Related Products: SD Module Family (SD1, SD2, SD3, SD4, SD5), AC Module Family (AC1, AC2, AC3)
Reference Waveform Distortion
My 400 Hz reference (excitation) is not a clean sine wave. Does harmonic distortion on the reference degrade the angle accuracy of an S/D converter?
For distortion that is common to the reference and the signal inputs, no. A tracking synchro/resolver-to-digital converter is inherently insensitive to the shape of the reference waveform. The reason is in how the loop works: the SIN and COS (or stator) inputs are multiplied by cos θ and sin θ, where θ is the converter’s output angle, the products are subtracted, and the difference is passed through a phase-sensitive detector and an integrator. The loop drives the integrator input to zero, which forces θ to the transducer angle φ.
If the excitation contains harmonics, every harmonic appears on both signal channels with the same amplitude and phase, because both channels are excited by the same rotor. When the harmonic terms are carried through the multiply-subtract-detect chain they all end up multiplied by the same sin(φ − θ) factor, and the detector output over each half cycle reduces to a constant times sin(φ − θ). That constant depends on the harmonic content, but it only sets the loop gain; the null still occurs at θ = φ. Because the converter uses a Type II servo loop, a large change in loop gain does not produce a static angle error. The Handbook analysis puts the practical limit well beyond anything a normal excitation source produces: even 20 % third harmonic on the reference has a negligible effect on the converter’s angle output.
Two practical consequences:
- An excitation derived from aircraft or shipboard 400 Hz power, or from a programmable reference source, does not need to be spectrally pure to get full converter accuracy. For example, the NAI AC reference modules specify total harmonic distortion of under 3 % (AC1/AC2, 47 Hz to 15 kHz; under 5 % from 15 kHz to 20 kHz) or under 5 % (AC3), well below the 20 % figure above.
- This tolerance applies to the waveform shape only. The reference must still be within the module’s specified voltage and frequency band; the SD modules measure reference voltage and frequency and report reference under- and over-voltage status. See the SD1-SD5 Manual for the limits.
Is there any harmonic distortion that does cause an error?
Yes: distortion that is present on one signal channel but not the other. If a fraction K of third harmonic (in phase with the carrier) is added to the SIN input while the COS input stays clean, the harmonic no longer cancels in the subtractor. At the worst-case angle (θ ≈ φ = 45°, where the sin φ·cos θ coefficient reaches 0.5) the detector sees 0.5·K of third harmonic alongside the fundamental error term. Integrating over one half cycle of the carrier and setting the result to zero gives
2·sin ε + K/3 = 0, so for small ε: ε ≈ −K/6 radians
Worked number: K = 0.01 (1 % third harmonic on one channel only) gives |ε| ≈ 0.01/6 rad ≈ 1.7 × 10−3 rad ≈ 0.095°, i.e. about 5.7 arc-minutes. That is several times the 1 arc-minute single-speed accuracy of the SD modules, so differential distortion is far from negligible.
In practice, however, there is normally no mechanism outside the converter that distorts one channel differently from the other: the transducer windings are excited by the same rotor voltage, and the reference source cannot affect one stator line and not another. Differential distortion therefore arises mainly inside the converter’s own signal path, for example from a nonlinear input amplifier on one channel, and the converter design has to guard against it. The NAI SD modules also synthesize their demodulation reference from the signal inputs themselves rather than from the raw external reference (see Phase Shift Limits and Quadrature Error), so the external reference waveform has even less influence on the demodulation than in the classic block diagram analyzed in the Handbook. If an external buffer or isolation amplifier is inserted in one signal line but not the other, its distortion should be checked against the K/6 rule above.
The results above are adapted from Appendix C, “Harmonic Distortion of the Reference Waveform”, of the Synchro/Resolver Handbook distributed by NAI.