, and assumed speed of sound — get those three right before you trust a centimetre. Log of a power ratio. 20 log is for amplitude (pressure), 10 log for intensity/power. Mixing them is a common error.

In this specialty

Ultrasound