Related Products: API 8810A, SD Module Family (SD1, SD2, SD3, SD4, SD5), DS Module Family (DS1, DS2, DS3, DS4, DS5, DS6, DS7, DS8, DS9, DSN)
Phase Shift Limits
Are there limits to the amount of phase shift possible (between the reference source and signal inputs from a synchro or resolver) connected to the API 8810A or Multifunction card S/D module? Also with regard to electronics that are not for bench top use, do you know of a standard or document(s) that describe limits for phase shifts of RDC’s, specific for synchros and resolvers?
Due to the inductive nature of synchros and resolvers there will be some inherent phase shift between the stator output and rotor excitation. Referring to the operations manual specifications for the 8810A or multifunction cards, under the heading “Phase Correction” or “Immediate Module Specifications”, the 8810A or S/D module will correct for and operate with up to +/- 60 degrees of phase shift between the reference (excitation) source and stator output. Phase Lock Loss Status is monitored and reported to the user. The module converters employ a technique which synthesizes a perfect internal reference signal from the stator (or SIN, COS) inputs thereby reducing the phase shift to essentially 0 degrees. There is no standard for RDC’s and phase shift. There is no military standard for resolver specifications. There is a standard for Synchros (Arinc 407-1). However, most technically-modern RDC’s now typically incorporate the design technique of utilizing a synthesized ref. circuit to correct the phase shift.
Quadrature Error
How do quadrature (90°-shifted) components in the stator or SIN/COS inputs affect converter accuracy, and how much error do phase shift and quadrature actually cause?
Where quadrature comes from. In an ideal synchro or resolver all of the signal voltages are in phase with the excitation; only their amplitudes change with shaft angle. In a real installation the individual signal paths never have exactly the same phase shift. Winding inductance, cable capacitance and unequal loading of the stator lines each shift the phase of one line slightly differently from the others. If one channel (say the cosine channel) is shifted by a small angle α relative to the other, expanding sin(ωt + α) shows that its voltage splits into an in-phase part proportional to cos α (≈ 1) and a part shifted by 90° that is proportional to sin α (≈ α). That 90° part is the quadrature voltage. It is distinct from the larger, common phase shift β between the whole signal set and the reference described in the question above, but the two interact, as shown below.
Why a tracking converter ignores quadrature to first order. A Type II tracking converter forms an error signal, demodulates it with a phase-sensitive detector that switches gain between +1 and −1 in step with the reference, and integrates the result. A component that is exactly 90° from the reference integrates to zero over every half cycle, so an ideal detector nulls only the in-phase component and the quadrature term drops out. Quadrature only becomes a direct problem if it is large enough to drive an amplifier into asymmetric limiting.
Residual error with no reference phase shift. The quadrature term is rejected, but the in-phase term is now scaled by cos α ≈ 1 − α²/2 instead of 1. At the worst-case angle (θ ≈ 45°, where the sin θ·cos φ factor peaks at 0.5) the loop settles with an angle error of
ε ≈ α²/4 radians (α in radians)
Because the degree-to-radian and degree-to-arc-minute conversions almost cancel (60 ÷ (4 × 57.3) ≈ 0.26), the same rule of thumb works with mixed units:
error (arc-minutes) ≈ α²/4 (α in degrees)
Worked number: a differential phase shift of α = 1° gives (1/57.3)² / 4 ≈ 7.6 × 10−5 rad ≈ 0.0044° ≈ ¼ arc-minute. The error is quadratic in α, so 2° gives about 1 arc-minute, and a realistic 0.2° gives about 0.01 arc-minute.
How big the quadrature voltage is. For a 90 V L-L 11CT4-type control transformer (transformation ratio R ≈ 0.64), the quadrature voltage on the rotor at the 45° worst case is α·R·V·0.5 (α in radians), which for V = 90 V rms works out to roughly 0.5 V rms per degree of differential phase shift. Turned around: 100 mV rms of quadrature on the rotor corresponds to about 0.2° of differential phase.
Combined effect with reference-to-signal phase shift. If the demodulation reference is itself shifted by β relative to the signals, the quadrature term is no longer exactly 90° from the reference and part of it is demodulated as if it were a real error. For small α and β the worst-case angle error becomes
ε ≈ 0.5·α·β radians (α and β in radians)
Worked number: α = 1° and β = 5° gives 0.5 × (1/57.3) × (5/57.3) ≈ 7.6 × 10−4 rad ≈ 0.044°, i.e. about 2.5 arc-minutes, roughly ten times the ¼ arc-minute obtained with β = 0. This is why a modest reference phase shift matters even though the converter “rejects quadrature”: it converts otherwise-harmless quadrature into in-phase error.
Realistic budget. The 1° differential phase used in the examples is deliberately pessimistic. The combined differential phase of a converter and a good control transformer is more typically 0.2° or less, i.e. under 100 mV of quadrature, so with the reference phase shift removed the residual error is negligible against the 1 arc-minute single-speed accuracy of the SD modules.
How the NAI S/D modules handle it. The SD module family synthesizes its demodulation reference from the SIN/COS (or stator) inputs themselves and, as stated in the question above, corrects up to ±60° of reference-to-signal phase shift. In terms of the formulas above this drives β to essentially zero, so the α·β term collapses and only the very small α²/4 residual remains.
A note for D/S users. Real synchros, control transmitters (CX) and control receivers/transformers alike, introduce a phase lead between excitation and output, and servo designers often add a balancing phase lead to the reference feeding the phase-sensitive detector. A D/S converter output has negligible phase shift relative to its reference, so replacing a CX with a D/S channel in an existing servo loop changes the phase relationship between the CT output and the reference; a corresponding correction has to be applied elsewhere in the loop.
The results above are adapted from Appendix F, “Effects of Quadrature Signals on Servo Systems”, of the Synchro/Resolver Handbook distributed by NAI. The harmonic-distortion companion question is covered in Reference Waveform Distortion.