Electronics- Wheatstone Bridge Circuitsdenethor.wlu.ca/pc320/lectures/wbbeam.pdfWheatstone bridges...

Wheatstone bridges

ElectronicsWheatstone Bridge Circuits

Terry Sturtevant

Wilfrid Laurier University

October 18, 2016

Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit

Wheatstone bridges

A common type of circuit is a Wheatstone bridge.It is really a pair of voltage dividers using a common voltagesource.It’s usually operated with the output voltage at or close tozero.

Wheatstone bridges

A common type of circuit is a Wheatstone bridge.

It is really a pair of voltage dividers using a common voltagesource.It’s usually operated with the output voltage at or close tozero.

Wheatstone bridges

A common type of circuit is a Wheatstone bridge.It is really a pair of voltage dividers using a common voltagesource.

It’s usually operated with the output voltage at or close tozero.

Wheatstone bridges

A common type of circuit is a Wheatstone bridge.It is really a pair of voltage dividers using a common voltagesource.It’s usually operated with the output voltage at or close tozero.

Vin Vout

This is a Wheatstone bridge.

Vin Vout

Here it’s redrawn to show the two voltage dividers.

Vin Vout

Here’s one voltage divider.

Vin Vout

Here’s the other voltage divider.

Often a Wheatstone bridge is used with one resistor variable,such as a resistive sensor.

Knowing the other resistors allows the variable one to beeasily determined.The circuit is very sensitive to small changes in the variableresistor.

Often a Wheatstone bridge is used with one resistor variable,such as a resistive sensor.Knowing the other resistors allows the variable one to beeasily determined.

The circuit is very sensitive to small changes in the variableresistor.

Often a Wheatstone bridge is used with one resistor variable,such as a resistive sensor.Knowing the other resistors allows the variable one to beeasily determined.The circuit is very sensitive to small changes in the variableresistor.

Vin VoutVA VB

The variable resistor could be in any of the four positions; this isone example.

Balancing a Wheatstone Bridge

When the bridge is “balanced”, Vo = 0 or VA = VB.(This will happen when R1

R2= Rv

For our diagram R1 → R2 is the reference branch, andRv → R4 is the evaluation branch.If Rv increases, VB will decrease, and vice versa.For optimum performance, all resistors should be of the sameorder of magnitude.If using a resistive sensor, use a meter to measure resistanceof sensor to get a correct order of magnitude.

When the bridge is “balanced”, Vo = 0 or VA = VB.

(This will happen when R1R2

= RvR4

.)For our diagram R1 → R2 is the reference branch, andRv → R4 is the evaluation branch.If Rv increases, VB will decrease, and vice versa.For optimum performance, all resistors should be of the sameorder of magnitude.If using a resistive sensor, use a meter to measure resistanceof sensor to get a correct order of magnitude.

R2= Rv

For our diagram R1 → R2 is the reference branch, andRv → R4 is the evaluation branch.

If Rv increases, VB will decrease, and vice versa.For optimum performance, all resistors should be of the sameorder of magnitude.If using a resistive sensor, use a meter to measure resistanceof sensor to get a correct order of magnitude.

R2= Rv

For our diagram R1 → R2 is the reference branch, andRv → R4 is the evaluation branch.If Rv increases, VB will decrease, and vice versa.

For optimum performance, all resistors should be of the sameorder of magnitude.If using a resistive sensor, use a meter to measure resistanceof sensor to get a correct order of magnitude.

R2= Rv

For our diagram R1 → R2 is the reference branch, andRv → R4 is the evaluation branch.If Rv increases, VB will decrease, and vice versa.For optimum performance, all resistors should be of the sameorder of magnitude.

If using a resistive sensor, use a meter to measure resistanceof sensor to get a correct order of magnitude.

R2= Rv

R Rv = R + ∆R

Vin VoutVA VB

If resistors are chosen to be equal, except for Rv , then the outputvoltage will vary with changes in Rv .

Specifically,

VA = V R2R = V /2

VB = V R2R+∆R = V R+∆R/2−∆R/2

2R+∆R = V /2− V ∆R/22R+∆R ≈

V /2− V ∆R/22R

If no current flows between A and B thenVA − VB ≈ V ∆R

4Rwhich can be rearranged to give∆R ≈ (VA−VB)

V 4RSo we can determine ∆R.(This approximation is true as long as ∆R << R)

Specifically,VA = V R

2R = V /2

VB = V R2R+∆R = V R+∆R/2−∆R/2

2R+∆R = V /2− V ∆R/22R+∆R ≈

V /2− V ∆R/22R

2R = V /2

VB = V R2R+∆R = V R+∆R/2−∆R/2

2R+∆R = V /2− V ∆R/22R+∆R ≈

V /2− V ∆R/22R

2R = V /2

VB = V R2R+∆R = V R+∆R/2−∆R/2

2R+∆R = V /2− V ∆R/22R+∆R ≈

V /2− V ∆R/22R

If no current flows between A and B then

VA − VB ≈ V ∆R4R

which can be rearranged to give∆R ≈ (VA−VB)

2R = V /2

VB = V R2R+∆R = V R+∆R/2−∆R/2

2R+∆R = V /2− V ∆R/22R+∆R ≈

V /2− V ∆R/22R

which can be rearranged to give∆R ≈ (VA−VB)

2R = V /2

VB = V R2R+∆R = V R+∆R/2−∆R/2

2R+∆R = V /2− V ∆R/22R+∆R ≈

V /2− V ∆R/22R

4Rwhich can be rearranged to give

∆R ≈ (VA−VB)V 4R

So we can determine ∆R.(This approximation is true as long as ∆R << R)

2R = V /2

VB = V R2R+∆R = V R+∆R/2−∆R/2

2R+∆R = V /2− V ∆R/22R+∆R ≈

V /2− V ∆R/22R

So we can determine ∆R.(This approximation is true as long as ∆R << R)

2R = V /2

VB = V R2R+∆R = V R+∆R/2−∆R/2

2R+∆R = V /2− V ∆R/22R+∆R ≈

V /2− V ∆R/22R

V 4RSo we can determine ∆R.

(This approximation is true as long as ∆R << R)

2R = V /2

VB = V R2R+∆R = V R+∆R/2−∆R/2

2R+∆R = V /2− V ∆R/22R+∆R ≈

V /2− V ∆R/22R

Wheatstone bridge optionsLead wire compensation

Temperature compensationInstrumentation amplifiersdifferential op amp circuit with voltage followers on the inputs

Wheatstone bridge optionsLead wire compensationTemperature compensation

Instrumentation amplifiersdifferential op amp circuit with voltage followers on the inputs

Wheatstone bridge optionsLead wire compensationTemperature compensationInstrumentation amplifiers

differential op amp circuit with voltage followers on the inputs

Wheatstone bridge optionsLead wire compensationTemperature compensationInstrumentation amplifiersdifferential op amp circuit with voltage followers on the inputs

Lead wire compensation

long leads;unknownresistance

Uncompensated

Lead wire compensation

No current flows in measurement lead; similar resistance in bothother leads

Temperature compensation

active

inactive

active

inactive

active

Temperature response of non-active sensor similar to active sensor

Doubling sensitivity

Sensors in diagonal positions produce opposite responses.

Wheatstone bridge current limitPut resistor in series with bridge

Choose Rs � Rt

thus current controlled by Rs (fixed) rather than Rt (variable).

Wheatstone bridge current limitPut resistor in series with bridgeChoose Rs � Rt

Reducing current

This is useful if the voltage supply is fixed.

Reducing current

Electronics- Wheatstone Bridge Circuitsdenethor.wlu.ca/pc320/lectures/wbbeam.pdfWheatstone bridges...

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