DC & AC BRIDGES Part 2 (AC Bridge)

Objectives Ability to explain operation of ac bridge circuit. Ability to identify bridge by name Ability to compute the values of unknown impedance following ac bridges.

AC Bridges AC bridges are used to measure inductance and capacitances and all ac bridge circuits are based on the Wheatstone bridge. The general ac bridge circuit consists of 4 impedances, an ac voltage source, and detector as shown in Figure below. In ac bridge circuit, the impedances can be either pure resistance or complex impedances. Fig. 5-7: General ac bridge circuit

A simple bridge circuits are shown below; Inductance Capacitance

Cont. Applications - in many communication system and complex electronic circuits. AC bridge circuits - are commonly used for shifting phase, providing feedback paths for oscillators and amplifiers, filtering out undesired signals, and measuring the frequency of audio signals. The operation of the bridge depends on the fact that when certain specific circuit conditions apply, the detector current becomes zero. This is known as the null or balanced condition. Since zero current means that there is no voltage difference across detector, the bridge circuit may be redrawn as in Fig. 5-8. The voltages at point a and b and from point a to c must be equal.

Definition of electrical impedance The impedance of a circuit element is defined as the ratio of the phasor voltage across the element to the phasor current through the element: It should be noted that although Z is the ratio of two phasors, Z is not itself a phasor. That is, Z is not associated with some sinusoidal function of time. For DC circuits, the resistance is defined by Ohm's law to be the ratio of the DC voltage across the resistor to the DC current through the resistor: where the VR and IR above are DC (constant real) values.

Definition of Reactance, X Reactance is the imaginary part of impedance, and is caused by the presence of inductors or capacitors in the circuit. Reactance is denoted by the symbol X and is measured in ohms. A resistor's impedance is R (its resistance) and its reactance, XR is 0. A capacitance impedance: XC = -1/C = -1/(2fC) An inductive impedance: XL = L = 2fL

Z and Y passive elements Impedance Admittance R Z= R Y= 1/R L Z= jωL Y=1/j ωL C Z=-j(1/ωc) Y=j ωc

Cont. Fig. 5-7: General ac bridge circuit Fig. 5-8: Equivalent of balanced ac bridge circuit

Cont. I1Z1 = I2Z2 (1) Similarly, the voltages from point d to point b and point d to point c must also be equal, therefore I1Z3 = I2Z4 (2) equation (1) divided by equation (2)

If impedance is written in the form where Z represents magnitude and the phase angle of complex impedance, its can be written as,

Example 5-5 The impedances of the AC bridge in Fig. 5-7 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) =[(150x250)/200] = 187.5

Cont. 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) – 30 = -70o

Cont. Hence, the unknown impedance Zx, can be written as Zx = 187.5 -700 = (64.13 – j176.19)  Where Zx  = Zx cos  + j Zx sin  Indicating that we are dealing with a capacitive element, possibly consisting of a series resistor and a capacitor

Fig. 5-9: AC bridge in balance Example 5-6 Fig. 5-9: AC bridge in balance Given the AC bridge of Fig. 5-8 in balance, find the components of the unknown arms Zx.

Similar Angle Bridge The similar angle bridge (refer figure below) is used to measure the impedance of a capacitive circuit. This bridge is sometimes called the capacitance comparison bridge of the series resistance capacitance bridge. Z1 = R1 Z2 = R2 Z3 = R3 –jXc3 Zx = Rx –jXcx

Maxwell Bridge to determine an unknown inductance with capacitance standard X - reactance Z = R + jX

Opposite Angle Bridge The Opposite Angle Bridge or Hay Bridge (see Figure below) is used to measure the resistance and inductance of coils in which the resistance is small fraction of the reactance XL, that is a coil having a high Q, meaning a Q greater than 10.

Wein Bridge The Wein Bridge shown in Figure below has a series RC combination in one arm and a parallel combination in the adjoining arm. It is designed to measure frequency (extensively as a feedback arrangement for a circuit). It can also be used for the measurement of an unknown capacitor with great accuracy.

Cont.. Equivalent parallel component Equivalent series component

Radio Frequency Bridge The radio frequency bridge shown in figure below is often used in laboratories to measure the impedance of both capacitance and inductive circuits at higher frequencies. C’1 & C’4 : new values of C1 & C4 after rebalancing

Schering Bridge used for measuring capacitors and their insulating properties for phase angle of nearly 90o. Zx =Rx –j/Cx Z2 = R2 Z3 = -j/C3 Z1 = 1/(R1 + jC1)

Summary The Wheatstone Bridge – most basic bridge circuit. Widely used to measure instruments and control circuits. Have high degree of accuracy. Kelvin Bridge – modification of Wheatstone Bridge and widely used to measure very low resistance. Thevenin’s theorem – analytical tool to analyzing an unbalance Wheatstone bridge. AC bridge – more general form of Wheatstone bridge. Different types of AC bridges differ in the types of impedances in the arms