electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...

, Anderson's bridge is a

bridge circuit A bridge circuit is a topology of electrical circuitry in which two circuit branches (usually in parallel with each other) are "bridged" by a third branch connected between the first two branches at some intermediate point along them. The bridge ...

used to measure the self-inductance of the coil. It enables measurement of inductance by utilizing other circuit components like resistors and capacitors. Anderson's bridge was invented by Alexander Anderson in 1891. He modified Maxwell's inductance capacitance bridge so that it gives very accurate measurement of self-inductance.

Balance conditions

The balance conditions for Anderson's bridge or, equivalently the values of the self-inductance and resistance of the given coil can be found using basic circuit analysis techniques such as KCL, KVL and using phasors. Consider the circuit diagram of Anderson's bridge in the given figure. Let L₁ be the self-

inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of t ...

and R₁ be the

electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallel ...

of the coil under consideration. Since the voltmeter is ideally assumed to have nearly infinite impedance, the currents in branches ab and bc and those in the branches de and ec are taken to be equal. Applying

Kirchhoff's current law Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhof ...

at node d, it can be shown that- :

\begin
   I_4 + I_c &= I_2
\end

Since the analysis is being made under the balanced condition of the bridge, it can be said that the voltage drop across the voltmeter is essentially zero. On applying

Kirchhoff's voltage law Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhof ...

to the appropriate loops(in the anti-clockwise direction), the following relations hold- :

\begin
   I_1(R_1 + r_1 + j \omega L_1) - I_2 R_2 - I_c r = 0 \\
   I_1 R_3 - \frac = 0 \\
   I_c r + \frac - I_4 R_4 = 0
\end

On solving these sets of equations, one can finally obtain the self-inductance and resistance of the coil as- :

\begin
   L_1 &= (\frac)(R_2 R_4 + r(R_2 + R_4))C \\
   R_1 &= \frac - r_1
\end

Advantages

The Anderson's bridge can also be used the other way round- that is, it can be used to measure the capacitance of an unknown

capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of a ...

using an inductor coil whose self-

and

have been pre-determined to a high degree of precision. An interesting point to note is the fact that the measured self-inductance of the coil does not change even on taking

dielectric loss Dielectric loss quantifies a dielectric material's inherent dissipation of electromagnetic energy (e.g. heat). It can be parameterized in terms of either the loss angle ''δ'' or the corresponding loss tangent tan ''δ''. Both refer to the ...

within the

into account. Another advantage of using this modified bridge is that unlike the variable capacitor used in

Maxwell bridge A Maxwell bridge is a modification to a Wheatstone bridge used to measure an unknown inductance (usually of low Q value) in terms of calibrated resistance and inductance or resistance and capacitance. When the calibrated components are a paral ...

, it makes use of a fixed capacitor which is relatively quite cheaper.

Disadvantages

One of the obvious difficulties associated with Anderson's bridge are the relatively complex balance equation calculations compared to the

. The circuit connections and computations are similarly more cumbersome in comparison to the

References

Measuring instruments Bridge circuits Analog circuits Irish inventions Impedance measurements {{Electronics-stub