Las mayores trabas para el profesorado chino en las clases de la Traducción del

In order to model the particle separator and simulate particle motion, the properties of the sys- tem must be known. This subsection describes briefly the appropriate aspects of the system and parameters, using the input impedance of the device to check the model description.

Transducer

For the transducer layer on the underside of the silicon matching layer, two different transducer types have been used: a bulk PZT material or a thick film printed material, the testing of which is described in Harris et al. [140]. The transducers are illustrated schematically in figure 6.1 which shows the various layers existing in each system. The bulk PZT is modelled according to the equivalent circuit in section 2.5.2 and uses established parameter values for the PZT material. However, the printed structure has electrodes arranged such that it represents two transducers operating back-to-back. When simulating this, the transducer elements seen in the equivalent circuit must be replaced with a pair of similar components placed in parallel. As the properties of the printed transducer element depends heavily on the PZT paste preparation and printing process, parameter values must be estimated experimentally.

Figure 6.1: Structure of transducer using a) bulk PZT material and b) thick film printed PZT material.

Resonator Layers

The separator device was introduced in section 2.5 describing the basic construction and operation of the system, with the devices tested in this chapter having a fluid layer depth of 175µm and a Pyrex reflector layer thickness of 1525µm.

The properties of the various layers are summarised in table 6.1 for which the quality factor for each material is selected by matching the simulated impedance with the measured impedance of the device, with the fluid channel both air filled and water filled. As the platinum layer has a thickness of only a few microns and is acoustically hard, it has a negligible influence upon the acoustic characteristics of the resonator and is therefore not included in the model as a separate layer.

Electrical Impedance

The transducer and layer data is used as input to the acoustic impedance transfer model coded within MATLAB (section 2.5.2) and describes the 1-d acoustic characteristics of the layered res-

Table 6.1: Properties of particle separator layers.

Layer Thicknessa Densityb Speed of soundb Quality factorc

(µm) (kg/m3) (m/s) Glued _{5 1160 2620 50} Silicon 525 2340e ₈₄₃₀e ₈₀ Air 175 1.293 331.6 50 Fluid

{

Nominal value given, but may be replaced by measured value.

b

Taken from acoustic material tables [135].

c_{Values determined by matching modelled impedance characteristics with measured data.} d

Glue layer not applicable to printed PZT device.

e_{Approximate values for anisotropic material used.}

onator. The electrical input impedance of the device or voltage across the transducer can be mea- sured over a range of frequencies and can be compared to that calculated by the acoustic model, as demonstrated for example by [2, 5].

The impedance of a bulk PZT device is illustrated in figure 6.2 (measured data taken from Hill et al. [126]) and shows the frequency response of the device. The shape of the impedance plot indicates several resonant frequencies; a large resonance at 2.5MHz due to the transducer resonance, with other frequencies attributed to resonant modes in various layers of the device, examples seen at 3.4MHz and 4.1MHz. When comparing the measured and modelled data there is reasonable agreement between the frequencies at which the more dominant resonant modes occur, especially the higher frequencies 3.4, 4.1 and 4.8MHz. However, the model is less reliable at the lower frequencies and does not predict the resonance occurring at 1.4MHz at all. The magnitude of impedance is predicted with reasonable accuracy at the higher frequencies although is significantly less accurate at frequencies below 3.4MHz. It is noted that there are many smaller features in the measured data which are not predicted by the model, possibly caused by more complex modes in the system attributed, for example, to 3-dimensional modes, misalignment in fabrication or uneven application of the glue layer none of which are considered by the acoustic simulation.

For the printed PZT devices the frequency response is significantly different. Figure 6.3(a) shows measured and modelled impedance data for such a device which generally shows a lower im- pedance value and a smoother profile than that of a bulk PZT device. Only three resonant fre- quencies can be discerned, two modes at approximately 3.4MHz and 4.5MHz attributed to the

Figure 6.2: Impedance of water filled particle separator using bulk PZT transducer showing (a) measured impedance (solid line) and modelled impedance (dotted line) and (b) modelled fluid layer energy density,h¯i, normalised relative to the peak energy density.

Figure 6.3: Impedance of water filled particle separator using printed PZT transducer showing a) measured impedance (solid line) and modelled impedance (dotted line) and b) modelled fluid layer energy density,h¯i, normalised relative to the peak energy density.

presence of water in the chamber and another due to the transducer/matching layer at 3.7MHz. The association between these frequencies and certain layers is in part confirmed by two things: a) only the 3.7MHz mode is present in experimentally measured and predicted impedance in an air filled device, and b) the acoustic energy in the fluid (water-filled) layer is higher at 3.4 and 4.5MHz frequencies as seen in figure 6.3(b). This also applies to the bulk PZT device where frequencies 3.4 and 4.1MHz are both associated with strong resonance within the fluid layer. In figure 6.3(b) a small peak in acoustic energy can be seen and is likely to correspond to a quarter-wavelength resonance in the fluid layer. This is a low energy resonance, and as no corresponding variation in the impedance can be seen it is difficult to locate based on changes in the electrical characteristics.

The key physical differences between the bulk and printed devices are the transducer structure and material, and the method of adhesion to the silicon. This suggests that the more complex profile

of the bulk PZT data is caused by additional degrees of freedom introduced by the adhesive layer. Further work investigating the efficiency of each transducer type would be of value, although no comparison in efficiency or power is made here. Instead it has simply been ensured that the frequency response can be modelled, an important consideration when simulating the acoustic field within each device.