- Maxwell Bridge Definition: A Maxwell Bridge measures the self-inductance of a circuit using components that balance inductive and capacitive impedances.
- Diagram Understanding: Diagrams of Maxwell Bridge show the configuration of resistors and capacitors or inductors necessary to balance the bridge.
- Resonance Principle: Resonance occurs when the bridge balances, eliminating current through the detector, a crucial aspect in understanding how Maxwell Bridge functions.
- Application Range: Maxwell Bridge is especially useful in measuring inductors at audio frequencies due to its frequency independence.
- Limitations and Alternatives: While effective for medium quality coils, the Maxwell Bridge has limitations for low-quality coils, prompting the use of alternatives like Hay’s bridge.
What is Maxwell Bridge
A Maxwell Inductance Capacitance Bridge, or Maxwell Bridge, is an adaptation of the Wheatstone bridge designed to measure a circuit’s self-inductance. It employs the null deflection method to determine unknown inductance values. If it includes a parallel capacitor and resistor, it’s called a Maxwell-Wien bridge.
The working principle is that the positive phase angle of an inductive impedance can be compensated by the negative phase angle of a capacitive impedance when put in the opposite arm and the circuit is at resonance (i.e., no potential difference across the detector and hence no current flowing through it). The unknown inductance then becomes known in terms of this capacitance.
There are two types of Maxwell bridges: Maxwell’s inductor bridge, and Maxwell’s inductor capacitance bridge. In Maxwell’s inductor bridge, only inductors and resistors are used. In Maxwell’s inductor capacitance bridge, a capacitor is also added to the circuit.
As both types of these Maxwell bridge is based on an AC bridge, we’ll first explain the working principle of an AC bridge before explaining a Maxwell bridge.
AC Bridges
An AC Bridge includes a source, a balance detector, and four arms, each containing an impedance. AC bridges evolve from Wheatstone bridges by substituting the DC battery with an AC source and replacing the galvanometer with a detector.
They are highly useful to find out inductance, capacitance, storage factor, dissipation factor etc.
Now let us derive the general expression for an AC bridge balance. The figure below shows an AC bridge network:
Here Z1, Z2, Z3 and Z4 are the arms of the bridge.
Now at the balance condition, the potential difference between b and d must be zero. From this, when the voltage drop from a to d equals to drop from a to b both in magnitude and phase.
Thus, we have from figure e1 = e2
From equation 1, 2 and 3 we have Z1.Z4 = Z2.Z3 and when impedance are replaced by admittance, we have Y1.Y4 = Y2.Y3.
Consider the basic form of an AC bridge, as depicted in the following circuit diagram: In this circuit R3 and R4 are pure electrical resistances. Putting the value of Z1, Z2, Z3 and Z4 in the equation that we have derived above for AC bridge.
Now equating the real and imaginary parts, we get:
Following are the important conclusions that can be drawn from the above equations:
- We get two balanced equations that are obtained by equating real and imaginary parts this means that for an ac bridge both the relation (i.e.magnitude and phase) must be satisfied at the same time. Both the equations are said to be independent if and only if both equations contain a single variable element. This variable can be inductor or resistor.
- The above equations are independent of frequency that means we do not require exact frequency of the source voltage and also the applied source voltage waveform need not to be perfectly sinusoidal.
Maxwell’s Bridge
There are two main types of Maxwell Bridges:
- Maxwell’s inductor bridge
- Maxwell’s inductor capacitance bridge
Maxwell’s Inductance Bridge
Let us now discuss Maxwell’s inductance bridge. The figure shows the circuit diagram of Maxwell’s inductor bridge.
In this bridge, the arms bc and cd are purely resistive while the phase balance depends on the arms ab and ad.
Here l1 = unknown inductor of r1.
l2 = variable inductor of resistance R2.
r2 = variable electrical resistance.
As we have discussed in AC bridge according to balance condition, we have at balance point:
We can vary R3 and R4 from 10 ohms to 10,000 ohms with the help of resistance box.
Maxwell’s Inductance Capacitance Bridge
In this configuration of the Maxwell Bridge, a standard variable capacitor measures the unknown inductor. Circuit of this bridge is given below,
Here, l1 is unknown inductance, C4 is a standard capacitor.
Now under balance conditions, we have from AC bridge that Z1.Z4 = Z2.Z3
Let us separate the real and imaginary parts, then we have,
Now the quality factor is given by,
Advantages of Maxwell’s Bridge
Maxwell Bridge offers several advantages:
- The frequency does not appear in the final expression of both equations, hence it is independent of frequency.
- Maxwell’s inductor capacitance bridge is very useful for the wide range of measurement of inductor at audio frequencies.
Disadvantages of Maxwell’s Bridge
The disadvantages of a Maxwell Bridge are:
- The variable standard capacitor is very expensive.
- The bridge is limited to measurement of low quality coils (1 < Q < 10) and it is also unsuitable for low value of Q (i.e. Q < 1) from this we conclude that a Maxwell bridge is used suitable only for medium Q coils.
The above all limitations are overcome by the modified bridge which is known as Hay’s bridge which does not use an electrical resistance in parallel with the capacitor.
