KLM Model Research Articles

PSPICE approach for designing the ultrasonic piezoelectric transducer for medical diagnostic applications

Ultrasound has become an effective and practical tool for obtaining medical information from within the human body without exposing the patient to X-rays. The emphasis of this paper is on the design of low-loss (high transmitting power) and wide-band transducers used for ultrasonic diagnostic. The approach we have used consists of impedance matching the front face of the transducer to the propagating medium and air-backing the rear face. By tuning the thickness and acoustical impedance of the matching layer, transducers with wide-band and high-transmitting power can be obtained. In imaging application, short time duration is required. The backed material was developed to improve time duration and analyze the influence of the insertion loss. PSPICE code of the KLM model is implemented to predict precisely the performance of the matched transducers. Since the transducer's characteristics of wide-band width and high-transmitting power are somewhat in conflict in the design criteria, a matching-layer thickness that is a little bit shorter or longer than one quarter wavelength is proposed as a good trade-off between the two criteria. Good agreement between the simulation results and experimental results has been achieved.

Pspice implementation for designing the acoustical matching layers of ultrasonic piezoelectric transducers

Ultrasound has become an effective and practical tool for obtaining medical information from within the human body without exposing the patient to X-rays. The emphasis of this paper is on the design of low-loss (high transmitting power) and wide-band transducers used for ultrasonic diagnostic. The approach we have used consists of impedance matching the front face of the transducer to the propagating medium and air-backing the rear face. By tuning the thickness and acoustical impedance of the matching layer, transducers with wide-band and high-transmitting-power can be obtained. PSPICE code of the KLM model is implemented to predict precisely the performance of the matched transducers. Since the transducer's characteristics of wide-band width and high-transmitting-power are somewhat in conflict in the design criteria, a matching-layer thickness that is a little bit shorter or longer than one quarter wavelength is proposed as a good trade-off between the two criteria. Good agreement between the simulation results and experimental results has been achieved.

Two-dimensional arrays for medical ultrasound using multilayer flexible circuit interconnection

The development of 2-D array transducers has received much recent interest. Unfortunately, fabrication of high density 2-D arrays is difficult due to the large number of electrical interconnections which must be made to the back side of the elements. A typical array operating at 2.2 MHz may have 256 or more connections within a 16.4 mm circular footprint. Interconnection becomes even more challenging as operating frequencies increase. To solve this problem, we have developed a multilayer flexible (MLF) circuit interconnect consisting of a polyimide dielectric with inter-laminar vias routing signals vertically and etched metal traces routing signals horizontally. A transducer is fabricated from an MLF by bonding a PZT chip to its surface and dicing the chip into individual elements, with the saw kerf extending partially into the top polyimide layer to ensure physical and electrical isolation of the elements. The KLM model was used to compare the performance of an MLF 2-D array to a conventional hand wired 2-D array. MLF and wire guide transducers were fabricated, each with 256 active elements, 0.4 mm interelement spacing, and 2.2 MHz center frequency. Vector impedance, pulse length, bandwidth, angular response, and cross-coupling were found to be comparable in both types of arrays. Using the MLF, however, fabrication time was reduced dramatically. More importantly, MLF technology may be used to increase 2-D array connection density beyond the limitations of current of hand wired fabrication techniques. Thus MLF circuits provide a means for the interconnection of current and future high frequency 2-D arrays.

Calculation of ultrasonic transducer signal-to-noise ratios using the KLM model

This paper describes a method for adding thermal and amplifier noise to a KLM model for a transducer element. The model is used to compare the magnitudes of various noise sources in a 5 MHz array element typical of those used for linear array imaging with and without an amplifier. Fundamental signal-to-noise ratio (SNR) issues of importance to array and amplifier designers are explored, including the effect on SNR of effective dielectric constant of the piezoelectric material, individual element size, changing the number of elements, and adding an amplifier to an element before and after a cable. SNR is considered both for the case in which the acoustic output is limited by the maximum rarefactive pressure which is considered safe for a particular application (Mechanical Index limitation) and the case in which acoustic output is limited by the maximum transmit voltage than can he delivered by the imaging system or tolerated by the transducer. It is shown that the SNR performance depends on many controllable parameters and that significant improvements in SNR can be achieved through proper design. The implications for 1.5-D and 2-D array elements are discussed.

Improved signal-to-noise ratio in hybrid 2-D arrays: experimental confirmation.

2-D array transducers have shown significant promise for medical ultrasound over conventional linear arrays, at the cost of increasing the number of channels, difficulty of fabrication and array element impedance. The increase in element impedance reduces the power coupled to a 2-D array element from a conventional 50 omega source in transmit mode. If the array is sparse, which is typical of 2-D arrays, then the net power coupled into the front acoustic load is reduced when compared to a fully sampled aperture. Furthermore, the received signal-to-noise ratio (SNR), when measured through a nonideal amplifier, is degraded because the high impedance 2-D array transducer element cannot efficiently drive the coaxial cable. The reduction in transmit sensitivity and received SNR can be circumvented with the application of multilayer piezoelectric elements. The improvement in transmit occurs because the transducer impedance is better matched to the impedance of the source. In receive, multilayer elements allow more of the open circuit received voltage to fall across the input of the high impedance preamplifier. In this case, the same number of layers are used in transmit and receive. Recently, it has been suggested that separate optimization of the transmit channel and receive channel (a hybrid array) would further improve the pulse-echo SNR. In this paper, we fabricated and tested a hybrid array operating at 1 MHz using a multilayer transmit element and single layer receive element. A 7 omega transmitter and high impedance preamplifier were placed adjacent to the transmit and receive elements within the transducer assembly. The hybrid pulse-echo SNR improved by 26.4 dB over the conventional array. The experimental result showed good agreement with the KLM model. Furthermore, KLM simulations showed that as the operating frequency of the array increases, the overall improvement over the conventional array increases. For example, a 1.5-D array operating at 2 M Hz had an improvement of 30 dB whereas a 7.5 M Hz 1.5-D array showed an increase of approximately 38 dB. The separate optimization of the transmit and receive channel for 2-D arrays showed even greater improvement than for 1.5-D arrays. For example, a 2 MHz 2-D array had an improvement of over 44 dB.

Characterization of polymer ultrasonic receivers by a photoacoustic method

Following the development of a small laser-ultrasound probe, theoretical and experimental parameters have been identified for the modelling of polymer transducers used as ultrasonic receivers. A laser-ultrasound signal is used as a standard input signal to the transducer. Using a o one-dimensional model as an approximation, a system identification approach is used to determine the key parameters of transducer behaviour. The method described in this paper has an advantage over the KLM model, since it does not require precise knowledge of the piezoelectric, dielectric and mechanical properties of the transducer. Nevertheless, it provides an insight into transducer characteristics and therefore has some advantage over a ‘black box’ modelling approach. Experimental validation shows that just three parameters may be used to characterize transducer behaviour over a range of input pressure signals extending to 150 kPa.

Optimization of Signal-to-Noise Ratio for Multilayer Pzt Transducers

In medical ultrasound imaging, two-dimensional (2-D) array transducers are desirable to implement dynamic focusing and phase aberration correction in two dimensions as well as volumetric imaging. Unfortunately, the small size of a 2-D array element results in a small clamped capacitance and a large electrical impedance near the resonance frequency. This results in poor signal-to-noise ratio (SNR) of the array elements. It has previously been demonstrated that transducers made from multilayer PZT ceramics have lower electrical impedance and greater SNR than comparable single layer elements. A simplified circuit model has been developed to optimize the SNR for multilayer ceramic (MLC) transducers. In this model, an electronic transmitter excites the array element and in the receive mode, the element drives a coaxial cable load terminated by a high impedance preamplifier. The transducer impedance is Zt/N2, where N is the number of piezoelectric layers. Maximum transmit signal is obtained when N = Ntx such that the transducer impedance, Zt/Ntx2, is matched to the source impedance. Maximum receive signal is obtained when N = Nrx such that the transducer impedance, Zt/Nrx2, is matched to the coaxial cable reactance. For maximum pulse-echo signal, the transducer should be designed with N = square root of Ntx Nrx, the geometric mean of Ntx and Nrx. Using this optimization technique, a 1.5-D array was designed with 3 layers for maximum pulse-echo SNR. Results of simulations from the simplified circuit analysis were consistent with those of the KLM model. The 3 layer array was fabricated as well as a single layer control array. The measured transmit signal and receive signal agreed with the simulation results.

Optimization of Signal-to-Noise Ratio for Multilayer PZT Transducers

In medical ultrasound imaging, two-dimensional (2-D) array transducers are desirable to implement dynamic focusing and phase aberration correction in two dimensions as well as volumetric imaging. Unfortunately, the small size of a 2-D array element results in a small clamped capacitance and a large electrical impedance near the resonance frequency. This results in poor signal-to-noise ratio (SNR) of the array elements. It has previously been demonstrated that transducers made from multilayer PZT ceramics have lower electrical impedance and greater SNR than comparable single layer elements. A simplified circuit model has been developed to optimize the SNR for multilayer ceramic (MLC) transducers. In this model, an electronic transmitter excites the array element and in the receive mode, the element drives a coaxial cable load terminated by a high impedance preamplifier. The transducer impedance is Z t/N 2, where N is the number of piezoelectric layers. Maximum transmit signal is obtained when N = N tx, such that the transducer impedance, Z t/N tx 2, is matched to the source impedance. Maximum receive signal is obtained when N = N rx such that the transducer impedance, Z t/N rx 2 is matched to the coaxial cable reactance. For maximum pulse-echo signal, the transducer should be designed with N = [formula] the geometric mean of N tx and N rx. Using this optimization technique, a 1.5-D array was designed with 3 layers for maximum pulse-echo SNR. Results of simulations from the simplified circuit analysis were consistent with those of the KLM model. The 3 layer array was fabricated as well as a single layer control array. The measured transmit signal and receive signal agreed with the simulation results.

Large-area ultrasonic gap profile measurements using two-dimensional PVDF "blanket array" transducers

A technique is described for utilizing two-dimensional ultrasonic transducer arrays to accurately measure the spacing (i.e., the gap profile) between large-area mating surfaces. The acoustic measurement theory for pulse-echo and pitch-catch gap profile measurements is derived from a generalized KLM model representation of ultrasonic transducers located within the gap between two mating structures. Expressions for the ultrasonically measured gap spacing are derived in terms of the thicknesses and longitudinal acoustic velocities of the constituent layers of the transducer element(s), adhesive layers(s), and gap medium. Extremely thin PVDF two-dimensional arrays were fabricated and adhered to the inside of a precision gap profile device for demonstrating the measurement technique. Two-dimensional gap profile measurements were made to /spl plusmn/0.001" accuracy for a variety of gap profiles in the range of 0-0.200" thickness. Gap profile measurements were made with both liquid and air as the gap medium and the results show potential for measuring otherwise inaccessible gap profiles between structures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Multilayer piezoelectric ceramics for two-dimensional array transducers

In medical ultrasound imaging, 2-D array transducers have become essential to implement dynamic focusing and phase-correction in the elevation dimension as well as real-time volumetric scanning. Unfortunately, the small size of a 2-D array element results in a small clamped capacitance and a large electrical impedance near resonance. These elements have poor sensitivity because their impedance is much higher than the electrical impedance of the transmit and receive circuitry. Sensitivity can be improved by using an N layer structure of PZT ceramic with the layers connected acoustically in series and electrically in parallel. For the multilayer ceramic (MLC), the damped capacitance is multiplied by a factor of N(2) and the electrical impedance by 1/N(2) compared to a single layer element of the same dimensions. A 3x43 phased-array transducer has been fabricated using 3 layer PZT-5H material. Each element had a thickness of 0.66 mm and an area of 0.37x3.5 mm. The MLC was manufactured using thick film technology with plated-through vias to electrically interconnect the electrode layers. The completed transducer was compared to a single layer control array of similar dimensions. With a light epoxy backing and a lambda/4 matching layer, the MLC array elements had an impedance of 100 Omega at series resonance of 2.25 MHz, compared to 800 Omega for the control elements. The lower impedance of the MLC elements resulted in a minimum round-trip insertion loss of 24.0 dB, compared to an 34.1 dB for the control array elements. These results were consistent with KLM modeling. B-scan images were made of cysts in a tissue-mimicking phantom and of the left kidney in vivo. The images clearly showed a higher signal-to-noise ratio for the MLC array compared to the control. As a result, 2-D arrays made of multilayer ceramics can be used to form images at a higher frequency and greater range than single layer arrays.

Modeling and optimization of high-frequency ultrasound transducers

Obtaining an accurate transducer model for a high-frequency transducer can be troublesome using traditional models, such as the KLM model, since it is often difficult to measure precisely the piezoelectric, dielectric, and mechanical properties of the transducer. This paper describes an alternative method of modeling transducers using network theory. The network theory model for a transducer is determined from a measurement of the transducer impedance in water and the pulse-echo response of the system for a given electrical source and load. A discussion of how this model can be used to optimize the design of an electrical matching circuit is given. This method is illustrated by designing a two-element transmission line matching circuit for a miniature 53 MHz transducer. Excellent agreement between the network model prediction and the experimental response is obtained. >

The relationship between KLM and MAK models for nonmonotonic inference operations

The purpose of this note is to make quite clear the relationship between two variants of the general notion of a preferential model for nonmonotonic inference: the models of Kraus, Lehmann and Magidor (KLM models) and those of Makinson (MAK models). On the one hand, we introduce the notion of the core of a KLM model, which suffices to fully determine the associated nonmonotonic inference relation. On the other hand, we slightly amplify MAK models with a monotonic consequence operation as additional ingredient. We give two equivalent characterizations of the cores of KLM models: they are precisely the amplified MAK models whose satisfaction relation: This gives corollary characterizations of certain particular classes of KLM models, notably those that are (in their terminology) cumulative and more specifically those they call preferential.

Experimental determination of the linear biphasic constitutive coefficients of human fetal proximal femoral chondroepiphysis

The mechanical properties of the cartilaginous regions of the proximal femoral epiphysis are an important factor in load transmission through the hip joint of young children. Cylindrical test specimens excised from the chondroepiphysis of human stillborn femoral heads were subjected to uniaxial loading in peripherally-unconfined compression, using a ramp/plateau input strain history. The corresponding load vs time curves were analyzed in terms of a recent analytical solution for a linear biphasic material (the well-known KLM model), allowing calculation of that model's three fundamental constitutive coefficients (permeability, equilibrium modulus and solid-phase Poisson ratio) for this material. The numerical algorithm developed to evaluate the biphasic solution yielded very precise replication of previously published KLM parametric plots. When fitted to experimental load histories, however, the model provided only a rather loose approximation of specimen behavior, due apparently to a substantial underestimation of the transient response component associated with interstitial fluid transport. Averaged over the series, the best-fit values for permeability (2.51 × 10 −15 m 4 N s −1) and equilibrium modulus (0.699 M Pa) were in the range of values accepted for human adult articular cartilage. A consequence of the coarseness of the analytical curve fits was that a solid-phase Poisson ratio of 0.0 was inferred for all specimens. The permeability vs equilibrium modulus exhibited a nearly linear ( r = 0.74) inverse relationship similar to that reported for adult articular cartilage.

FET pulse generator for ultrasonic pulse echo applications

Ultrasonic NDT applications are frequently based on the spike excitation of piezoelectric transducers by means of efficient pulsers which usually include a power switching device (e.g. SCR or MOS-FET) and some rectifier components. In this paper we present an approximate frequency domain electro-acoustic model for pulsed piezoelectric ultrasonic transmitters which, by integrating partial models of the different stages (driving electronics, tuning/matching networks and broadband piezoelectric transducer), allows the computation of the emission transfer function and output force temporal waveform. An approximate frequency domain model is used for the evaluation of the electrical driving pulse from the spike generator. Tuning circuits, interconnecting cable and mechanical impedance matching layers are modeled by means of transmission lines and the classical quadripole approach. The KLM model is used for the piezoelectric transducer. In addition, a PSPICE scheme is used for an alternative simulation of the broadband driving spike, including the accurate evaluation of non-linear driving effects. Several examples illustrate the capabilities of the specifically developed software.