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

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Presentation on theme: "1 CHAPTER 7 EMT 113: March 27, 2007 School of Computer and Communication Engineering, UniMAP Prepared By: Prepared By: Amir Razif b. Jamil Abdullah Alternating."— Presentation transcript:

1 1 CHAPTER 7 EMT 113: March 27, 2007 School of Computer and Communication Engineering, UniMAP Prepared By: Prepared By: Amir Razif b. Jamil Abdullah Alternating Current Bridge.

2 2 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. 7.0 AC Bridge.

3 3 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.

4 4 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.Cont’d…

5 5  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.Cont’d…

6 6 Example 7.1: AC Bridge. 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 Z 1 Z x =Z 2 Z 3 Z x =(Z 2 Z 3 /Z 1 ) = [(150 * 250)/200] =  Figure 7.4: Circuit For Example 7.1.

7 7  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 + (-40 o ) – 30 o = -70 o  The unknown impedance Z x, can be written as, Z x =  / -70 = (64.13 – j176.19)   This indicate that we are dealing with a capacitive element, possibly consisting of a series resistor and a capacitor. Cont’d…

8 8  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. 7.2 Similar-Angle Bridge Figure 7.5: Similar-Angle Bridge.

9 9  The impedance of the arm can be written,  Substitute in the balance equation,  Further simplification, Cont’d…

10 10  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. 7.3 Maxwell-Wein Bridge Figure 7.6: Maxwell-Wein Bridge.

11 11  The impedance of the arm can be written as,  Substitute in the balance equation,  Set real and imaginary part to zero, Cont’d…

12 12  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. 7.4 Opposite-Angle Bridge Figure 7.7: Opposite-Angle Bridge.

13 13  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. Cont’d…

14 14 Example 7.2 (T2 2005): Opposite Angle Bridge. Given the Opposite-Angle bridge of Figure 5. Find, (i) The equivalent series resistance, R x. (ii) The inductance, L x. Solution:

15 15  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. 7.5 Wein Bridge Figure 7.8: Wein Bridge.

16 16  The Scherning Bridge is useful for measuring insulating properties, that is for phase angles of very nearly 90 o.  Figure 7.9 is the Scherning Bridge.  Arm 1 contains only a capacitor C 3. This capacitor has very low losses (no resistance) and therefore the phase angle of approximately 90 o. 7.6 Schering Bridge. Figure 7.9: Scherning Bridge.

17 17  The impedance of the arm of the Schering bridge is,  Substitute the value,  Expand,  Equating the real and imaginary terms,Cont’d…

18 18 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. R 1 = 470 k  C 1 = 0.01 mF R 2 = 100 k  C 3 = 0.1 mF Solution: Find R x and C x, ..


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