Resolution of an Encoder！

The resolution of an encoder represents the smallest change
in measurement that can be measured realistically. Since
an encoder can be used to measure both displacement and
velocity, a resolution can be identified for each case.

Displacement Resolution
• Displacement resolution is governed by the number of windows N
in the code disk and the digital size (number of bits) r of the buffer
(counter output). The physical resolution is determined by N. If
only one pulse signal is used (i.e., no direction sensing), and if the
rising edges of the pulses are detected (i.e., full cycles of the
encoder are counted), the physical resolution is given by (360/N)

But if both pulse signals (quadrature signals) are available and
the capability to detect rising and falling edges of a pulse is
also present, four counts can be made per encoder cycle,
thereby improving the resolution by a factor of four.
• Hence, the physical resolution is given by (360/4N)°. When the
two signals V1 and V2 are added, the resulting signal has a
transition at every quarter of the encoder cycle. By detecting
each transition (through edge detection or level detection), four
pulses can be counted within every main cycle.

Assuming that the maximum angle measured is 360° (or
±180°), the digital resolution is given by:

 
• A digital word containing r bits can represent 2r different
values (unsigned). Note that 0° and 360° represent the same
position of the code disk. An ambiguity does not arise if we
take the minimum value of θ to be 360°/2r, not zero.

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