Bridges

Bridge Instruments

Bridge Instruments
Various types of bridge circuits are used in instrumentation. They can operate in either deflection mode or null principle. They give very high degree of accuracy.
Bridges Instruments are used to measure
•
Resistance, Inductance, Capacitance
•
Purity of components
•
Impedances and admittances
•
Physical parameters

Bridge Instruments
Types of Bridges
•
•

AC Bridge
DC Bridge

DC Current Bridge Instruments
• Wheatstone bridge and Kelvin Bridge
• Used for measurement of resistance
• Made sensitive to temperature, pressure and light • Complex physical phenomena such as dew point humidity, mass flow
• Range from 100 Ω to several hundred kΩ

WHEATSTONE BRIDGE

•R1 & R2 Known ratio arm
•R3 standard variable (adjustable) resistor
•R4 unknown resistor
•Detector – Galvanometer, CRO, Digital display

WHEATSTONE BRIDGE
The bridge can be used in null or deflection mode
1. At balance condition

Or

R4 R2
=
R3 R1
R2
R4 = R3
R1

This equation is independent of characteristics of detector provided • Detector observes unbalance
• deflect with required degree of precision

WHEATSTONE BRIDGE
The fractional uncertainty in the measurement is-- ∆R 4
∆R 1 2 ∆R 2 2 ∆R 3 2
= (
) +(
) +(
)
R4
R1
R2
R3

Sensitivity to Unbalance
The sensitivity to unbalanced of the bridge is measured by analyzing the bridge circuit for small unbalance • Change in one resistance
• Change in all resistances
• Equal resistance bridge
• Unequal resistance bridge

Sensitivity to Unbalance
• Change in one resistance

Assume Battery resistance is zero

Sensitivity to Unbalance
• Change in one resistance
ETH

⎛ R1
⎞
R2
= E⎜
⎜ R + R − R + R + ∆R ⎟
⎟
3
2
4
⎝ 1
⎠

RTH

R1 R3
R2 ( R4 + ∆ R )
=
+
R1 + R3 R 2 + R 4 + ∆ R

ETH
Ig =
RTH + Rg

Equal Resistance Bridge:
R1 = R2 = R3 = R4 = R

R ⎞
⎛1
⎛ ∆R ⎞
ETH = E⎜ −
⎟ ≅ E⎜ ⎟
⎝ 2 2R + ∆R ⎠
⎝ 4R ⎠

RTH ≅