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 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 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 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 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 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 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 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 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 The impedance of the arm can be written, Substitute in the balance equation, Further simplification, Cont’d…
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 The impedance of the arm can be written as, Substitute in the balance equation, Set real and imaginary part to zero, Cont’d…
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 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 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 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 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 The impedance of the arm of the Schering bridge is, Substitute the value, Expand, Equating the real and imaginary terms,Cont’d…
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, ..