Before introducing sine and cosine encoders , let's review square wave incremental encoders.
The output of a square wave incremental encoder is an orthogonal AB pulse signal, i.e., a high level or a low level. We call the change of the signal from low to high a rising edge. The encoder output is a periodic repetition of one rising edge to another. The encoder's resolution corresponds one-to-one with the code disk lines. During one revolution of the encoder, this AB signal will repeat periodically many times. For example, an encoder with 1024 code disk lines will have 1024 such signal cycles output during one revolution. Therefore, the encoder's resolution is said to be 1024 lines, or 1024 pulses, referring to the number of signal cycles output per revolution of the encoder.
To improve the resolution of incremental encoders , frequency quadruple is sometimes used, which means that the rising edge is calculated at the same time as the falling edge, so that each cycle can be subdivided into four steps.
In addition to the AB pulse signal, there is another reference marker, also known as the reference signal or zero-position marker, which is crucial for determining the position. Typically, the zero-position marker appears only once per revolution and is used to indicate the encoder 's origin. In other words, an incremental encoder can generally only determine one absolute position within one revolution.
To further improve encoder resolution, the density of the code disk lines needs to be increased. However, the resolution of square wave incremental encoders is limited by two factors. First, it is limited by the code disk size. An encoder with a 60mm outer diameter typically has no more than 10,000 physical lines. Second, the output frequency is directly proportional to the encoder's rotational speed and resolution. Higher resolution means higher output frequency, but high frequencies cannot achieve long-distance transmission.
The sine and cosine encoders are similar to the AB quadrature pulse signals of ordinary square wave incremental encoders. The difference is that the sine encoder outputs sine and cosine wave signals with a peak-to-peak value of 1V or 2V through the A and B channels. When the encoder rotates one revolution, it will also periodically generate multiple sine and cosine cycles, such as 512(29), 1204(210) or 2048(211).
Although the number of sine and cosine cycles (physical resolution) may not seem very high, in the controller or driver, each sine and cosine cycle can be subdivided into many steps through arctangent interpolation by processing and calculation of the encoder input circuit, thereby achieving a very high resolution.
X = Arctan(Sin(X)/Cos(X))
Based on the real-time amplitudes of the sine and cosine signals, the exact position (electrical angle) of the encoder within one sine/cosine cycle can be determined using Arctan calculations. Depending on the resolution of the analog-to-digital converter (ADC) and the quality of the sine/cosine signals, each sine/cosine cycle can typically be subdivided into 2^12 to 2^14 steps. The number of sine/cosine cycles per revolution of the encoder itself, multiplied by the number of subdivision steps per sine/cosine cycle, constitutes the total resolution per revolution of the sine/cosine encoder after subdivision.
Total resolution per lap after subdivision = Number of cycles per lap x Number of subdivision steps per cycle
For example, a sine/cosine encoder with 1024 cycles per revolution has a total resolution of 2^10 x 2^13 = 2^10 + 13 = 2^23 after 13-bit subdivision.
It is worth noting that the subdivided resolution is calculated by the controller or driver through the input circuit, and is not directly output by the encoder.
