Synthesis of a digitally controlled impedance element

A practical design for the synthesis of a digitally controlled electrical impedance element is presented. The impedance element comprises a real impedance element in series with a voltage source whose magnitude is determined by the applied voltage multiplied by a factor k. The value of k is shown strongly to affect the circuit's performance. Results are presented which demonstrate the correspondence between circuit models and practical measurements. When negative values for k were employed the circuit element offered a controlled impedance range of 1:1000 and was stable to at least 1.5 MHz, providing that low source impedance values were used. With a positive k, a restricted range of impedance values could be obtained and the value of source impedance was less critical, though the circuit's performance was acceptable only to about 100 kHz. Consideration is given to the specification of a multiplier that would permit the circuit's range of application to be extended to low megahertz frequencies.