CHAPTER 7 Alternating Current Bridge. School of Computer and Communication Engineering, UniMAP Prepared By: Amir Razif b. Jamil Abdullah EMT 113: March 27, 2007

7.0 AC Bridge. 7.1 Introduction to AC Bridge. 7.2 Similar-Angle Bridge. 7.3 Maxwell-Wein Bridge. 7.4 Opposite Angle Bridge. 7.5 Wein Bridge. 7.6 Scherning Bridge.

7.1 Introduction to AC Bridge. AC bridges are used to measure inductance and capacitance. All the AC bridges are based on the Wheatstone bridge. In the AC bridge the bridge circuit consists of four impedances and an ac voltage source. The impedances can either be pure resistance or complex impedance. Other than measurement of unknown impedance, AC bridge are commonly used for shifting phase. Figure 7.1: General AC Bridge Circuit.

Figure 7.2: Equivalent of Balance (nulled) AC Bridge. Cont’d… Operation of AC Bridge: When the specific circuit conditions apply, the detector current becomes zero, which is known as null or balance condition. Since zero current, it means that there is no voltage difference across the detector, Figure 7.2. Voltage at point b and c are equal. The same thing at point d. From two above equation yield general bridge equation; Figure 7.2: Equivalent of Balance (nulled) AC Bridge.

Figure 7.3: (a) and (b) are Simple AC Bridge Circuit. Cont’d… Figure 7. 3(a) and 7.3 (b) is a simple AC Bridge circuit. Figure 7.3: (a) and (b) are Simple AC Bridge Circuit.

Example 7.1: AC Bridge. Solution: The impedances of the AC bridge in Figure 7.4 are given as follows, Determine the constants of the unknown arm. Solution: The first condition for bridge balance requires that Z1Zx=Z2Z3 Zx =(Z2Z3/Z1) = [(150 * 250)/200] = 187.5  Figure 7.4: Circuit For Example 7.1.

The unknown impedance Zx, can be written as, Zx = 187.5  / -70 Cont’d… The second condition for balance requires that the sums of the phase angles of opposite arms be equal, 1+  x = 2 + 3  x = 2 + 3 - 1 = 0 + (-40o) – 30o = -70o The unknown impedance Zx, can be written as, Zx = 187.5  / -70 = (64.13 – j176.19)  This indicate that we are dealing with a capacitive element, possibly consisting of a series resistor and a capacitor .                    

Figure 7.5: Similar-Angle Bridge. Figure 7.5 is a simple form of Similar–Angle Bridge, which is used to measure the impedance of a capacitive circuit. Sometimes called the capacitance comparison bridge or series resistance capacitance bridge. Figure 7.5: Similar-Angle Bridge.

The impedance of the arm can be written, Cont’d… The impedance of the arm can be written, Substitute in the balance equation, Further simplification,                    

7.3 Maxwell-Wein Bridge It is used to measure unknown inductances with capacitance standard. Because the phase shifts of inductors and capacitors are exactly opposite each other, a capacitive impedance can balance out an inductive impedance if they are located in opposite legs of a bridge Figure 7.6 is the Maxwell-Wein Bridge or sometimes called a Maxwell bridge. Figure 7.6: Maxwell-Wein Bridge.

The impedance of the arm can be written as, Cont’d… The impedance of the arm can be written as, Substitute in the balance equation, Set real and imaginary part to zero,                    

7.4 Opposite-Angle Bridge This bridge is from Similar-Angle Bridge but the capacitance is replace with the inductance, Figure 7.7. It is used to measure inductance. Sometimes called a Hay bridge. Figure 7.7: Opposite-Angle Bridge.

Equivalent series of inductance, Cont’d… Equivalent series of inductance, Equivalent series of resistance, For the opposite angle bridge, it can be seen that the balance conditions depend on the frequency at which the measurement is made.                    

Example 7.2 (T2 2005): Opposite Angle Bridge. Given the Opposite-Angle bridge of Figure 5. Find, (i) The equivalent series resistance, Rx. (ii) The inductance, Lx. Solution:

7.5 Wein Bridge The Wein Bridge is versatile where it can measure either the equivalent –series components or the equivalent-parallel components of an impedance, Figure 7.8. This bridge is used extensively as a feedback for the Wein bridge oscillator circuit. Figure 7.8: Wein Bridge.

7.6 Schering Bridge. The Scherning Bridge is useful for measuring insulating properties, that is for phase angles of very nearly 90o. Figure 7.9 is the Scherning Bridge. Arm 1 contains only a capacitor C3. This capacitor has very low losses (no resistance) and therefore the phase angle of approximately 90o. Figure 7.9: Scherning Bridge.

Cont’d… The impedance of the arm of the Schering bridge is, Substitute the value, Expand, Equating the real and imaginary terms,

Example 7.3: Schering Bridge. Find the equivalent series element for the unknown impedance of the Schering bridge network whose impedance measurements are to be made at null. R1 = 470 k C1 = 0.01 mF R2 = 100 k C3 = 0.1 mF Solution: Find Rx and Cx , .