Acoustic beam characteristics of ultrasonic transducers

A conventional single crystal longitudinal wave ultrasonic transducer works like a piston that can emit high-frequency mechanical vibrations. The vibrations produced by the transducer are sound waves.

When a voltage is applied to the piezoelectric transducer chip (commonly called a crystal), it undergoes compression deformation perpendicular to the surface of the chip.

After the voltage disappears, usually within a microsecond, the chip rebounds, generating a mechanical energy pulse that forms an ultrasonic wave.

The conceptual example in the figure below shows the response of a piezoelectric crystal to a brief voltage pulse.

Working Principle of Conventional Ultrasonic Transducers

The most commonly used transducer types in ultrasonic non-destructive testing share the following basic functional attributes:

Type:

According to the function of the transducer, it can be divided into contact type, delay line type, angle beam type, or immersion type.

The characteristics of the material being tested, such as surface roughness, temperature, accessibility, location of defects within the material, and inspection speed, will all affect the user's choice of transducer type.

Size:

Size refers to the diameter of the activated transducer crystal. The crystal is usually housed in a slightly larger casing.

Frequency:

Frequency refers to the number of vibration cycles completed by the sound wave per second, usually expressed in kilohertz (kHz) or megahertz (MHz).

Most industrial ultrasonic testing is performed in the frequency range of 500 kHz to 20 MHz, so most transducers have frequencies within this range.

However, users can also purchase commercial transducers with frequencies below 50 kHz and above 200 MHz. Lower frequencies have stronger penetration; higher frequencies have higher resolution and focusing power.

Bandwidth:

Bandwidth is the portion of the frequency response that falls within a specific amplitude range. In this case, it should be noted that typical ultrasonic transducers do not generate sound waves of a single frequency, but only within a frequency range centered on the rated frequency value.

The industry standard defines this bandwidth at the -6 dB (or half-amplitude) point.

Waveform Duration - Waveform duration refers to the number of oscillation cycles generated after each time the transducer is triggered by a pulse.

Narrow-bandwidth transducers generate more oscillation cycles than wide-bandwidth transducers.

Crystal diameter, substrate material, electronic tuning, and the way the transducer is excited all affect waveform duration.

Sensitivity:

Sensitivity refers to the relationship between the amplitude of the excitation pulse and the amplitude of the echo reflected from a specified target.

We can effectively illustrate this concept with the following analogy.

The sound beam emitted from a typical unfocused disc transducer is often imagined as a column of energy originating from the activated crystal area, which diffuses in the diameter direction and eventually disappears.

Ultrasonic Sound Beam

In reality, the actual sound beam shape is more complex, as pressure gradually changes both laterally and axially.

In the sound beam shape diagram below, red represents the area with the highest energy, while green and blue represent areas with lower energy.

Ultrasonic Sound Beam Energy Distribution

The transducer's sound field is divided into two regions: the near field and the far field. The near field is the region close to the transducer.

In this region, sound pressure repeatedly reaches maximum and minimum values several times.

The end of this region is the location of the last maximum sound pressure value on the axis.

The distance from this location to the transducer surface is represented as N, which is the near-field distance. The near-field distance N represents the transducer's natural focal length.

Ultrasonic Near Field Zone

The far field is the region beyond the near-field distance (N value). In this region, the sound pressure gradually decreases to zero as the sound beam diameter expands and sound energy dissipates.

The near-field distance is a function of the interaction between the transducer frequency, crystal diameter, and the speed of sound in the material being tested.

Using the following formula, this function value can be calculated for square or rectangular crystals commonly used in phased array testing:

Near Field Zone Calculation Formula for Square or Rectangular Crystals

Due to the varying sound pressure in the near field, it is difficult to accurately evaluate defects using amplitude-based techniques (although thickness measurements in the near field are not problematic).

Furthermore, the N value represents the maximum distance at which the transducer's sound beam can be focused using acoustic lens or phase adjustment techniques.

The aspect ratio constant is calculated based on the length ratio of the short side and long side of the crystal or aperture:

Ratio of Short Side/Long Side

If it is an annular crystal, the k value is not used, but the crystal diameter (D) is used instead of the length term:

Near Field Zone Calculation Formula for Circular Crystals

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