Based on work done between 1972 to 1976 to which acess was initially restricted for commercial reasons. Presented at University of Southampton, England 1998.
Before doing this work a search and retrieval of prior publications was made by way of a database in the UK's National Lending Library. It produced well over fifty papers nealy all of which refered to computer simulations as to what might be expected from acoustic waves impinging on materieals of various acoustic properties. Basically, theortical acoustic equivalents of the sort of thing done for such as selecting layers of various refractive index to aid the transmission of light through optical lenses. Computer simulations had become 'popular' in academia during the previous decade. Surprisingly, annoyingly from my point of view, only three, as referenced in the paper below, related to practical aspects. Pursuing current work done in various universities in the UK at the time revealed nothing above the simplest knowledge of the transducer characteristics being used.
The work outlined below was done because although not originally planned to be a part of the overall project being pursued, it was considered more needed to be known about the actual characteristics of the transducers being used. Almost no details were available for commercially available devices and in any event they were not available in the sizes or forms thought useful for the bigger project.
A subsequent test of transducer designs described below against a commercially available transducer showed the former superior in a number of important ways.
Experimental development of ultrasonic transducers
Abstract. Designs for simple, workshop fabricated ultrasonic transducers using piezo-electric ceramics for use at selected frequencies between 0.5 MHz and 5 MHz are shown with a selection of experimental results which characterize their performance.
The paper refers to experiments to quickly identify the characteristics and ways to make piezoelectric ceramic based ultrasonic transducers for use at selected frequencies between 0.5 MHz to 5 MHz. The requirement was for transducers that; transmitted and received small signal sinusoids into and from water at several bars pressure without being fully immersed, and were efficient, robust and easy to make reproducibly by simple workshop methods.
Prototypes included 'wetted' designs, in which the ceramics were in direct
contact with water, and 'dry' designs in which they were protected behind hydraulically
secure metal face plates.
3. Impedance variations
Measuring the electrical signal amplitude Va at the transducer when driving air at a chosen resonance, compared to voltage Vw when driving water, gave a quick measure Va-Vw to indicate a transducer’s effectiveness transmitting into water at that frequency.
4. Beam shapes
Measuring maximum transmitted signal Vm against range, allowed the plotting
of curves of relative signal strength against the dimensionless range function
R*/d2. This identified the range at which the wave field became geometrically
controlled, i.e. the Fraunhoffer region, and so appropriate for recording beam
shapes for simple identification of form. All transducers yielded curves very
much like in Fig. 2.
Within the Fraunhoffer region all prototypes had beam shapes much as shown in Fig. 3. These were all of the correct form but of a beam width representative of a transducer with a diameter only about 60 % that of the actual ceramic diameter --- based on the calculated beam width of a piston radiator. Scale varied with transducer type and the frequency at which any particular transducer was used.
5. Face plate effects
Investigations of how dry transducer impedance and transmission varied with face plate thickness, used a transducer with the construction of Fig. 1D, with a 20 mm diameter ceramic glued to the face plate with neat epoxy glue. Tests were made with face plate thickness
ranging from 4.82 mm to 1.96 mm in approximately 0.13 mm increments. The effect of some face plate grooves and edge profiles were also investigated. At each step curves such as shown in Fig. 4 were produced. The recordings of transmitted signal in these diagrams are those of maximum amplitude, i.e. the peak of the beam shapes as illustrated in Fig. 3, at a range of 150mm. Figs. 4A and 4B are typical of over 20 diagrams obtained.
6. Principle resonances
Measuring the resonant frequencies of dry transducers, as recorded in the many diagrams like Fig. 5, and plotting resonant frequency, face plate thickness product against face plate thickness, produced Fig. 5. The straight line corresponding to the ceramic's resonance was evidence of its resonant frequency’s independence of mountings or coupling into water. It can be seen that face plate resonances were not similarly independent.
For dry transducers plotting Va-Vw, against face plate thickness gave Fig. 6. This highlighted the increase in acoustic coupling efficiency as face plate thickness resonances approached the ceramic's thickness resonances, and gave a rough measure of the relative efficiency loss to be expected for non optimal face plate thickness.
None of the prototypes showed significant electrical or acoustic ill effects from constraint by the ceramic’s mountings, resonances in those mountings, reflections from the back of acoustic loading materials [1, 2], or an earth plane very close to the ceramic’s edge. For both wetted and dry designs there was no need to provide acoustic loading to stabilize electrical characteristics because the water provided the necessary damping. There was also no need to pot with more flexible materials near the edges of the ceramics, or use a groove in the face plate of dry transducer designs, to improve acoustic efficiency or modify beam width.
The transducer of Fig. 1A was difficult to seal against a hydraulic pressure of more than a few tens of millibars. The electrical and acoustic properties of the relatively robust Fig. 1B transducer were almost indistinguishable from that of Fig. 1A. Transducers, like Fig. 1C could easily be made hydraulically secure.
In wetted transducer designs the electrical connection to the ceramic’s front electrode was mechanically vulnerable, but coating the transducer’s front face with epoxy and machining it to the height of the solder blob alleviated this. The epoxy layer also improving hydraulic integrity and, if thin, had little effect on transducer efficiency .
Optimally designed dry transducers were almost as efficient as wetted designs but had a narrower frequency band over which high efficiency could be achieved. Figs. 4A and 4B were typical in showing good transmission at face plate resonances but poor transmission at the ceramic’s resonances. To achieve high efficiency required experimental confirmation of a ceramic’s half wave resonant frequency and tight machining tolerances on face plate thickness, Fig. 6. The addition of silicon rubber and hard rubber wave plates of various thicknesses , aimed at improving efficiency, seemed to have a slightly contrary effect.
The dry transducer designs of Fig. 1D, with the ceramic attached to the face plate with solder, were difficult to make, had very low repeatability of electrical and acoustic properties and were very inefficient, probably because of poor bonding. Fig. 1D type transducers with the ceramic glued to the face plate with silver powder loaded epoxy glue (to ensure good electrical contact) and even neat epoxy, yielded range functions and beam shapes much like those of wetted transducer designs, Ref. Section 4.
Initial dry transducer designs were hewn from solid blocks of brass but it proved difficult to make a very flat surface on which to fix the ceramic. Much easier was to fabricate transducers from a separate face plate and barrel of relatively malleable stainless steel 316, Fig. 1D, 1E and 1F then, after gluing the ceramic to the face plate, spin rolling the face plate and barrel together. Gluing the ceramic to the face plate with neat epoxy was simple, gave good, reproducible acoustic performance, and hydraulically acceptable transducers.
Using a spring to press an oil smeared ceramic against the face plate, Fig. 1E, produced strong thickness resonance but weak and ‘ragged’ radial resonances. It made no clear difference whether spring pressure was 200 grams or 1 Kg., or whether spring pressure was applied at a point in the centre of the back of the disc, Fig. 1E, or around the back outer edge of the disc, or, to suppress harmonics, at 2/3 the disc's radius, Fig. 1F.
Why all transducers exhibited larger than expected beam widths remained unresolved. The cause seemed to be neither mechanical constraint nor electrical fringe effects at the ceramic’s periphery. The matter was not pursued because of no importance for the application required.
 Lutsch A 1962 Solid Mixtures with Specific Impedances and High Attenuation
for Ultrasonic Waves J. Acous. Soc. Am. 34 131-132
 Kossoff G 1966 Effects of Backing and Matching on the Performance of Piezo- electric Ceramic Transducers IEEE Trans. Sonics & Ultrasonics SU-13 No. 1 20-31
 Highmore P J 1973 Impedance Matching at Ultrasonic Frequencies Using Thin Transition Layers Ultrasonics Int’l Conf. Imperial College London UK