What's the Difference Between Electric Pulse Width and Acoustic Pulse Width?

1. Problem Statement

Not only does GB/T27664 "Non-destructive Testing - Performance and Verification of Ultrasonic Equipment" fail to clearly distinguish between these two concepts, but textbooks on ultrasonic testing and various research papers also generically refer to both as "pulse width" without emphasizing their differences, causal relationships, or the potential harm caused by confusing them. This article presents some preliminary observations on this matter, and we welcome any corrections or feedback.

2. Differences and Causal Relationships

The natural frequency (approximately the nominal frequency) fo of a transducer is determined by the crystal thickness t and sound velocity c, expressed as:

fo = c/(2t) ... (1)

However, when the transducer is excited, the quality of the generated acoustic pulse signal (such as excitation effectiveness and presence of spurious signals) is related to the shape and width of the exciting electric pulse. In my journal entry "UT Notes: Transformer Effect of Crystals" dated April 18, 2012, noted: "Square wave excitation produces better ultrasonic quality, and the intensity and amplitude can be doubled compared to sharp peak electric pulse excitation (with proper square wave width adjustment)." The "square wave width" mentioned here refers to the exciting electric pulse width td, as shown in Figure 10 a) of GB/T27664.1.

The adjustment of td is a matter of how the ultrasonic instrument's transmission circuit is designed. Generally, the following formula is provided:

2πfo = 3n/td (n = 1, 2, 3, ...) ... (2)

Where:

• fo = transducer nominal frequency

• td = exciting electric pulse width

• n = selectable natural number (n = 1, 2, 3, ...)

• π = pi (3.1416)

Generally, n = 1 is considered optimal. If π ≈ 3, formula (2) can be rewritten as:

2fo·td ≈ n ... (3)

Selecting n = 1:

2fo·td ≈ 1 ... (4)

According to formula (4), the rising and falling edges of the square wave differ by half a period (180 degrees), which can double the excitation effect. Furthermore, from the above formulas, we can conclude that from a circuit design perspective, the exciting electric pulse (square wave) width td should be inversely proportional to the transducer's natural frequency fo.

The adjustment of exciting electric pulse width td is a means to improve electromechanical coupling quality and the quality of acoustic pulses transmitted by the transducer, but it has no relation to the acoustic pulse width generated by the transducer. The acoustic pulse width generated by the transducer depends solely on the quality of the transducer's inherent damping.

Therefore, the exciting electric pulse width (see Figure 10 in GB/T27664.1) and the ultrasonic pulse width transmitted or received by the transducer (see Figure 1 in GB/T27664.2) are distinctly different concepts, each with its own measurement methods, and should not be confused.

3. Potential Harm

Confusing these two concepts can lead to the misleading conclusion that acoustic pulse width t also has an inverse relationship with frequency fo. However, since acoustic pulse width t is not electric pulse width td, the product of 2t and fo does not equal 1. In other words, acoustic pulse width t is fundamentally unrelated to frequency—it depends solely on the quality of the transducer's inherent damping.

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