Impedance mismatch

The use of air-bome ultrasound for the excitation and reception of surface or bulk waves introduces a number of problems. The acoustic impedance mismatch which exists at the transducer/air and the air/sample interfaces is the dominant factor to be overcome in this system. Typical values for these three media are about 35 MRayls for a piezo-ceramic (PZT) element and 45 MRayls for steel, compared with just 0.0004 MRayls for air. The transmission coefficient T for energy from a medium 1 into a medium 2 is given by... 

Equations (8.9) and (8.10) are more appropriate when the tensile excursion, o min. (or do — measured interface history before the signal reverberation from the spall plane arrives at the interface. 

Because of the different models of programming and persistence, impedence mismatch becomes a major development cost. It is alleviated by products that help automate the mapping. 

In view of the formidable technical difficulties, the results that have been achieved are all the more impressive. Figure 3.3(a) (see colour plate section) is an acoustic image of a bipolar transistor on a silicon integrated circuit taken at 4.2 GHz. There is a very severe acoustic impedance mismatch between helium and a material such as silicon. Even for normally incident waves 99 per cent of the power is reflected straight off the surface, and for waves incident at an angle greater than 3° all the power is reflected. For a lens of N.A. = 0.5,... 

For the accurate determination of detonation pressure (Pq), a technique of impedance mismatch is applied. The explosive is detonated in contact with water (its equation of state is known and is transparent which facilitates record of shock propagation by shadowgraphy technique). Then, after measuring the transmitted shock velocity in water, detonation pressure is calculated by Equation 3.12 ... 

Particle velocity is an important parameter in the so-called impedance-mismatch method of determining whether the shock from one material enters as a shock or rarefaction into another material in contact with the first material (see Vol 7, HI79-83 and Vol 9, S60). Two of the three commonly used Hugoniot curves (see Vol 7, H179—83) are in the form of P vs u or U vs u plots, and the third form, P vs v, depends on v, usually obtained via Eq 2 (see Vol 7, HI 80) The writer has suggested that input shock particle velocity is a better criterion for the shock sensitivity threshold of expls than input shock pressure (see Vol 9, S76)... 

When selective layers are deposited, the whole structure must be treated as a multiple resonator in which the reflection and/or refraction of the acoustic energy occurs at each interface. For example, when a polymer film is deposited on top of the gold electrode of the QCM, it is the polymer-Au interface with which we are concerned. When the mass loading of multiple structures becomes too high, the effect of the impedance mismatches becomes significant and the crystal ceases to oscillate. Even approximate treatment of the multiple resonator is difficult because densities, as well as thicknesses and shear moduli, of the individual layers must be known. 

The packaging (i.e., electrical insulation for operation in electrolytes) is more difficult with SAWs due to their rectangular geometry. SAWs are easier to fabricate with lithographic microfabrication techniques and therefore are more suitable for use in an array (Ricco et al., 1998). The choice of electrode materials is critical for QCM, where acoustic impedance mismatch can result in substantial lowering of the Q factor of the device. On the other hand, it does not play any role in the SAW devices. The energy losses to the condensed medium are higher in SAWs and this fact makes them even less suitable for operation in liquids. Nevertheless, SAW biosensors have been reported (Marx, 2003). 

We now check whether Eq. (1), with S /3 = e2/ and modified as above to account for finite propagation time, can explain our data. The unknown parameters are the resistance Rq and the effective environment noise temperature Tq. We checked that the impedance of the samples was frequency independent up to 1.2 GHz within 5%. Fig. 2 shows the best fits to the theory, Eq. (1), for all our data. The four curves lead to Ro = 42 12, in agreement with the fact that the electromagnetic environment (amplifier, bias tee, coaxial cable, sample holder) was identical for the two samples. We have measured the impedance Zenv seen by the sample. Due to impedance mismatch between the amplifier and the cable, there are standing waves along the cable. This causes Zenv to be complex with a phase that varies with frequency. We measured that the modulus Zenv varies between 30 12 and 70 12 within the detection bandwidth, in reasonable agreement with f o = 42 12 extracted from the fits. 

Physical Modelling. The last method of synthesis, physical modeling, is the modeling of musical instruments by their simulating their acoustic models. One popular model is the acoustic transmission line (discussed by Smith in his chapter), where a non-linear source drives the transmission line model. Waves are propagated down the transmission line until discontinuities (represented by nodes of impedance mismatches) are found and reflected waves are introduced. The transmission lines can be implemented with lattice filters. 

Typically the source is tuned with the sample in place and then locked to match the cavity resonance frequency so as to achieve maximum energy storage and minimum reflected power. This reflected power is directed through a one-way coupler called a circulator to a crystal diode detector to convey information about sample absorption in the cavity. An iris opening to the cavity is adjusted to match the impedance of the cavity to that of the source so as to produce minimum reflection of radiation from the cavity. This condition gives maximum sensitivity for the impedance mismatch produced when sample absorption occurs in the cavity. 

With a sensitive pump-probe technique, possibly within a common-path interferometer, one can detect the acoustic vibrations of an individual gold nanoparticle [36]. This measurement directly gives the vibration s damping time, a parameter inaccessible to measurements on ensembles of nanoparticles, because of the inhomogeneity in sizes and shapes of populations of nanoparticles. The damping of vibrations of a nanoparticle depends critically on the acoustic impedance mismatch between particle and substrate materials, as well as on the mechanical contact area between them. Acoustic damping is therefore a probe of this contact, which may often be limited to a few nanometers only in diameter. 

If transmission measurements are impossible, another approach is to measure the amount of sound reflected at the interface between the sample and a known solid— often the container wall. The amount of sound reflected is a function of the impedance mismatch between sample and solid defined by a reflection coefficient, R 2. where z is the acoustic impedance of the material (= cp) (5). 

A typical signal from the center gauge in the target array is shown in Figure 22. The trace rose first to the impact stress in the acrylic and then to the stress in the explosive sample. The spike results from the impedance mismatch of the adhesive bond with the Plexiglas and lead azide. 

The dielectric constant of the substrate is the prime property because the propagation speed of the signal is inversely related to it. At these speeds the system has to be designed as a transmission line which must match the impedance of the devices used. Impedance mismatch can lead to reflected signals, and hence to signal distortion. The characteristic impedance of the line is also dependent on the dielectric constant, and for the devices now being used higher impedances are required and, therefore, low dielectric constant substrates. In addition, it is also important to have low-loss materials to prevent distortion of the pulses. 

Many times, in an effort to reduce amplifier noise, capacitors are added across the output of the amplifier, and occasionally at the input (45). These capacitors frequently reduce the response time of the amplifier, which causes a shift in the curve peaks and also a loss of peak resolution. A proper value of capacitor must be used, if noise is a problem, to form a compromise between noise reduction and loss of peak resolution. Amplifier impedance mismatch can also cause nonlinear output voltages, which can distort the curve peaks. 

Another device which may be very useful is called by various names such as a reflectance bridge, a standing wave meter, or a directional wattmeter. It can be used to measure the impedance match between a coil and its voltage source, for example, the transmitter or the decoupler, by monitoring the power reflected at an impedance mismatch. 

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