Bridges
The bridge circuit shown in the applet below is known as the
MaxwellWien bridge (often called the Maxwell bridge), and is
used to measure unknown inductances in terms of calibrated resistance
and capacitance. Calibrationgrade inductors are more difficult
to manufacture than capacitors of similar precision, and so the
use of a simple "symmetrical" inductance bridge is not
always practical. Because the phase shifts of inductors and capacitors
are exactly opposite each other, a capacitive impedance can balance
out an inductive impedance if they are located in opposite legs
of a bridge, as they are here.
Unlike this straight Wien bridge, the balance of the MaxwellWien
bridge is independent of the source frequency. In some cases, this
bridge can be made to balance in the presence of mixed frequencies
from the AC voltage source, the limiting factor being the inductor's
stability over a wide frequency range.
Exercise: Using the equations
within the applet, calculate appropriate values for C and R2 for
a set of probe values. Then, using your calculated values, balance
the bridge. The oscilloscope trace representing current (brightest
green) across the top and bottom of the bridge should be minimized
(straight line).
In the simplest implementation, the standard capacitor (C) and
the resistor in parallel with it are made variable, and both must
be adjusted to achieve balance. However, the bridge can be made
to work if the capacitor is fixed (nonvariable) and more than
one resistor is made variable (at least the resistor in parallel
with the capacitor, and one of the other two). However, in the
latter configuration it takes more trialanderror adjustment
to achieve balance as the different variable resistors interact
in balancing magnitude and phase.
Another advantage of using a Maxwell bridge to measure inductance
rather than a symmetrical inductance bridge is the elimination
of measurement error due to the mutual inductance between the two inductors.
Magnetic fields can be difficult to shield, and even a small amount
of coupling between coils in a bridge can introduce substantial
errors in certain conditions. With no second inductor to react
within the Maxwell bridge, this problem is eliminated.
