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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.
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.
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.
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.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
R1 R3
R2 R4
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
R1 R3
R2 R4
Vin
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
R1 R3
R2 R4
Vin Vout
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
R1 R3
R2 R4
Vin Vout
This is a Wheatstone bridge.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
R1 R3
R2 R4
Vin Vout
Here it’s redrawn to show the two voltage dividers.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
R1 R3
R2 R4
Vin Vout
Here’s one voltage divider.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
R1 R3
R2 R4
Vin Vout
Here’s the other voltage divider.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
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.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
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.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
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.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
R1 Rv
R2 R4
Vin VoutVA VB
The variable resistor could be in any of the four positions; this isone example.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Balancing a Wheatstone Bridge
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.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Balancing a Wheatstone Bridge
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.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Balancing a Wheatstone Bridge
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.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Balancing a Wheatstone Bridge
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.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Balancing a Wheatstone Bridge
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.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Balancing a Wheatstone Bridge
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.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Balancing a Wheatstone Bridge
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.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
R Rv = R + ∆R
R R
Vin VoutVA VB
If resistors are chosen to be equal, except for Rv , then the outputvoltage will vary with changes in Rv .
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Specifically,
VA = V R2R = V /2
VB = V R2R+∆R = VR+∆R/2−∆R/2
2R+∆R = V /2− V∆R/2
2R+∆R ≈V /2− V ∆R/22RIf no current flows between A and B thenVA − VB ≈ V ∆R4Rwhich can be rearranged to give∆R ≈ (VA−VB)V 4RSo we can determine ∆R.(This approximation is true as long as ∆R

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Specifically,VA = V R2R = V /2
VB = V R2R+∆R = VR+∆R/2−∆R/2
2R+∆R = V /2− V∆R/2
2R+∆R ≈V /2− V ∆R/22RIf no current flows between A and B thenVA − VB ≈ V ∆R4Rwhich can be rearranged to give∆R ≈ (VA−VB)V 4RSo we can determine ∆R.(This approximation is true as long as ∆R

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Specifically,VA = V R2R = V /2
VB = V R2R+∆R = VR+∆R/2−∆R/2
2R+∆R = V /2− V∆R/2
2R+∆R ≈V /2− V ∆R/22R
If no current flows between A and B thenVA − VB ≈ V ∆R4Rwhich can be rearranged to give∆R ≈ (VA−VB)V 4RSo we can determine ∆R.(This approximation is true as long as ∆R

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Specifically,VA = V R2R = V /2
VB = V R2R+∆R = VR+∆R/2−∆R/2
2R+∆R = V /2− V∆R/2
2R+∆R ≈V /2− V ∆R/22RIf no current flows between A and B then
VA − VB ≈ V ∆R4Rwhich can be rearranged to give∆R ≈ (VA−VB)V 4RSo we can determine ∆R.(This approximation is true as long as ∆R

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Specifically,VA = V R2R = V /2
VB = V R2R+∆R = VR+∆R/2−∆R/2
2R+∆R = V /2− V∆R/2
2R+∆R ≈V /2− V ∆R/22RIf no current flows between A and B thenVA − VB ≈ V ∆R4R
which can be rearranged to give∆R ≈ (VA−VB)V 4RSo we can determine ∆R.(This approximation is true as long as ∆R

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Specifically,VA = V R2R = V /2
VB = V R2R+∆R = VR+∆R/2−∆R/2
2R+∆R = V /2− V∆R/2
2R+∆R ≈V /2− V ∆R/22RIf no current flows between A and B thenVA − VB ≈ V ∆R4Rwhich can be rearranged to give
∆R ≈ (VA−VB)V 4RSo we can determine ∆R.(This approximation is true as long as ∆R

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Specifically,VA = V R2R = V /2
VB = V R2R+∆R = VR+∆R/2−∆R/2
2R+∆R = V /2− V∆R/2
2R+∆R ≈V /2− V ∆R/22RIf no current flows between A and B thenVA − VB ≈ V ∆R4Rwhich can be rearranged to give∆R ≈ (VA−VB)V 4R
So we can determine ∆R.(This approximation is true as long as ∆R

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Specifically,VA = V R2R = V /2
VB = V R2R+∆R = VR+∆R/2−∆R/2
2R+∆R = V /2− V∆R/2
2R+∆R ≈V /2− V ∆R/22RIf no current flows between A and B thenVA − VB ≈ V ∆R4Rwhich can be rearranged to give∆R ≈ (VA−VB)V 4RSo we can determine ∆R.
(This approximation is true as long as ∆R

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Specifically,VA = V R2R = V /2
VB = V R2R+∆R = VR+∆R/2−∆R/2
2R+∆R = V /2− V∆R/2
2R+∆R ≈V /2− V ∆R/22RIf no current flows between A and B thenVA − VB ≈ V ∆R4Rwhich can be rearranged to give∆R ≈ (VA−VB)V 4RSo we can determine ∆R.(This approximation is true as long as ∆R

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Wheatstone bridge optionsLead wire compensation
Temperature compensationInstrumentation amplifiersdifferential op amp circuit with voltage followers on the inputs
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Wheatstone bridge optionsLead wire compensationTemperature compensation
Instrumentation amplifiersdifferential op amp circuit with voltage followers on the inputs
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Wheatstone bridge optionsLead wire compensationTemperature compensationInstrumentation amplifiers
differential op amp circuit with voltage followers on the inputs
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Wheatstone bridge optionsLead wire compensationTemperature compensationInstrumentation amplifiersdifferential op amp circuit with voltage followers on the inputs
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Lead wire compensation
long leads;unknownresistance
Uncompensated
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Lead wire compensation
No current flows in measurement lead; similar resistance in bothother leads
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Temperature compensation
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Temperature compensation
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Temperature compensation
active
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Temperature compensation
inactive
active
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Temperature compensation
inactive
active
Temperature response of nonactive sensor similar to active sensor
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Doubling sensitivity
Sensors in diagonal positions produce opposite responses.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Doubling sensitivity
Sensors in diagonal positions produce opposite responses.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Doubling sensitivity
Sensors in diagonal positions produce opposite responses.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Wheatstone bridge current limitPut resistor in series with bridge
Choose Rs � Rtthus current controlled by Rs (fixed) rather than Rt (variable).
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Wheatstone bridge current limitPut resistor in series with bridgeChoose Rs � Rt
thus current controlled by Rs (fixed) rather than Rt (variable).
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Wheatstone bridge current limitPut resistor in series with bridgeChoose Rs � Rtthus current controlled by Rs (fixed) rather than Rt (variable).
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Reducing current
Rs
This is useful if the voltage supply is fixed.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Reducing current
Rs
This is useful if the voltage supply is fixed.
Terry Sturtevant Electronics Wheatstone Bridge Circuits

Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit
Reducing current
Rs
This is useful if the voltage supply is fixed.
Terry Sturtevant Electronics Wheatstone Bridge Circuits
Wheatstone bridgesBalancing a Wheatstone BridgeWheatstone bridge optionsWheatstone bridge current limit