# Wha is an Owen’s Bridge : Circuit, Theory and Its Phasor Diagram

The modern communication system uses AC bridges with complex electrical and electronic circuits and many more. The different types of AC bridges used in electronic circuits are Maxwell’s bridge, Maxwell’s Wein bridge, Anderson bridge, Hay’s bridge, Owen’s bridge, De Sauty bridge, Schering bridge, and Wien series bridge. Though there are different types of AC bridges for measuring quality factors of the coil, they are limited to a small range. For example, Maxwell’s bridge is limited to measuring the quality factor greater than 10. Hay’s bridge is suitable for the quality factor range of 1 to 10. Anderson bridge is used to measure inductance values ranging from a few micro Henry’s. Hence we need a bridge circuit, that should be suitable to measure a wide range of inductors. That bridge circuit is called Owen’s bridge.

## Owen’s Bridge Definition

**Definition:** Owen’s bridge circuit is defined as, the AC bridge that is used to measure a wide range of unknown inductance in terms of resistance and capacitance. It usually works on the principle of comparison. That means the measured unknown inductance value is compared with the standard or known capacitor. This type of bridge circuit uses a standard capacitor and a variable resistor connected with AC sources for excitation.

### Owen’s Bridge Circuit

Owen’s bridge circuit contains four arms connected in a square or in a rhombus shape. An AC voltage signal and a null detector are connected across the junctions of the arms. The circuit diagram of Owen’s bridge is shown below.

- From the above circuit, we can observe that ab, bc, cd, and da are the four arms connected as a bridge.
- The arm ‘ab’ contains unknown self-inductance ‘L1’ with resistance ‘R1’
- The arm ‘bc’ contains pure resistor ‘R3’
- The other arm ‘cd’ contains a fixed standard capacitor ‘C4’
- The last arms ‘da’ contains variable non-inductive resistor ‘R2’ in series with a variable standard capacitor ‘C2’.
- A null detector is connected to determine the balance condition of the bridge circuit.

The modified Owen’s bridge contains a voltmeter in parallel with resistance connected to one of the arms. An ammeter is also connected in series to the bridge circuit to measure DC current while the AC current can be measured using a voltmeter. The Modified circuit of Owen’s bridge is shown below.

### Theory of Owen’s Bridge

The theory of Owen’s bridge states that the unknown inductance ‘L1’ is compared with the known capacitor ‘C4’ connected to the arm ‘cd’ of the bridge circuit. In the balance condition, the non-inductive resistor ‘R2’ and the variable standard capacitor ‘C2’ can be varied independently. Hence, no current flows through the bridge circuit and no potential will be recorded by the null detector.

From Owen’s bridge circuit we can observe that,

Unknown self-inductance ‘L1’

Pure resistor ‘R3’ (fixed non-inductive resistance)

Fixed standard capacitor ‘C4’

Variable non-inductive resistor ‘R2’ in series with a variable standard capacitor ‘C2’.

A null detector is connected to determine the balance condition of the bridge circuit.

Consider the balanced equation of a basic AC bridge circuit,

**Z1Z4=Z2Z3**

Now substitute the impedances of Owen’s bridge circuit in the above equation

Then

**(R1+jωL1)(1/jωC4) = (R2+1/jωC2)R3**

Now separate the real and imaginary terms from the above equation

We get,

**L1=R2R3C4**

The unknown inductance can be measured from the above equation

**R1= R3 (C4/C2)**

The value of a variable standard capacitor ‘C2’ is measured.

### Phasor diagram of Owen’s Bridge

The phasor diagram of Owen’s bridge is shown below.

From the above phasor diagram, we can observe that,

The horizontal axis represents the current I1, E3 = I3R3, and E4 = ωI2C4 that are in the same phase. And also the voltage drop of ‘i1r1’ also represents the horizontal axis.

The voltage drop ‘e1’ represents the sum of inductive voltage drop (ωL1I1) and resistive voltage drop (I1R1)

At the balance condition of the bridge circuit, the voltage drops ‘E1’ and ‘E2’ are equal across the arms and represented on the same axis.

Similarly, the voltage drop ‘E4’ is the sum of the resistive voltage drop (I2R2) and capacitive voltage drop (I2/wC2). Due to the fixed capacitor, the current i1 becomes perpendicular (90degrees) voltage drop ‘e4’. The current ‘I2’ and the voltage drop I2R2 represent the vertical axis. The supply voltage represents ‘E1’ and ‘E3’.

### Advantages

The advantages of Owen’s bridge are;

- The main advantage of Owen’s bridge circuit is, the unknown inductance L1 is measured.
- The balance equation can be obtained very easily, and simple.
- It is used to measure a wide range of inductance in terms of capacitance.
- It is also used to measure a wide range of capacitance values ( we get from the final balance equation ).

### Disadvantages

The disadvantages of Owen’s bridge includes are

- A variable standard capacitor used in this bridge circuit is very costly. So, the cost of Owen’s bridge circuit also increases.
- The accuracy of the variable standard capacitor used in the circuit is very low ( nearly 1%)
- The usage of a larger variable standard capacitor would increase the range of a quality factor of the coil measured. This can increase the cost of the circuit further.

### FAQs

**1). What is a null detector?**

It helps to find the balance condition of the AC bridge circuit (when the given value is zero). And also it compares the unknown value (inductance/resistance/capacitance/ impedance) with a known value (reference or standard value).

**2). What do you mean by the quality factor (q factor) of the coil?**

It is the ratio of the reactance of the coil to its resistance at the operating frequency.

**Q = ωL/R =XL/R**

**3). What are the types of errors that occured in AC bridges?**

Magnetic field leakage errors eddy current errors, frequency errors, and waveform errors.

**4). What type of bridge is used to measure capacitance?**

Wien bridge is used to measure capacitance in terms of calibrated resistance and frequency.

**5). Why AC bridges don’t use galvanometer instead of the null detector?**

A galvanometer is not used in AC bridges because it measures the flow of direct current (DC) only.

Thus, this is all about the definition, circuit, theory, advantages, and disadvantages of Owen’s bridge. Here is a question for you, “What are the applications of Owen’s bridge?”