Owens Bridge Circuit and Advantages

Different bridges measure inductor and quality factors: Hay’s bridge for quality factor over 10, Maxwell’s bridge for factors between 1 and 10, and Anderson bridge for inductors from microhenries to several henries. So why do we need Owens Bridge?

The answer is simple: we need a bridge that can measure inductors over a wide range. Owens Bridge is the circuit that meets this need.

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 r₁ and l₁. The arm bc consists of pure electrical resistance marked by r₃ as shown in the figure given below and carrying the current i₁ at balance point which is same as the current carried by arm ab.
Arm cd has a pure capacitor with no resistance. Arm ad has a variable resistor and capacitor, with a detector between points b and d. How does this bridge work? It measures inductance using capacitance. Let’s derive the expression for the inductor in this bridge.

Here l₁ is unknown inductance and c₂ 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 z₁, z₂, z₃ and in above equation we get,

Equating and then separating the real and the imaginary parts we get the expression for l₁ and r₁ as written below:

We need to modify the circuit to calculate the incremental inductance. Below is the modified Owens Bridge circuit:

A valve voltmeter is placed across the resistor r₃. 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 r₃.
Now at the balance point we have, incremental inductor l₁ = r₂r₃c₄
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, l₁ is incremental inductance.
Let us mark drop across arm ab, bc, cd and ad as e₁, e₃, e₄ and e₂ 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. i₁) is chosen as reference in order to draw phasor diagram. Current i₂ is perpendicular to current i₁ as shown and drop across inductor l₁ is perpendicular to i₁ as it is an inductive drop while the drop across capacitor c₂ is perpendicular to i₂. At balance point e₁ = e₂ which is shown in the figure, now resultant of all these voltage drops e₁, e₂, e₃, e₄ will give e.

Advantages of Owen’s Bridge

1. The for inductor l₁ that we have derived above is quite simple and is independent of frequency component.
2. This bridge is useful for the measurement of inductor over wide range.

Disadvantages of Owen’s Bridge

1. 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.
2. As the measuring quality factor increases the value of standard capacitor required increases thus expenditure in making this bridge increases.