In this paper, a digital switching demodulator is presented for use in ac-based electrical capacitance tomography systems. Implementing a switching phase-sensitive demodulator (PSD) digitally offers the following advantages: 1) Demodulation can be implemented using a programmable digital device, and hence, CMOS switches, which are used in a conventional switching PSD, are no longer needed; 2) compared with the widely used digital quadrature PSD, this proposed demodulator is simple in configuration because neither a reference signal nor multiplication is required; 3) according to the specific requirements, the new demodulator can be implemented in two operation modes, i.e., the amplitude mode and the phase-sensitive mode; and 4) because only subtractions and accumulations are needed, the proposed demodulator can be easily implemented with low-cost logic devices, e.g., a complex programmable logic device (CPLD). By simulation, the feasibility and effectiveness of the proposed demodulator have been confirmed. CPLD-based and field-programmable-gate-array-based capacitance measurement circuits are constructed, and the performances of different demodulation methods are compared. Both simulation and experiment show that the proposed demodulator can provide demodulation results with high signal-to-noise ratio. The system design can be simplified using the digital switching demodulator.

A Digital Switching Demodulator for Electrical Capacitance Tomography

Capacitance measurement accuracy is affected by phase conformity between signal and reference. This work describes phase detection scheme which is necessary for phase synchronization in tomography application. Core processing for calculating phase and amplitude of the detected signal was built on FPGA (Field-Programmable Gate-Array) platform. Phase shift demodulation algorithm employs IP core provided by Xilinx FPGA. Direct digital synthesizer (DDS), multiplier, accumulator, and CORDIC (coordinate rotation digital computer) modules were used as excitation-reference signal generator, signal multiplication, accumulation, and conversion to polar coordinate in order to conduct trigonometric operation respectively. Hardware design was emulated on MATLAB-Xilinx System Generator to observe its performance. Phase detection range 0-114.58 o and mean absolute error 0.58 o have been achieved. Data processing rate solely at digital signal stage was approximately 100data/s suitable for 32-channel electrical capacitance volume tomography (ECVT) system.

Design and Simulation of Quadrature Phase Detection in Electrical Capacitance Volume Tomography

The invention relates to a current-voltage mapping construction method based on an adjacent stimulus measurement model. The current-voltage mapping construction method based on the adjacent stimulus measurement model aims at the adjacent stimulus measurement model of a sensor which is provided with N electrodes in electrical tomography, utilizes a formula which is reduced by calculating parameters such as an impedance matrix and an electric current density matrix to uniquely calculate a current-voltage matrix and to construct current-voltage mapping based on the adjacent stimulus measurement model. The invention provides the current-voltage mapping construction method based on the adjacent stimulus measurement model. The current-voltage mapping construction method based on the adjacent stimulus measurement model can be applied to a direct reconstruction algorithm in an electrical tomography field, provides direct physical significance of the current-voltage mapping, does not relate to matrix inversion and is easy to operate.

Current-voltage mapping construction method based on adjacent stimulus measurement model

Core processing for calculating phase andamplitude of the detected signal was built on FPGA (Field-Programmable Gate-Array) platform. Phase shift demodulationalgorithm employs IP core provided by Xilinx FPGA. Directdigital synthesizer (DDS), multiplier, accumulator, and CORDIC(coordinate rotation digital computer) modules were used asexcitation-reference signal generator, signal multiplication,accumulation, and conversion to polar coordinate in order toconduct trigonometric operation respectively. Hardware designwas emulated on MATLAB-Xilinx System Generator to observeits performance. Phase detection range 0-114.58o and meanabsolute error 0.58o have been achieved. Data processing ratesolely at digital signal stage was approximately 100data/s suitablefor 32-channel ECVT (electrical capacitance volumetomography) system.

Hardware Design for Quadrature Phase Detection Algorithm in ECVT

In this paper, a new digital demodulation method was proposed for capacitance measurement in AC-based electrical capacitance tomography (ECT) systems. The proposed demodulation method can be carried out in the following steps: (1) measure the phase difference between the in-phase reference signal, i.e., the digital form of the excitation signal, and the digitalized measurement signal by using the SignalTap II Logic Analyzer integrated in FPGA development kits; (2) delay the in-phase reference signal by a specified number of sampling periods according to the phase difference obtained in step (1) to ensure that the adjusted reference signal is completely in phase with the digitalized measurement signal; (3) multiply the digitalized measurement signal with the delayed reference signal point-by-point within one sine wave period, and then accumulate the products to obtain the demodulation result. The feasibility and effectiveness of the proposed digital demodulation method has been analyzed and verified by experimental results. Compared with the commonly used digital quadrature demodulation method, the proposed method can save resources of logic, memory and multiplier elements in the FPGA to a large extent without decreasing the signal to noise ratio (SNR) of the measurement result.

An alternative digital multiplication demodulation method for electrical capacitance tomography

A factorization method was introduced to electromagnetic tomography (EMT) in this paper. Compared with the traditional methods based on the sensitivity theorem, the proposed method can generate the reconstructed images directly. Neither matrix inversion nor iterations is needed in the reconstruction process. The reconstruction process is simple, as the test function is calculated according to the fundamental solution to the governing equation, i.e. the Helmholtz equation. Simulated data were used to validate the feasibility and effectiveness of the proposed method for EMT.

Direct image reconstruction for electromagnetic tomography by using the factorization method

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An alternative digital multiplication demodulation method for electrical capacitance tomography

Direct image reconstruction for electromagnetic tomography by using the factorization method