^{1}

^{2}

^{*}

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The paper describes an improvement of the chopper method for elimination of parasitic voltages in a low resistance comparison and measurement procedure. The basic circuit diagram along with a short description of the working principle are presented and the appropriate low resistance comparator prototype was designed and realized. Preliminary examinations confirm the possibility of measuring extremely low voltages. Very high accuracy in resistance comparison and measurement is achieved (0.08 ppm for 1,000 attempts). Some special critical features in the design are discussed and solutions for overcoming the problems are described.

Standard methods for measurement and low resistance comparison are based on Thompson (Kelvin) bridges, DC current comparators, potentiometers, etc [

The circuit diagram of the proposed chopper stabilized comparator is given in _{X} and reference _{R}) provides the adequate voltages in them, _{X}_{R}_{X} could be expressed as:

The maximum relative measurement error is:
_{R} is reference resistance error (could be less than 10^{−6}) and _{X}, _{R} are measurement errors for the appropriate voltages.

In low resistance measurement (four-terminal resistors [

Thermo-electric or Peltier voltage is generated at the thermocouple junctions of different metals. Even when all the junctions are at the same temperature, the thermoelectric voltage can reach a value of about 0.1μV/°C. The most significant disturbances are a consequence of offset voltages of the operational amplifiers and can be higher than 50 μV. These are direct current (DC) parasitic voltages. Alternating current (AC) unwanted voltages can also occur. The AC parasitic voltages are a consequence of AC power supply inductive or capacitive influence, noise, etc. AC parasitic voltages cause dispersion of measured results around the mean value. The mains influence (inductive and capacitive) is periodic and can be efficiently decreased (shielding, filtering, etc). Noise is a random occurrence with a zero mean and its disturbance may be reduced to acceptable levels by filtration. DC parasitic voltages cause systematic measurement errors and need to be removed from the measurement voltage as much as possible. One solution for minimization of the influence of these parasitic voltages is presented in this paper.

There are several known methods for removing DC parasitic voltages. The main idea of DC voltage elimination is presented in

According to the figure, the voltages can be expressed as:
_{P}

The measured voltage _{P}

It is possible to use integrated operational amplifiers with chopper stabilized input voltage offset, such as ICL7650 [

The principle circuit diagram of the low resistance comparator is shown in _{X}_{R}

The maximal value of resistances _{X}_{R}_{X}_{R}

The controller switches the measuring current on and off and controls the functions of the voltage circuit analog switch. It is adjusted so that the duration of current pulse of 1 A is 60% of one controller cycle. During the remaining 40% of a cycle the current is switched off. While the measuring current is switched off, the amplifier's output should be zero, but parasitic voltage at the amplifier input occurs and it is amplified 1,000 times, as well.

Using correction and feed back circuits, this amplified voltage can be reduced to an acceptable value, below 10 μV. This is done for both resistances (_{X}_{R}_{X}_{R}_{OR}_{OX}

The described solution for low resistance measurement allows a very useful possibility: to perform the measurement with a known value of resistor _{R}_{X}_{R}

In order to reach high measurement accuracy the instrument must have extremely high sensitivity. In such cases unwanted influences can occur. Some critical points of design, construction and practical realization are listed below:

For a complete elimination of error caused by common mode rejection ratio (CMRR) input voltage, a special way of switching was applied. A third switch was added to connect the reference potential of the voltage circuit with the negative resistor potential terminal.

The influence of transient processes was avoided by the use of appropriate length of dead time in controller cycle (pause,

The leakage current of output sample and hold circuits should be extremely small because the voltage drop down mustn’t exceed 10 μV. The controller cycle is synchronized in such a way that the cycle step duration is a multiple of the main frequency period to be able to reach these conditions and thus eliminate the capacitive and inductive disturbances.

In order to reduce the mains supply influence the controller cycle is synchronized with the mains supply frequency.

Excellent quality operational amplifiers with very high open loop gain are used in the design.

To achieve very high linearity, the complete amplification is realized with three-stage amplifiers with low gain (10 times each). The described solution allows the possibility of not only the resistance comparison., but with voltage ratio measurement (_{X}/_{R}) and high quality reference resistor R_{R} (standard resistor for example) it is possible to measure the resistance R_{X} with very high accuracy (milliohm meter).

A 6½ digits A/D converter is embedded in the realized prototype instrument. The applied resistance of _{R}

- U_{OX}, U_{OR} ≈ 10 V (corresponding R_{X}, R_{R} =10

The realized prototype instrument is shown in

An improvement of the chopper method for elimination of parasitic voltages in a procedure of a small resistance comparison and measurement are presented in this paper. The realized instrument prototype had to overcome many practical difficulties. Some of them were solved empirically (i.e. choosing appropriate operational amplifiers) [

Circuit diagram of chopper stabilized comparator.

Parasitic voltage elimination.

The controllers timing diagram.

Low resistance comparator prototype.

The experimental results.

_{O}=U_{OX}-U_{OR}) |
||||
---|---|---|---|---|

100 | 11,2 | 11,2 | 25,6 | 0,26 |

1000 | 4,5 | 4,5 | 24,3 | 0,08 |