IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 51, NO. 6, DECEMBER 2002 1323 DVM Input and Leakage Resistance Analysis in the DVM-Based Resistance Measurement Systems Roman Malaric ´, Josip Butorac, and Ivan Leniˇ cek Abstract—The digit voltmeter (DVM) input and leakage resis- tances have been analyzed in the DVM-based resistance measure- ment system using one or two DVMs. The results are given both theoretically and experimentally. Shunting errors due to DVM- input and leakage resistances were substantially reduced by using a proper measurement method. The method is being further inves- tigated for measuring high-ohm standard resistors. Index Terms—Digit voltmeters (DVM) input resistance, leakage resistance, resistance measurement. I. INTRODUCTION R ESISTANCE standards are usually calibrated using the current comparator bridge. Since their introduction onto the market, the use of 8 1/2-digit voltmeters (DVMs) has been investigated with the purpose of measuring the Quantum Hall Resistance Standards, as well as the wire-wound standards. Such a measurement system is easy to build, and the published results from several different laboratories around the world using the DVM-based method have been very close to those of the current comparator bridges. To compare the standard resistors, the DVM can be used in two possible ways: as a voltage-measuring device and as a detector in a classic potentiometric method. In the first method, while the DVM is measuring the voltage drop, it is also shunting the standard resistors, thus producing an error if the DVM-input resistance is not much higher than the resistance it is measuring. On the other hand, if the DVM is used as a detector, the problem of DVM-input bias current arises. This bias current is un- stable, though very small, and practically serves as a current source. Therefore, the DVM-input resistance, DVM-input bias, and also leakage resistances to the ground, along with other uncertainty contributions, have been the limiting factors in using digital voltmeters to measure resistance standards. The first paper describing the possible use of the DVM to measure resistance standards was published by Cage et al. [1]. This paper, along with [2], which discusses the sources of uncertainties in a DVM-based measurement system, is used as a reference for most other papers dealing with similar subjects. The method described in these papers uses one DVM to mea- sure alternatively the voltage drop across the standard resistors connected in series. The use of two voltmeters instead of one is discussed in [3]. The use of two voltmeters does not require a stable voltage source if DVMs are triggered simultaneously, Manuscript received May 29, 2001; revised September 30, 2002. The authors are with the Faculty of Electrical Engineering and Computing, Department of Electrical Engineering Fundamentals and Measurements, Uni- versity of Zagreb, Zagreb, Croatia (e-mail: roman.malaric@fer.hr). Digital Object Identifier 10.1109/TIM.2002.808016 Fig. 1 Schematic diagram of the measurement method using one DVM. The DVM measures the voltage drop first on a, , and then on b, . and the measurement process takes half the time. In this paper, DVM-input and leakage resistance shunting errors have been analyzed in the DVM-based resistance measurement systems. II. MEASUREMENT METHOD USING ONE DVM The measurement method described in [1] uses one DVM, which alternatively measures the voltage drop across each of the two resistors connected in series as in Fig. 1. Neglecting the DVM errors in the following analysis, the re- sistance ratio can be calculated as: (1) Here, is the shunting error, and and are the DVM read- ings at positions 1) and 2), respectively. In reference [1], the au- thors claim “that the shunting error of the ratio is approx- imately if one neglects the small changes in current that arise when the DVM is moved from position 1) to position 2).” Here, stands for the DVM-input impedance, and is the nominal ratio of and . The shunting error can also be written as . However, if the small change in the current is not neglected when the DVM moves from position 1) to position 2), then the shunting error is calculated differently. If is the voltage from the source, and is the resistor used to control the current in the circuit, current when the DVM is in position 1) can be calculated as (2) The current when the DVM changes to position 2) is (3) 0018-9456/02$17.00 © 2002 IEEE