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Wheatstone bridges Electronics Wheatstone Bridge Circuits Terry Sturtevant Wilfrid Laurier University October 18, 2016 Terry Sturtevant Electronics Wheatstone Bridge Circuits

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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 non-active 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