Synchros (aka Selsyns) seem to fall in a gray area of electronics. Neither my electronic reference nor electrical reference books cover them with any clarity. I have found that there is quite a bit of misinformation in print and on the net regarding their application.
The Synchro is a specially wound "motor" comprised of two windings.
The Rotor is a single winding with slip rings & brushes.
The Stator is a 3 section winding, Y connected.
Many synchros have rear mounted screw terminals marked with Rx & Sx designations. Others have flying leads. The Standard Color Code for units with flying leads is:
R1 Red (or White/Red)
R2 Black (or White/Black)
With a sinusoidal excitation voltage (VR) applied to the rotor, the stator voltages are nominally:V(S1-S3) = K * VR * Sin(θ)
Where θ (theta) is the shaft angle referenced to electromechanical zero and K is a constant defined by the winding ratios.
Synchros are (were?) commonly manufactured with these (rotor) voltage ratings:115V at 400Hz 115V at 60Hz
Normal system operation connects the corresponding rotor (Rx) and stator (Sx) wires of a synchro transmitter to a synchro receiver with a five wire cable. The position of the synchro transmitter's input shaft is then repeated on the synchro receiver's output shaft.
The Four-Wire connection.
The US military, and also the commercial aviation sector, employed many (26V / 400Hz) synchros in this manner for Radio Compass applications. One of the rotor leads, R2 (Black), is commoned with one of the stator connections, S2 (Black), to save a pin on the connectors and a wire in the interconnecting cable -- a valid consideration when building several hundred thousand units. Note: I have seen military drawings which incorrectly identify the phases even though the connections are correct.
An AN3102-14S-2P connector (Note: The cable mate is an AN3106-14S-2S) is commonly used on the later version units but, the pinout is NOT consistent.
I have seen:
On the ARN-6 seriesR2-S2 A
On a Lear unitR2-S2 A
A four wire system may be directly calibrated. In a five wire system, temporarily connect a jumper lead between R2 and S2.1. Connect an AC voltmeter, set to a range at least 2X the excitation voltage, between S1 & S3.
Amplifying or repeating the synchro signal
A 26 volt 4-wire connected system may be extended to multiple readout devices, or alternatively employing a small transmitter to drive a larger receiver, by buffering just the S1 & S3 signals with a pair of power Op-Amps (Typ: Texas Instrument OPA-544T) connected as followers operating on +/- 24 volt rails referenced to S2 -- system "ground" in this instance.
My "Telephone Wire" 4 conductor connection color code:R1 Red