en.m.wikipedia.org/wiki/Variable_reluctance_sensor
That's not a resolver.
A resolver is a transformer with some parts that are stationary and some that rotate with the shaft.
There is one primary coil which is driven with an excitation signal and then two secondary coils which provide the "sin" and "cos" outputs.
The two secondary coils are arranged at 90 degrees so that the efficiency of the transformer coupling between them is different, and varies as the system rotates.
There is some info here:
www.siglenteu.com/application-note/resol...-waveform-generator/
But bear in mind that the waveform graph shown is rather misleading. It is showing the inputs and outputs plotted against time _and_ angle on the same axis.
For a fixed rotor position the input will typically be a sine wave of fixed amplitude. The outputs will be two sine waves of differing amplitudes, in phase with each other and with the excitation. The amplitude of either output can be negative, though, which looks like 180 degrees out of phase.
Interpreting the output is easier than it might seem. You just measure the amplitude of both outputs at a point in time (preferably at the peak of the excitation voltage) and take the arctan of the ratio of the two voltages to get a rotor angle.
This is really easy with a modern microcontroller but was really rather difficult several decades ago.
(Arduino code:
wiki.linuxcnc.org/cgi-bin/wiki.pl?ResolverToQuadratureConverter
)
The STMBL doesn't bother with sine wave excitation, it sends a square wave and it works perfectly well.
The Mesa 7i49 does use sine-wave excitation.
Some resolvers are almost exactly as shown in the link above, with brushes transferring the excitation to a rotating primary coil. But most are brushless, with an input coil driving a secondary on the rotor which in turn drives the excitation primary.
Brushless resolvers are extremely tough. All they contain is copper wires encased in epoxy. They work full of water, full of oil, when very hot or very cold. They withstand shock and vibration.
The angular resolution depends on the interface electronics. They are an analogue device so have infinite resolution. The Mesa 7i49 has 12 bits of accuracy, equivalent to a 4096 count encoder. However many (most?) resolvers are multi-pole, typically with the same number of pole pairs as the attached motor, but in some applications very many more.
The hard part of making a resolver is making the output linear with angle. Encoders are typically more accurate in that area, but very expensive resolvers can be very good.
I like them