2 1. IntroductionBridge circuits (DC & AC) are an instrument to measure resistance, inductance, capacitance and impedance.Operate on a null-indication principle. This means the indication is independent of the calibration of the indicating device or any characteristics of it.# Very high degrees of accuracy can be achieved usingthe bridges.Used in control circuits.# One arm of the bridge contains a resistive elementthat is sensitive to the physical parameter(temperature, pressure, etc.) being controlled.
3 1. IntroductionTWO (2) TYPES of bridge circuits are used in measurement:1) DC bridge:a) Wheatstone Bridgeb) Kelvin Bridge2) AC bridge:a) Similar Angle Bridgeb) Opposite Angle Bridge/Hay Bridgec) Maxwell Bridged) Wein Bridgee) Radio Frequency Bridgef) Schering Bridge
5 Figure 5.1: Wheatstone Bridge Circuit The Wheatstone bridge is anelectrical bridge circuit usedto measure resistance.It consists of a voltage sourceand a galvanometer thatconnects two parallel branches,containing four resistors.Figure 5.1: Wheatstone Bridge CircuitOne parallel branch contains one known resistance and oneunknown; the other parallel branch contains resistors of knownresistances.
6 Figure 5.1: Wheatstone Bridge Circuit In the circuit at right, R4 is the unknown resistance; R1, R2 and R3 are resistors of known resistance where the resistance of R3 is adjustable.How to determine the resistance of the unknown resistor, R4?“The resistances of the other three are adjusted and balanced until the current passing through the galvanometer decreases to zero”.Figure 5.1: Wheatstone Bridge Circuit
7 Figure 5.1: Wheatstone Bridge Circuit R3 is varied until voltage between the two midpoints (B and D) will be zero and no current will flow through the galvanometer.ABCDFigure 5.1: Wheatstone Bridge CircuitFigure 5.2: A variable resistor; the amount of resistance between the connection terminals could be varied.
8 Figure 5.1: Wheatstone Bridge Circuit When the bridge is in balance condition (no current flows through galvanometer G), we obtain;voltage drop across R1 and R2 isequal,I1R1 = I2R2voltage drop across R3 and R4 isI3R3 = I4R4Figure 5.1: Wheatstone Bridge Circuit
9 Figure 5.1: Wheatstone Bridge Circuit In this point of balance, we alsoobtain;I1 = I3 and I2 = I4Therefore, the ratio of two resistances in the known leg is equal to the ratio of the two in the unknown leg;Figure 5.1: Wheatstone Bridge Circuit
11 2. Wheatstone Bridge Sensitivity of the Wheatstone Bridge When the pointer of a bridge galvanometer deflects to right or to left direction, this means that current is flowing through the galvanometer and the bridge is called in an unbalanced condition.The amount of deflection is a function of the sensitivity of the galvanometer. For the same current, greater deflection of pointer indicates more sensitive a galvanometer.Figure 5.4.
12 2. Wheatstone Bridge Sensitivity of the Wheatstone Bridge (Cont…) Sensitivity S can be expressed in units of:How to find the current value?Figure 5.4.
13 Fig. 5.5: Thevenin’s equivalent voltage 2. Wheatstone BridgeThevenin’s TheoremThevenin’s theorem is a approach used to determine the current flowing through the galvanometer.Thevenin’s equivalent voltage is found by removing the galvanometer from the bridge circuit and computing the open-circuit voltage between terminals a and b.Fig. 5.5: Thevenin’s equivalent voltageApplying the voltage divider equation, we express the voltage at point a and b, respectively, as
14 Fig. 5.6: Thevenin’s resistance 2. Wheatstone BridgeThevenin’s Theorem (Cont…)The difference in Va and Vb represents Thevenin’s equivalent voltage. That is,Fig. 5.5: Wheatstone bridge with the galvanometer removedThevenin’s equivalent resistance is found by replacing the voltage source with its internal resistance, Rb. Since Rb is assumed to be very low (Rb ≈ 0 Ω), we can redraw the bridge as shown in Fig. 5.6 to facilitate computation of the equivalent resistance as follows:Fig. 5.6: Thevenin’s resistance
15 2. Wheatstone Bridge Thevenin’s Theorem (Cont…) Fig. 5.6: Thevenin’s resistanceIf the values of Thevenin’s equivalent voltage and resistance have been known, the Wheatstone bridge circuit in Fig. 5.5 can be changed with Thevenin’s equivalent circuit as shown in Fig. 5.7,Fig. 5.5: Wheatstone bridge circuitFig. 5.7: Thevenin’s equivalent circuit
16 Fig. 5.7: Thevenin’s equivalent circuit 2. Wheatstone BridgeThevenin’s Theorem (Cont…)If a galvanometer is connected to terminal a and b, the deflection current in the galvanometer isFig. 5.7: Thevenin’s equivalent circuitwhere Rg = the internal resistance in the galvanometer
17 2. Wheatstone Bridge Example 2 R2 = 1.5 kΩ R1 = 1.5 kΩ Rg = 150 Ω E= 6 VFigure 5.8 : Unbalance Wheatstone BridgeRg = 150 ΩR3 = 3 kΩR4 = 7.8 kΩCalculate the current through the galvanometer ?
18 Slightly Unbalanced Wheatstone Bridge If three of the four resistors in a bridge are equal to R and the fourth differs by 5% or less, we can develop an approximate but accurate expression for Thevenin’s equivalent voltage and resistance. Consider the circuit in Fig- 5.9, the voltage at point a is given asThe voltage at point b is expressed asFigure 5.9: Wheatstone Bridge with three equal arms
19 2. Wheatstone Bridge Slightly Unbalanced Wheatstone Bridge (Cont…) Thevenin’s equivalent voltage is the difference in this voltageIf ∆r is 5% of R or less, Thevenin equivalent voltage can be simplified to be
20 Figure 5.10: Resistance of a Wheatstone. 2. Wheatstone BridgeSlightly Unbalanced Wheatstone Bridge (Cont…)Thevenin’s equivalent resistance can be calculated by replacing the voltage source with its internal resistance and redrawing the circuit as shown in Figure Thevenin’s equivalent resistance is now given asoRR + ΔrIf ∆r is small compared to R, the equation simplifies toorFigure 5.10: Resistance of a Wheatstone.
21 2. Wheatstone Bridge Slightly Unbalanced Wheatstone Bridge (Cont…) We can draw the Thevenin equivalent circuit as shown in Figure 5.11Figure 5.11: Approximate Thevenin’s equivalent circuit for a Wheatstone bridge containing three equal resistors and a fourth resistor differing by 5% or less
22 3. Kelvin Bridge Kelvin bridge is a modified version of the Wheatstone bridge.The purpose of the modification isto eliminate the effects of contactand lead resistance whenmeasuring unknown lowresistances.The measurement with a highdegree of accuracy can be doneusing the Kelvin bridge forresistors in the range of 1 Ω toapproximately 1 µΩ.Fig. 5.12: Basic Kelvin Bridge showing a second set of ratio armsSince the Kelvin bridge uses a second set of ratio arms (Ra and Rb, it issometimes referred to as the Kelvin double bridge.
23 3. Kelvin BridgeFig. 5.12: Basic Kelvin Bridge showing a second set of ratio armsThe resistor Rlc represents the lead and contact resistancepresent in the Wheatstone bridge.The second set of ratio arms (Ra and Rb in figure) compensatesfor this relatively low lead-contact resistance.
24 3. Kelvin BridgeWhen a null exists, the value for Rx is the same as that for the Wheatstone bridge, which isorAt balance the ratio of Rb to Ra must be equal to the ratio of R3 to R1. Therefore,