We have various bridges to measure inductor and thus quality factor, like Hay’s bridge is highly suitable for the measurement of a quality factor greater than 10, Maxwell’s bridge is highly suitable for measuring medium quality factor ranging from 1 to 10, and Anderson bridge can be successfully used to measure inductor ranging from few micro Henry to several Henry. So what is the need for **Owen’s Bridge**?.

The answer to this question is very easy. We need a bridge that can measure the inductor over a wide range. The bridge circuit which can do that is known as Owen’s bridge.

It is an AC bridge just like Hay’s bridge and Maxwell bridge which use a standard capacitor, inductors and variable resistors connected with AC sources for excitation. Let us study **Owen’s bridge circuit** in more detail.

## Theory of Owen’s Bridge

An **Owen’s bridge circuit** is given below.

The AC supply is connected at a and c point. The arm ab is having inductor having some finite resistance let us mark them r_{1} and l_{1}. The arm bc consists of pure electrical resistance marked by r_{3} as shown in the figure given below and carrying the current i_{1} at balance point which is same as the current carried by arm ab.

The arm cd consists of pure capacitor having no electrical resistance.The arm ad is having variable resistance as well as variable capacitor and the detector is connected between b and d. Now how this bridge works? this bridge measures the inductor in terms of capacitance. Let us derive an expression for inductor for this bridge.

Here l_{1} is unknown inductance and c_{2} is variable standard capacitor.

Now at balance point we have the relation from AC bridge theory that must hold good i.e.

Putting the value of z_{1}, z_{2}, z_{3} and in above equation we get,

Equating and then separating the real and the imaginary parts we get the expression for l_{1} and r_{1} as written below:

Now, there is a need to modify the circuit, in order to calculate the incremental value of inductance. Given below is the modified **circuit of Owen’s bridge**:

A valve voltmeter is placed across the resistor r_{3}. The circuit is fed from both AC and DC source in parallel. The inductor is used to protect DC source from very high alternating current and the capacitor is used to block direct current from entering the AC source. The ammeter is connected in series with battery to measure the DC component of current while the AC component can be measured from the reading of the voltmeter (which is not sensitive to DC) connected across the resistance r_{3}.

Now at the balance point we have, incremental inductor l_{1} = r_{2}r_{3}c_{4}

also inductor

Therefore incremental permeability is

N is the number of turns, A is the area of flux path, l is the length of flux path, l_{1} is incremental inductance.

Let us mark drop across arm ab, bc, cd and ad as e_{1}, e_{3}, e_{4} and e_{2} respectively as shown in the above figure. This will help us to understand the phasor diagram well.

In general the most lagging current (i.e. i_{1}) is chosen as reference in order to draw phasor diagram. Current i_{2} is perpendicular to current i_{1} as shown and drop across inductor l_{1} is perpendicular to i_{1} as it is an inductive drop while the drop across capacitor c_{2} is perpendicular to i_{2}. At balance point e_{1} = e_{2} which is shown in the figure, now resultant of all these voltage drops e_{1}, e_{2}, e_{3}, e_{4} will give e.

### Advantages of Owen’s Bridge

- The for inductor l
_{1}that we have derived above is quite simple and is independent of frequency component. - This bridge is useful for the measurement of inductor over wide range.

### Disadvantages of Owen’s Bridge

- In this bridge we have used variable standard capacitor which is quite expensive item and also the accuracy of this is about only one percent.
- As the measuring quality factor increases the value of standard capacitor required increases thus expenditure in making this bridge increases.