I'm crossing Diamond Bridge
I don't wanna go there
But I can't stay here.

("Diamond Bridge," by Blondie, 2003)

The above drawing shows the two parallel circuits of a Wheatstone Bridge forming the upper half and lower half of a  diamond.

Hey, that's like a real "Diamond Bridge!"

PTOA Readers and Students learned in PTOA Segment #114 that RTDs made out of platinum are incorporated into the circuitry of a Wheatstone Bridge.

PTOA Readers and Students also learned that the purpose of the  Wheatstone Bridge is to translate the ohms output from the RTD into a voltage output.

The basic Wheatstone Bridge circuit is represented by the  electrical diagram shown at the top of this page.

In the real world, a circuit board representation of a Wheatstone Bridge might look something like the picture to the right.

Instrument-Techie PTOA Readers and Students need to grasp the fundamentals of Wheatstone Bridge technology because:

• RTDs incorporated into modified Wheatstone Bridge circuits accurately measure process temperatures.
• Wheatstone Bridge technology is also incorporated into  popular industrial pressure-measuring devices called strain gauges.

In summary ...

Wheatstone Bridge technology is used to measure both process temperatures AND pressures.

Hey!

Wheatstone Bridges are so popular a beer has been named after the technology!

And Fred the Stickman has a warning to PTOA Readers and Students that follow gluten-free diets:

 

 

"You must resist this brew!
Yuk! Yuk!Yuk!"

 

 

WHEATSTONE BRIDGE BASICS

The Basic Bridge Structure

Without getting too wonky about it, here's an introductory focus on Wheatstone Bridge technology based upon the diamond-shaped bridge diagram below:

Find the battery that is supplying the direct current to the circuit.

The battery is on the bottom of the circuit.

 

The battery is represented as 4 vertical hash marks with positive pole on the left (+) and negative pole on the right (-) as shown in the nearby photo.

The current is shown flowing out of the battery as a red line.

The current flows to a junction and then the single current is split into two parallel circuits:

• The current can "take the high road" and flow "up" through resistor R1 and then "down" through resistor R2 ... OR ...
• The current could flow "down" through resistor R3 and "up" through resistor Rx.

R1, R2, and R3 have known, fixed resistances.

However, the resistance of resistor Rx can vary and is unknown.

The above schematic shows a galvanometer (G in the circuit) connected to both P1 and P2 of the Wheatstone Bridge.

A galvanometer is a very sensitive ammeter. That means the job of a galvanometer is to measure very small currents.

The difference in voltage (aka potential difference) between  P1 and P2 makes it possible for the galvanometer to measure a current because ...

... as all PTOA Readers and Students learned in PTOA Segment #106

I = V/R

How convenient that the galvanometer converts a difference in voltage into a standard signal of milliAmps!

 

The Balanced Bridge is where Temperature = 0.

When all 4 resistors in the Wheatstone Bridge are at the same resistance and therefore the same ohms, the currents running through R1 and R3 are equal and there is no potential difference (aka change in voltage) sensed between P1 and P2.

In the 100% balanced state, galvanometer does not detect current because ...

I = 0 Voltage / R      will equal 0 every time!

When the four resistances are balanced at equivalent resistance, the temperature measured will be zero.

Note: The above does not mean that the four resistances will be 0 Ω; if all four resistances were balanced at 100 Ω that would also be the zero of the temperature scale.

 

THE RTD IS Rx IN THE WHEATSTONE BRIDGE CIRCUIT 

When Wheatstone Bridge/RTD technology is used to measure temperatures, the RTD plays the role of the unknown, variable resistance in the bridge circuit.

In other words, the lead wires coming out of the RTD sensing element are connected into the Wheatstone Bridge circuit.

 

Two leads are shown coming out of the RTD sensing element that is shown on the lower right quadrant of the drawing above.

One lead of the RTD would be attached at P2.

The other lead would be connected near the junction where the two parallel circuits join back together (the junction near the negative sign).

Initially the circuit can be calibrated to an inferred zero temperature measurement by balancing all the resistors to an equivalent ohms output.

A change of temperature sensed by the RTD changes its ohms output (aka resistance) in the Rx leg of the bridge.

The difference in voltage between P1 and P2 (aka potential difference) will be compared to the difference in voltage between P1 and P2 when the bridge is balanced (which is where the temperature = 0).

The greater the temperature of the stuff that is having its temperature measured by the RTD → the greater the resistance and ohms output from Rx → the greater the potential difference will increase between P1 and P2.

Mathematical relationships known to exist between the 4 legs of the diamond-shaped circuit can determine the varying resistance, Rx, which is the RTD's resistance.

The fancy name for sequentially performing math steps to solve for an unknown is "algorithm." Components of the DCS can perform the algorithm that determines the value of the RTD's output.

Once known, the RTD's resistance can then be correlated to temperature.

And, it goes without saying that the whole shebang only works because of the linear relationships between:

• The RTD's resistance output and temperature.
• The Wheatstone Bridge's voltage output and temperature.

 

 

SOURCES OF RTD MEASUREMENT ERROR

Of course, the real-world situation is never quite as easy as stated.

Self Heating Resistance Interference

A source of DC current (the battery) must be supplied so that a potential difference voltage can be generated and hence correlated back to a temperature.

However, the mere fact of energizing the RTD wire will self-heat the wire ... which will generate a resistance that is not related to temperature measurement.

For this reason the DC current is maintained at just a level to achieve 'excitation.'

 

Beware: Lead-Wire Error

The lead wires (pronounced "leed wires") that connect to the bridge will naturally have an electrical resistance to current ... because they are metal wires with current flowing through them!

The resistance generated by the lead wires is determined by:

• What the wires are made of (usually copper).
• The wire diameter (aka wire gauge).
• The wire length.

The lead wires are also impacted by changes in ambient temperature which will likewise impact their resistance.

Lead-wire error can cause significant error in the temperature measurement and must therefore be corrected.

For example, assume these facts to be true:

• R1, R2, and R3 are each fixed resistances that are known to be 100 Ω.
• The RTD resistance (Rx)  is determined to be 139 Ω.
• The lead wires of the RTD (aka Rx) are made of 250 feet of #16 gauge copper wire. The two leads made of the material, diameter size, and length as described will contribute 1 Ω resistance each to the total potential difference detected.

In the situation described, only 137 Ω are generated solely due to temperature change.

The two ohms generated because of lead wire error cause a temperature measurement error of 5.9%.

 

THREE AND FOUR LEAD RTDs AND BRIDGES

The solution to lead-wire error is to modify the Wheatstone Bridge into a 3-lead wire ... and even better 4-lead wire RTD and bridge circuit.

Adding additional leads and connecting the leads in arrangements that cancel out the sources of lead-wire error makes it possible to generate a net resistance that is only related to changes in the temperature being measured. 

Compared diagrams for Wheatstone Bridge circuits are shown below:

• A is a basic Wheatstone 2-lead wire RTD circuit.
• B is a modified Wheatstone 3-lead wire RTD circuit.
• C is a modified Wheatstone 4-lead wire RTD circuit.

The RTD sensing element is shown as variable resistor Rt.

The leads from the RTD are identified with the letter "L."

The 5.9% error of the 2-lead wire RTD described above would be reduced to 0.1 °C for a 3-lead wire RTD and 0.03 °C for a 4-lead wire RTD.

The cutaway drawing below shows what the sensing element of a 4-lead wire RTD would look like in the real world.

Each of the four platinum wire coils would be connected to individual copper lead wires at the other end.

TAKE HOME MESSAGES: Wheatstone Bridge technology is used to measure both temperature and pressure.

To measure temperature, RTDs are incorporated into Wheatstone Bridge circuits as the 4th and unknown, variable resistance.

The voltage produced in an RTD-Wheatstone Bridge circuit is actually detected as a difference in voltage (or potential difference) between two parallel circuits that have been split apart from a single circuit.  

When all 4 of the resistances in the Wheatstone Bridge are the same magnitude, the Wheatstone Bridge is balanced and no potential difference (voltage) is sensed. The temperature measurement of a balanced bridge will be 0 degrees. 

Lead-wire error will add significant error to the temperature measurement.

RTDs with 3-lead wires and 4-lead wires connected to modified Wheatstone Bridge circuits greatly reduce the error caused by lead-wire error.

©2016 PTOA Segment 00115
PTOA Process Variable Temperature Focus Study Area
PTOA Process Industry Automation Focus Study Area

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