TIDUA05B June 2015 – March 2025
The ideal interpolated angle resolution is a function of the Sin/Cos encoder’s line count and the resolution of the dual ADC. The equivalent interpolated angle resolution can be calculated as:

Figure 1-7 illustrates the achievable interpolated angle resolution as a function of the line count for no interpolation, interpolation with an ideal 12-bit, and a 16-bit dual ADC.
Figure 1-7 Ideal Interpolated Angle Resolution versus Line Count versus ADC ResolutionThe ideal resolution with a Sin/Cos encoder with 2048 line counts using a 16-bit dual ADC equals 28-bit, if the ADC’s full-scale input range is used.
This high resolution is typically not required for position control, but for very precise speed control, especially at lower mechanical speed. Figure 1-8 outlines the ideal speed resolution derived at a sample rate of 1.6 kHz without low-pass filtering. This assumes the industrial drive’s speed closed-loop control runs 10 times lower than the current closed-loop control and PWM at 16 kHz.
Figure 1-8 Ideal Speed Resolution versus Mechanical Speed at 1.6-kHz Sample Rate and Encoder With 1000 Line CountPractically, low-pass filtering will be applied and improves resolution and immunity to noise, but with a filter specific propagation (group) delay or latency.
Following the ideal resolution, Table 1-7, Figure 1-9, and Figure 1-10 outline the impact of a quantization, offset, gain, or phase error to the interpolated angle.
| ERROR SOURCE | EXAMPLE | PHASE ERROR [MAX] |
|---|---|---|
| Quantization of signals A and B | 12-bit | 0.012% [0.045°] |
| Offset error of signals A and B | 0.1% | 0.05% [0.18°] |
| Gain error of signals A and B | 0.1% | 0.04% [0.15°] |
| Phase shift between input signals A and B | 90 + 0.36° [0.1%] | 0.1% [0.36°] |
Figure 1-9 Phase Error With +0.1% Offset With Signals A and B
Figure 1-10 Phase Error With (90 + 0.36°) Phase Shift Between Signals A and BNote that the phase error introduced due to a phase shift between the input signals A and B exhibits the double period. This signature can be leveraged for detection and correction of a constant phase shift using signal processing algorithms. However, these are beyond the scope of this design guide.