ELECTROMAGNETIC MEASUREMENTS AND TECHNIQUES Accurate determination of the input impedance of digital voltmeters G. Rietveld Abstract: A good knowledge of the input impedance of digital voltmeters is sometimes needed in precision measurements, for example in some resistance measurements where the input impedance of the voltmeter shunts the resistors that are being measured. How to determine this input impedance is described. It appears that an accurate determination is only possible when the input bias current generated by the voltmeter input circuitry is taken into account. In addition to a direct current, large current peaks are generated by the input circuitry of the voltmeter due to the switching of this circuitry between the high and low input terminals of the voltmeter. These so- called ‘pump-out’ current peaks can significantly affect the measurement, requiring an adjustment of the measuring method. 1 Introduction When a digital voltmeter (DVM) is used in precision measurements its input impedance often affects the measurement results. One such application is sketched in Fig. 1, where a DVM is used to measure the ratio of the voltages across two resistors with the same current flowing through them. In this case the required resistance ratio R S / R X is to a first order equal to the voltage ratio measured by the DVM. To second order however, the input resistance of the DVM has to be taken into account, since this resistance is shunting the resistor it is connected to. We can neglect the change in current due to the input resistance R in when R P 4R S þ R X [1]. It can then be readily derived that the deviation d in in the resistance ratio R S /R X caused by R in is equal to d in ¼ðR S  R X Þ=R in ð1Þ In many measurement situations this deviation can be neglected given the very high input impedance of modern DVMs. For example, the Agilent 3458A DVM has a specified input resistance of larger than 100 GO. However, when this DVM is used for measuring 10 kO resistance standards against the quantum Hall effect with a resistance of 12.9 kO [2–4], the effect of R in is significant [5] . With an input resistance of 100 GO, the deviation in this case amounts to (12.9–10 k)/100 GO which is approximately 3 parts in 10 8 . Since the final uncertainty aimed for in this measurement is at the level of 1–2 parts in 10 8 , the input resistance of the DVM needs to be accurately determined. 2 Measurement of DVM input resistance The basic approach for the measurement of the input resistance of a DVM is simple [2]. The voltage V S supplied by a voltage source is measured by the DVM with a resistance R div in the line connecting the voltage source and the DVM (see Fig. 2). For an ideal voltmeter the voltage read by the DVM is simply that of the voltage source. However, when the input resistance R in of the DVM is not infinite, this resistance forms a resistive divider together with R div , and the DVM is reading the divided voltage V div . From this voltage the value of R in can be calculated through R in ¼ R div V div =ðV S  V div Þ ð2Þ A more complete model of the input circuitry of the DVM contains not only a noninfinite input resistance R in but also a nonzero input capacitance C in , a nonzero DC bias I bias , and a pulsed ‘pump-out’ current I p-o (see Fig. 2). The effect of the pump-out current is discussed in more detail subsequently. For the correct determination of R in especially the effect of I bias is important, since this causes an additional voltage drop across R div . When this effect is taken into DVM R S R X R P V DVM Fig. 1 Schematic set-up used for scaling resistance values with digital voltmeter which is successively measuring the voltage drop across R S and R X DVM R div V R in C in I bia s I p- o L V div DVM V R in Cin I bias I p-o H Fig. 2 Schematic set-up for measurement of input resistance R in of digital voltmeter. Input circuit has been modelled with input resistance R in , input capacitance C in , input bias current I bias , pump- out current I p-o , and ideal voltmeter V The author is with the NMi Van Swinden Laboratorium, P.O. Box 654, 2600 AR Delft, The Netherlands r IEE, 2004 IEE Proceedings online no. 20040700 doi:10.1049/ip-smt:20040700 Paper first received 17th December 2003 and in revised form 6th May 2004 IEE Proc.-Sci. Meas. Technol., Vol. 151, No. 5, September 2004 381