IMPLEMENTATION OF DSP BASED ALGORITHMS FOR IMPEDANCE MEASUREMENTS Pedro M. Ramos 1 and Fernando M. Janeiro 2 1 Instituto de Telecomunicações, Instituto Superior Técnico, DEEC, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal, e-mail: Pedro.Ramos@Lx.it.pt 2 Instituto de Telecomunicações, Universidade de Évora, Departamento de Física, Rua Romão Ramalho 59, 7000-671 Évora, Portugal, e-mail: fmtj@uevora.pt ABSTRACT In this paper, two DSP based algorithms are implemented for impedance measurements. The algorithms (the seven- parameter sine-fitting algorithm and the ellipse fitting algorithm) are implemented and tested in a commercial DSP kit. The complete system is used to compare the algorithms by measuring 105 different impedances, using the four-wire impedance measurement method. The strategic selection of appropriate reference impedances, intrinsic to the impedance measurement method, is also described. The results of each algorithm are compared in terms of speed and accuracy. This is the ground work for a portable DSP based impedance measurement device to be implemented in specifically designed hardware. Index Terms— Impedance measurements, sine- fitting, ellipse-fitting, DSP implementation 1. INTRODUCTION Impedance measurements are paramount in many fields of science. The measurement of many physical quantities is often reduced to the problem of measuring a change in the impedance of a transducer. Therefore, procedures to accurately measure impedances have been devised, depending on the impedance magnitude range and on the measurement frequency range. The rapid development of electronic devices has led to a revolution in impedance measurement procedures by eliminating many of the frequency dependent analog components. The use of analog to digital converters (ADCs) and signal processing algorithms can increase the accuracy of the measurement process. A simple computer based impedance measuring system can be composed of a data acquisition board (DAQ), a function generator and the signal processing algorithms required to analyze the acquired data. A portable low-cost accurate impedance measurement device can be developed by implementing the algorithms in a DSP. The objective of this work is to evaluate the performance of two algorithms and identify the hardware requirements for a portable impedance measurement device. 2. MEASUREMENT METHOD The measurement method is based on the acquisition by two ADCs of the voltages across the unknown impedance and across the reference impedance. The two impedances are connected in series and the current (at the measurement frequency) is supplied by a function generator, as shown in Figure 1. Figure 1. Measurement circuit. FG is the function generator, R Z is the reference impedance, Z is the unknown impedance and ADC represents the analog to digital converter that samples the voltage across each impedance. The two ADCs sample the voltage simultaneously to extract the phase difference between the two sine-signals. After the samples are acquired, signal processing algorithms are responsible for the estimation of the sine amplitudes and phase difference. Each acquired channel is modelled by a sine signal () ( ) 1 1 1 1 cos 2 u t D ft C = π + φ + (1a) () ( ) 2 2 2 2 cos 2 u t D ft C = π + φ + (1b) where D i , C i and φ i are the sine amplitude, DC component and phase of channel i. f is the common frequency. From this model, the impedance parameters are determined by 2 1 R D Z Z D = , (2a) 2 1 R R Z Z Z ϕ = φ - φ + ϕ =Δφ + ϕ (2a) 816 1-4244-1236-6/07/$25.00 © 2007 IEEE 2007 IEEE International Conference on Signal Processing and Communications (ICSPC 2007), 24-27 November 2007, Dubai, United Arab Emirates