Anderson′s Bridge | Advantages Disadvantages of Anderson′s Bridge

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Key learnings:

Anderson’s Bridge Definition: Anderson’s Bridge is used to measure low-quality factor circuits by comparing known resistance and capacitance values.
Double Balance: It achieves double balance by fixing the capacitance and varying resistance.
High Accuracy: Known for its precision in measuring inductors ranging from micro Henry to several Henry.
Experimental Method: Set the signal frequency, adjust resistances, and use the derived formulas to find the unknown inductance.
Advantages and Disadvantages: Easier to balance for low-quality factors but involves complex equations and shielding difficulties.

Anderson’s Bridge

Anderson’s bridge is the low-Q inductance bridge. Maxwell bridge covers medium Q. Hay’s bridge covers high Q. Maxwell and Hay both struggle to null a low-Q coil.

Use Hay for high Q and Maxwell for medium Q. Anderson’s Bridge is a modified Maxwell’s inductance-capacitance bridge with an extra resistor-capacitor path for low Q.

Anderson’s Bridge is a modified Maxwell inductor capacitance bridge. Balance uses a fixed capacitance and you trim electrical resistance instead of a variable standard capacitor.

Textbooks quote a working span from a few microhenry up to several henry for inductors on this bridge. The unknown L is compared with known R and C. The circuit diagram of Anderson’s Bridge is below.

The unknown inductor sits between a and b. r₁ is the series resistance of that coil.

Arms bc, cd and da are resistors r₃, r₄ and r₂. A standard capacitor sits in series with variable resistor r, and that series pair is connected in parallel with cd.

The source is connected between b and e.
Balance then gives l₁ and r₁:

At null the following relations hold:

Equating voltage drops then gives

Substitute i_c in those equations to get

Equation (7) is heavier than the Maxwell pair. Alternate trims of r₁ and r in Anderson’s bridge converge faster than moving both at once.

The classic lab null uses headphones. Set the signal generator in the audio band. Trim r₁ and r until the phones are quietest.

Read those r₁ and r settings with a multimeter. Put them in the formula above to get the unknown inductance. Repeat with another standard capacitor if you want a check.

Phasor Diagram of Anderson’s Bridge

Mark the voltage drops across ab, bc and cd, plus ad, as e₁, e₂, e₃ and e₄ as shown in the figure above.

In the phasor diagram of Anderson’s bridge, i₁ is the reference. i_c is drawn at 90° to i₁ because of the capacitor at ec. i₄ and i₂ lead the reference by the angles shown.

The source voltage e is the phasor sum of e₁, e₂ and e₃ plus e₄. As shown in the phasor diagram of Anderson’s bridge the drop i₁ (R₁ + r₁) plus i₁.ω.l₁ (drawn at 90° to i₁) is e₁. e₂ is i₂.r₂ at angle ‘A’ to the reference.

e₄ is the drop i₄.r₄ at angle ‘B’ to the reference.

Advantages of Anderson’s Bridge

A low-Q coil is easier to null on Anderson’s bridge than on a Maxwell inductance-capacitance bridge.
The standard capacitor can be a fixed value. You do not need a variable standard C.
The same network can also give capacitance from a known inductance.