Wheatstone bridge

The Wheatstone bridge (short: Wheatstone bridge ) is a measuring device for measuring

• Electrical resistances of ohmic type (direct current resistance),
• Small ohmic resistance changes.

It is composed of four resistors, which are connected together to form a closed ring or a square, comprising a voltage source in one diagonal and a voltage measuring device in the other.

It was invented in 1833 by Samuel Hunter Christie, however, named after the British physicist Sir Charles Wheatstone [ wi ː tstən ], who recognized its importance and its broad circulation.

• 4.1 Billing
• 4.2 applications

Description

A graphically different arrangement more clearly shows that each two resistors form a voltage divider; two voltage dividers are parallel to each other. The voltmeter is between these Establish a cross- relation, which gives the circuit the name of the bridge circuit. The directly measured value of the arrangement is referred to the voltage difference between the voltage dividers, and diagonal voltage or bridge voltage cross.

The original Wheatstone bridge used for the measurement of resistance values ​​by applying the trimming method. First, the three well-known resistance must be as long as varied by the bias voltage is zero. Then can be calculated from the resistances of the fourth, unknown value calculated. The availability of cheaper digital instruments ( that work with other methods ), this measurement method is rarely used. One exception is the precision measurements.

A common also as a Wheatstone bridge (or deflection resistance measuring bridge ) described method is a modification of the deflection process in which only small variations in the resistance can be determined.

Illustrative example: A bridge having a temperature measuring resistor in a voltage divider is located at a reference temperature in the balanced state. If the temperature at the measuring resistor, then the diagonal voltage changes approximately proportional to the temperature change. The deflection method takes in the modern measurement technology a firm place.

Basis

The two parallel voltage divider, the voltage across any resistor (e.g., R1 ) is compared with the corresponding voltage in the parallel branch ( then R3). If these voltages are equal (but not zero ), is called matched the bridge. As long as the bridge cross- branch flows a negligibly small current (which applies to balance always, otherwise if R5 » R1, R2, R3, R4 ), the voltage divider are unloaded, and we have:

In the measurement of this voltage is to be noted that it is associated with a considerable resistance Rq source due to the voltage divider. In an ideal source of supply voltage (with the terminal between the upper and the lower terminal of R4, R3 ) is seen directly in the circuit:

For a symmetrical bridge with so true.

Together with a non-ideal voltage meter can ∞ with an internal resistor R5 < lead to a considerable error of measurement, because the measured voltage relative to the open circuit voltage U5 is smaller by a factor; see real voltage source.

Matching method

We define the balanced state by U5 = 0; then

Or

This equation says that if three resistances are known, one can calculate a fourth. This provides a measurement method to measure resistance, which is also called zeroing method of the Wheatstone bridge.

Measurement with resistance decades

When the resistor Rm is to be measured at the position of R1, the following applies

And it is in the illustrated circuit with a four-digit value R3 and R2: R4 the measurement range, usefully a magnitude factor, eg 1:1 or 1:10 or 100:1. The application area covers approximately the range from Rm = 1 Ω ... 1 M.

The last equation is independent of the supply voltage U0. However, please note: - U0 should be so large that almost the bridge is balanced adjustment of R3 by one step on the least significant digit still causes a noticeable change in the cross- bridge voltage U5. - U0 should be so small that the inevitable heating of the resistors this is not changed recognizable.

The bridge can also be operated with tone frequency instead of DC voltage and used as an indicator of a headset that is also a very sensitive indicator. However, then the direction in which must be matched, no more recognizable, since the ear of the phase position can not be detected.

Measurement with slide-wire potentiometer

The introduced by Gustav Kirchhoff (1824-1887) version only requires a precision resistor and a slide-wire potentiometer. The resistance wire is stretched on a board or wound on a tube. The ends of the wire are connected to the supply voltage and the sliding contact part engages from the voltage of the potentiometer. The aspect ratio a / b is equivalent to the resistance ratio. In the balanced condition, the unknown resistance Rx is calculated as follows:

The accuracy depends mainly on the mechanical ratio a / b and the reference resistor Rv from. In the historic use a galvanometer was used to display the detuning. To perform the zero adjustment more precise, there is a button in series with the indicator, as a movement of the pointer is more recognizable than a position.

The comparison resistor Rv should be in the order as Rx, because the accuracy decreases towards the ends of the abrasive wire.

Development

The Wheatstone bridge is still used today at most for precision measurements, see also calibration. Due to the high accuracy of the digital multimeter and the availability of precision operational amplifiers, direct-reading measuring methods can be used almost anywhere.

Wheatstone bridges as laboratory instruments like the one pictured are therefore no longer in the commercial and professional use, the modification of the rash - resistance bridge does.

The Wheatstone bridge is used to measure small resistances ( value < 1 Ω ) is not suitable because the cables and connectors that connect the resistor to be measured Rx with the meter, falsify the measurement. From the Wheatstone bridge for the originated Thomson bridge. Also, this is no longer in trade and professional use. For an alternative see ohmmeter.

Instead of ohmic resistances connected to a DC voltage for supplying also generally impedances can be measured by the AC voltage supply, see AC bridge.

Deflection method

In metrology, non-electrical quantities the Wheatstone bridge of considerable importance to accommodate small changes in resistance from the balanced state is out. Then she works as a transmitter, for instance in connection

• With temperature-dependent resistors (resistance thermometer )
• With influenced by deformation resistance ( strain gauges ).

Account

In these cases, a voltage U5 is created as a measure of a change in resistance? R; the bridge works on the rash method. Specifically: If R1 changes from the balanced state out, R1 → R1 ¨ R1, then created according to the initially prepared equation

Is with the detuning and the bridge ratio

As long or applies the approximation

The function has a maximum at k = 1, where it has the value of f ( 1) = ¼. This means that the bridge has a maximum sensitivity when it is symmetrical ( in balance all resistors equal = R). Then

Example: Relative change in resistance ¨ R1 / R = 10-3; U0 = 10 V. Then U5 = 2.5 mV. These are still 25 digit ( a digit ), if the voltage meter measuring range 200 mV dissolves in 2000 digits.

This means: Without the resistor to know exactly small changes to that quality can be determined, is determined with the U5. While the subtraction of two nearly equal measured values ​​always leads to very unreliable results, here the difference is formed in the circuit and as such is directly and reliably measurable!

Allowing all four resistors in each case a small change in the balance out, then you get in the above underlying arrangement with a symmetrical bridge

Rule of thumb for the sign: Based on the influence of the change of any resistance to the change of an adjacent U5 in the bridge resistance of opposite sign comes in and the change of the diagonally opposite resistance with the same sign.

Example: If two adjacent resistors to change depending 2 ‰, then their effect cancels U5.

Applications

In this equation is constructed in microelectronics and sensor technology to a very considerable extent. In strain sensitive resistors can react with positive or negative change in resistance and complement in the equation, while temperature effects, which act the same on all pick up on deformation depending on the application of the resistors. Resistors that are located on a flexible base so that detect forces, pressures, torques etc. Small relative changes in length at 10-4 may be so acquired. The picture shows a pressure gauge in this technique: A membrane made ​​of silicon, which has high elastic properties, is deformed by pressure; in places with particularly strong bending resistors are diffused; with in each case three bonding wires is formed in each half of a Wheatstone bridge.

When measuring temperature using a resistance thermometer only one resistor of the bridge is configured to be adjustable. Because of the quite comfortable measuring effect - the resistance of a standard platinum resistance thermometer doubles in the range 0 ... 266 ° C - working with unbalanced bridge, k »1, which reduces the sensitivity, but the area enlarged in which the linear approximation is valid. In addition, when connected in three-wire circuit, the bridge circuit for eliminating the influence of temperature makes the resistance of the cable.