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A transducer converts energy from one form to another. Examples include:

• Motors and generators (electrical ↔ mechanical energy)

• Lasers (electro-optical)

• Electroacoustic transducers (e.g., microphones, speakers, sonar devices)

Sonar Transducers:

• Sonar transducers often use the piezoelectric effect to convert energy.

• Other effects like the ferroelectric effect may also be used.

• Terminology can vary: "aperture," "antenna," "projector/transmitter," and "hydrophone/receiver" are sometimes used interchangeably.

Direct Effect: Some materials generate voltage when squeezed or stretched due to changes in molecular symmetry.

Converse Effect: Applying voltage causes the material to deform, rearranging its dipoles.

Materials Used:

1. Lead Zirconate Titanate (PZT):

   • A ceramic material commonly used for sonar.

   • Needs to be polarized first.

2. Polyvinylidene Fluoride (PVDF):

   • A flexible polymer.

   • Lower acoustic impedance than PZT.

     
     

1. Frequency of Operation: The desired range of frequencies (e.g., 20–30 kHz for the example).

2. Radiation Pattern: The shape and direction of the sound emitted or received.

3. Size Constraints: Ensuring it fits on the platform.

4. Efficiency: Optimizing energy conversion for sending/receiving sound.

5. Source Level/Sensitivity: Achieving required performance for transmitting/receiving.

6. Mounting Method: Ensuring stable and functional attachment to the platform.

KiwiSAS Sonar Transmitter (Tonpilz Design):

• Tonpilz Transducer: Named for its shape, this design is commonly used in acoustic applications.

• Active Element: Consists of eight stacked PZT discs, connected in parallel via copper plates.

• Radiating Face: Made of aluminum, providing a good match between PZT and water impedance.

• Energy Reflection: A tail piece with high impedance reflects energy towards the radiating face to enhance efficiency.

• Pre-Stressed PZT Elements: A bolt applies compression to the fragile PZT material to prevent shattering under high voltage.

FEM Insights:

• Reveals resonant frequencies and displacement of the radiating face.

• Helps identify additional resonances caused by design elements like lip-mounting.

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Electrical Analysis:

• Admittance: Measures how efficiently the transducer converts electrical to mechanical energy at different frequencies.

• Harmonics: High-frequency harmonics (e.g., from switching amplifiers) must be managed to avoid resonant damage.

• Butterworth-Van Dyke (BVD) Model: A common circuit model using capacitance and resonant branches to simulate a transducer's electrical behavior.

1. Projectors (e.g., vibrating plate designs) are driven by electrical signals.

2. The transducer acts as a filter, modifying the input signal’s spectrum based on its transfer function (H(f)).

3. The shape of the transducer and the wave type determine the field it generates.

• The Fresnel approximation simplifies calculating the distance r in wave propagation by using a second-order approximation.

• It applies beyond the near-field region, a zone close to the aperture (a few wavelengths away). Beyond this, the integral for the radiated field can be simplified into a Fresnel transform, which still accounts for phase changes due to the wave’s curvature.

Fraunhofer Approximation

• The Fraunhofer approximation is a further simplification, valid at even greater distances (in the Fraunhofer region). It neglects second-order terms.

• The radiated field is then expressed in terms of the Fourier transform of the aperture function, making calculations easier and faster. For common aperture shapes (e.g., rectangular or circular), Fourier transforms can often be solved analytically.

Fraunhofer Region and Rayleigh Distance

• The Fraunhofer approximation is valid beyond the Rayleigh distance, defined as:

  • R=2D^2/λ

    • where D is the aperture width and λ is the wavelength.

• Beyond this distance, errors in the approximation are small (at most 1/16th of the wavelength). This makes it suitable for far-field calculations.

Beampattern

• The beampattern describes how sound is radiated from a transducer in different directions.

• It separates the radiated field into three components:

  1. Driving Signal: The input to the transducer.

  2. Aperture Effect: How the transducer's shape affects the radiation pattern.

  3. Spherical Spreading: The natural attenuation with distance.

Coordinate Systems

• The beampattern can be represented in:

  1. Cartesian Coordinates: Useful for calculations.

  2. Spherical Coordinates: Defined by azimuth ψ and polar angles θ, common in sonar applications.

  3. Angular Coordinates: Azimuth ϕ and elevation θ for describing the direction relative to the transducer's normal.

Circular Beampattern

• Circular transducers produce axisymmetric patterns due to their geometry.

• The Fourier transform involves a Bessel function of the first kind.

• The beampattern, often referred to as an Airy disk, features a strong central lobe and concentric side lobes.

• Example: A 0.1 m radius circular transducer at 30 kHz creates a symmetric pattern ideal for focused sound radiation.

1. Beamwidth measures the width of the main lobe in the beampattern. Common types:

   1. 3dB Beamwidth: Width where intensity is within 3dB of the peak.

   2. 6dB Beamwidth: Width where intensity is within 6dB of the peak.

   3. Null-to-Null Beamwidth: Angular range between null points (destructive interference).

2. Beamwidth depends on aperture sizeand wavelength, with formulas provided for rectangular and circular transducers.

3. Smaller apertures D<λ do not produce defined nulls.

Directivity Index (DI)

• Measures how directional a transducer is compared to an omnidirectional source.

• Key Observations:

  • Frequency Dependence: Higher frequencies result in higher DI due to narrower beamwidths.

  • A transducer radiates more energy in the forward direction as DI increases with aperture size and frequency.

The behavior of a transducer as a transmitter applies equally to its function as a receiver:

• Receiver Directivity Index: Indicates sensitivity to signals from specific directions over omnidirectional noise.

• Transmitters generate high-power acoustic waves, while receivers are more sensitive to detecting smaller incoming signals.

• Material Use:

  • PZT Transducer: Used for transmitting due to its ability to generate high-intensity waves.

  • PVDF Receiver: Preferred for detecting small signals due to better impedance matching.