OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

AC Bridges

Sajan P. PhilipAP/ECE/BIT

June 16, 2013

Sajan P. Philip AP/ECE/BIT AC Bridges

AC Bridges by Sajan P. Philip, is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. You are free to use, distribute and modify it, including for commercial purposes, provided you acknowledge the source and share-alike.To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/4.0/

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Schematic Diagram of AC Bridge 1

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Schematic Diagram of AC Bridge 1

The Power source supplies an AC voltage to the bridge at a desired frequency.

For measurement of low frequencies, the power line may serve as the source ofexcitation.

Higher frequencies, an ocillator generally supplies the excitation voltage.

The null detector can be:

A headphoneAn Amplifier with an output meter

An electron tube

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Schematic Diagram of AC Bridge 1

The Power source supplies an AC voltage to the bridge at a desired frequency.

For measurement of low frequencies, the power line may serve as the source ofexcitation.

Higher frequencies, an ocillator generally supplies the excitation voltage.

The null detector can be:

A headphoneAn Amplifier with an output meter

An electron tube

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Schematic Diagram of AC Bridge 1

The Power source supplies an AC voltage to the bridge at a desired frequency.

For measurement of low frequencies, the power line may serve as the source ofexcitation.

Higher frequencies, an ocillator generally supplies the excitation voltage.

The null detector can be:

A headphoneAn Amplifier with an output meter

An electron tube

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Schematic Diagram of AC Bridge 1

The Power source supplies an AC voltage to the bridge at a desired frequency.

For measurement of low frequencies, the power line may serve as the source ofexcitation.

Higher frequencies, an ocillator generally supplies the excitation voltage.

The null detector can be:

A headphoneAn Amplifier with an output meter

An electron tube

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Schematic Diagram of AC Bridge 1

The Power source supplies an AC voltage to the bridge at a desired frequency.

For measurement of low frequencies, the power line may serve as the source ofexcitation.

Higher frequencies, an ocillator generally supplies the excitation voltage.

The null detector can be:

A headphone

An Amplifier with an output meter

An electron tube

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Schematic Diagram of AC Bridge 1

The Power source supplies an AC voltage to the bridge at a desired frequency.

For measurement of low frequencies, the power line may serve as the source ofexcitation.

Higher frequencies, an ocillator generally supplies the excitation voltage.

The null detector can be:

A headphoneAn Amplifier with an output meter

An electron tube

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Schematic Diagram of AC Bridge 1

The Power source supplies an AC voltage to the bridge at a desired frequency.

For measurement of low frequencies, the power line may serve as the source ofexcitation.

Higher frequencies, an ocillator generally supplies the excitation voltage.

The null detector can be:

A headphoneAn Amplifier with an output meter

An electron tube

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Schematic Diagram of AC Bridge 1

The Power source supplies an AC voltage to the bridge at a desired frequency.

For measurement of low frequencies, the power line may serve as the source ofexcitation.

Higher frequencies, an ocillator generally supplies the excitation voltage.

The null detector can be:

A headphoneAn Amplifier with an output meter

An electron tube

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Schematic Diagram of AC Bridge 2

The four bridge arms Z1,Z2,Z3, and Z4 are indicated as unspecified impedancesand the detector is represented by Headphones.

Balance adjustments to obtain a null response is made by varying one or moreof the bridge arms.

The General equation for bridge balance is obtained by using ’ComplexNotation’ for the impedances of the bridge circuit.

The condition for bridge balance requires that the potential difference from A to

C should be zero.

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Schematic Diagram of AC Bridge 2

The four bridge arms Z1,Z2,Z3, and Z4 are indicated as unspecified impedancesand the detector is represented by Headphones.

Balance adjustments to obtain a null response is made by varying one or moreof the bridge arms.

The General equation for bridge balance is obtained by using ’ComplexNotation’ for the impedances of the bridge circuit.

The condition for bridge balance requires that the potential difference from A to

C should be zero.

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Schematic Diagram of AC Bridge 2

The four bridge arms Z1,Z2,Z3, and Z4 are indicated as unspecified impedancesand the detector is represented by Headphones.

Balance adjustments to obtain a null response is made by varying one or moreof the bridge arms.

The General equation for bridge balance is obtained by using ’ComplexNotation’ for the impedances of the bridge circuit.

The condition for bridge balance requires that the potential difference from A to

C should be zero.

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Schematic Diagram of AC Bridge 2

The four bridge arms Z1,Z2,Z3, and Z4 are indicated as unspecified impedancesand the detector is represented by Headphones.

Balance adjustments to obtain a null response is made by varying one or moreof the bridge arms.

The General equation for bridge balance is obtained by using ’ComplexNotation’ for the impedances of the bridge circuit.

The condition for bridge balance requires that the potential difference from A to

C should be zero.

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Schematic Diagram of AC Bridge 2

The four bridge arms Z1,Z2,Z3, and Z4 are indicated as unspecified impedancesand the detector is represented by Headphones.

Balance adjustments to obtain a null response is made by varying one or moreof the bridge arms.

The General equation for bridge balance is obtained by using ’ComplexNotation’ for the impedances of the bridge circuit.

The condition for bridge balance requires that the potential difference from A to

C should be zero.

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 3

This will be the case when the voltage drop from B to A equals the voltage dropfrom B to C, in both magnitude and phase.

In complex notation;

EBA=EBC

I1Z1=I2Z2 (1)

For the balanced condition

I1= EZ1+Z3

(2)

I2= EZ2+Z4

(3)

Substitute (2) and (3) in (1)

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 3

This will be the case when the voltage drop from B to A equals the voltage dropfrom B to C, in both magnitude and phase.

In complex notation;

EBA=EBC

I1Z1=I2Z2 (1)

For the balanced condition

I1= EZ1+Z3

(2)

I2= EZ2+Z4

(3)

Substitute (2) and (3) in (1)

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 3

This will be the case when the voltage drop from B to A equals the voltage dropfrom B to C, in both magnitude and phase.

In complex notation;EBA=EBC

I1Z1=I2Z2 (1)

For the balanced condition

I1= EZ1+Z3

(2)

I2= EZ2+Z4

(3)

Substitute (2) and (3) in (1)

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 3

This will be the case when the voltage drop from B to A equals the voltage dropfrom B to C, in both magnitude and phase.

In complex notation;EBA=EBC

I1Z1=I2Z2 (1)

For the balanced condition

I1= EZ1+Z3

(2)

I2= EZ2+Z4

(3)

Substitute (2) and (3) in (1)

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 3

This will be the case when the voltage drop from B to A equals the voltage dropfrom B to C, in both magnitude and phase.

In complex notation;EBA=EBC

I1Z1=I2Z2 (1)

For the balanced condition

I1= EZ1+Z3

(2)

I2= EZ2+Z4

(3)

Substitute (2) and (3) in (1)

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 3

This will be the case when the voltage drop from B to A equals the voltage dropfrom B to C, in both magnitude and phase.

In complex notation;EBA=EBC

I1Z1=I2Z2 (1)

For the balanced conditionI1= E

Z1+Z3(2)

I2= EZ2+Z4

(3)

Substitute (2) and (3) in (1)

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 3

This will be the case when the voltage drop from B to A equals the voltage dropfrom B to C, in both magnitude and phase.

In complex notation;EBA=EBC

I1Z1=I2Z2 (1)

For the balanced conditionI1= E

Z1+Z3(2)

I2= EZ2+Z4

(3)

Substitute (2) and (3) in (1)

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 3

This will be the case when the voltage drop from B to A equals the voltage dropfrom B to C, in both magnitude and phase.

In complex notation;EBA=EBC

I1Z1=I2Z2 (1)

For the balanced conditionI1= E

Z1+Z3(2)

I2= EZ2+Z4

(3)

Substitute (2) and (3) in (1)

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 3

This will be the case when the voltage drop from B to A equals the voltage dropfrom B to C, in both magnitude and phase.

In complex notation;EBA=EBC

I1Z1=I2Z2 (1)

For the balanced conditionI1= E

Z1+Z3(2)

I2= EZ2+Z4

(3)

Substitute (2) and (3) in (1)

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 4

EZ1Z1+Z3

= EZ2Z2+Z4

Z1(Z2 + Z4)=Z2(Z1 + Z3)

Z1Z2 + Z1Z4=Z2Z1 + Z2Z3

Z1Z4=Z2Z3 (4)

Y1Y4=Y2Y3 (In terms of Admittance)

Equation (4) is the general equation for the balance of an AC Bridge.

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 4

EZ1Z1+Z3

= EZ2Z2+Z4

Z1(Z2 + Z4)=Z2(Z1 + Z3)

Z1Z2 + Z1Z4=Z2Z1 + Z2Z3

Z1Z4=Z2Z3 (4)

Y1Y4=Y2Y3 (In terms of Admittance)

Equation (4) is the general equation for the balance of an AC Bridge.

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 4

EZ1Z1+Z3

= EZ2Z2+Z4

Z1(Z2 + Z4)=Z2(Z1 + Z3)

Z1Z2 + Z1Z4=Z2Z1 + Z2Z3

Z1Z4=Z2Z3 (4)

Y1Y4=Y2Y3 (In terms of Admittance)

Equation (4) is the general equation for the balance of an AC Bridge.

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 4

EZ1Z1+Z3

= EZ2Z2+Z4

Z1(Z2 + Z4)=Z2(Z1 + Z3)

Z1Z2 + Z1Z4=Z2Z1 + Z2Z3

Z1Z4=Z2Z3 (4)

Y1Y4=Y2Y3 (In terms of Admittance)

Equation (4) is the general equation for the balance of an AC Bridge.

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 4

EZ1Z1+Z3

= EZ2Z2+Z4

Z1(Z2 + Z4)=Z2(Z1 + Z3)

Z1Z2 + Z1Z4=Z2Z1 + Z2Z3

Z1Z4=Z2Z3 (4)

Y1Y4=Y2Y3 (In terms of Admittance)

Equation (4) is the general equation for the balance of an AC Bridge.

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 4

EZ1Z1+Z3

= EZ2Z2+Z4

Z1(Z2 + Z4)=Z2(Z1 + Z3)

Z1Z2 + Z1Z4=Z2Z1 + Z2Z3

Z1Z4=Z2Z3 (4)

Y1Y4=Y2Y3 (In terms of Admittance)

Equation (4) is the general equation for the balance of an AC Bridge.

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 4

EZ1Z1+Z3

= EZ2Z2+Z4

Z1(Z2 + Z4)=Z2(Z1 + Z3)

Z1Z2 + Z1Z4=Z2Z1 + Z2Z3

Z1Z4=Z2Z3 (4)

Y1Y4=Y2Y3 (In terms of Admittance)

Equation (4) is the general equation for the balance of an AC Bridge.

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 5

Equation (4) states that the product of impedances of one pair of opposite armsmust be equal to the product of impedances of the other pair of opposite arms.

If impedance is expressed in Complex Notation in the form Z=Z∠θ, where Zrepresentes the magnitude and θ represents the phase angle of the compleximpedance.

Then the equation (4) becomes

(Z1∠θ1)(Z4∠θ4)=(Z2∠θ2)(Z3∠θ3) (5)

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 5

Equation (4) states that the product of impedances of one pair of opposite armsmust be equal to the product of impedances of the other pair of opposite arms.

If impedance is expressed in Complex Notation in the form Z=Z∠θ, where Zrepresentes the magnitude and θ represents the phase angle of the compleximpedance.

Then the equation (4) becomes

(Z1∠θ1)(Z4∠θ4)=(Z2∠θ2)(Z3∠θ3) (5)

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 5

Equation (4) states that the product of impedances of one pair of opposite armsmust be equal to the product of impedances of the other pair of opposite arms.

If impedance is expressed in Complex Notation in the form Z=Z∠θ, where Zrepresentes the magnitude and θ represents the phase angle of the compleximpedance.

Then the equation (4) becomes

(Z1∠θ1)(Z4∠θ4)=(Z2∠θ2)(Z3∠θ3) (5)

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 5

Equation (4) states that the product of impedances of one pair of opposite armsmust be equal to the product of impedances of the other pair of opposite arms.

If impedance is expressed in Complex Notation in the form Z=Z∠θ, where Zrepresentes the magnitude and θ represents the phase angle of the compleximpedance.

Then the equation (4) becomes

(Z1∠θ1)(Z4∠θ4)=(Z2∠θ2)(Z3∠θ3) (5)

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 5

Equation (4) states that the product of impedances of one pair of opposite armsmust be equal to the product of impedances of the other pair of opposite arms.

If impedance is expressed in Complex Notation in the form Z=Z∠θ, where Zrepresentes the magnitude and θ represents the phase angle of the compleximpedance.

Then the equation (4) becomes

(Z1∠θ1)(Z4∠θ4)=(Z2∠θ2)(Z3∠θ3) (5)

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 6

In multiplication of complex numbers, the magnitudes are multiplied and thephase angles are added.

Hence, Z1Z4∠(θ1 + θ4)=Z2Z3∠(θ2 + θ3) (6)

Equation (6) shows that two conditions must be met simultaneously when

balancing an ac bridge;

The product of the magnitudes of the opposite arms must be equal, ie,Z1Z4=Z2Z3

The sum of the phase angles of the opposite arms must be equal, ie,

∠θ1 + ∠θ4=∠θ2 + ∠θ3

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 6

In multiplication of complex numbers, the magnitudes are multiplied and thephase angles are added.

Hence, Z1Z4∠(θ1 + θ4)=Z2Z3∠(θ2 + θ3) (6)

Equation (6) shows that two conditions must be met simultaneously when

balancing an ac bridge;

The product of the magnitudes of the opposite arms must be equal, ie,Z1Z4=Z2Z3

The sum of the phase angles of the opposite arms must be equal, ie,

∠θ1 + ∠θ4=∠θ2 + ∠θ3

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 6

In multiplication of complex numbers, the magnitudes are multiplied and thephase angles are added.

Hence, Z1Z4∠(θ1 + θ4)=Z2Z3∠(θ2 + θ3) (6)

Equation (6) shows that two conditions must be met simultaneously when

balancing an ac bridge;

The product of the magnitudes of the opposite arms must be equal, ie,Z1Z4=Z2Z3

The sum of the phase angles of the opposite arms must be equal, ie,

∠θ1 + ∠θ4=∠θ2 + ∠θ3

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 6

In multiplication of complex numbers, the magnitudes are multiplied and thephase angles are added.

Hence, Z1Z4∠(θ1 + θ4)=Z2Z3∠(θ2 + θ3) (6)

Equation (6) shows that two conditions must be met simultaneously when

balancing an ac bridge;

The product of the magnitudes of the opposite arms must be equal, ie,Z1Z4=Z2Z3

The sum of the phase angles of the opposite arms must be equal, ie,

∠θ1 + ∠θ4=∠θ2 + ∠θ3

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 6

In multiplication of complex numbers, the magnitudes are multiplied and thephase angles are added.

Hence, Z1Z4∠(θ1 + θ4)=Z2Z3∠(θ2 + θ3) (6)

Equation (6) shows that two conditions must be met simultaneously when

balancing an ac bridge;

The product of the magnitudes of the opposite arms must be equal, ie,Z1Z4=Z2Z3

The sum of the phase angles of the opposite arms must be equal, ie,

∠θ1 + ∠θ4=∠θ2 + ∠θ3

Sajan P. Philip AP/ECE/BIT AC Bridges

OutlineIntroduction to AC Bridges

Maxwell’s BridgeHay Bridge

Schering BridgeWein Bridge

Schematic Diagram of AC BridgeBalance Equation of AC Bridges

Balance Equation of AC Bridges 6

In multiplication of complex numbers, the magnitudes are multiplied and thephase angles are added.

Hence, Z1Z4∠(θ1 + θ4)=Z2Z3∠(θ2 + θ3) (6)

Equation (6) shows that two conditions must be met simultaneously when

balancing an ac bridge;

The product of the magnitudes of the opposite arms must be equal, ie,Z1Z4=Z2Z3

The sum of the phase angles of the opposite arms must be equal, ie,

∠θ1 + ∠θ4=∠θ2 + ∠θ3

Sajan P. Philip AP/ECE/BIT AC Bridges