
TMC428 DATA SHEET (V. 1.00 / February 12, 2001)
37
Copyright 2000, TRINAMIC Microchips GmbH
M I C R O C H I P S
37
Micro Step Enhancement
Sine cosine micro stepping is not sufficient for all types of real stepper motors not even for those stepper
motors labeled as optimized for micro stepping operation. A periodic trapezoidal or triangular function
similar to a sine function or a superposition of these function as a replacement of the pure sine wave
function (Figure 16) is a better choice for different types of stepper motors. Taking the physics of stepper
motors into account, the choice of the function for micro stepping can be simply determined by a single
shape parameter
s
as explained below. The programmability of the micro step look-up table of the
TMC428 also during operation– on-the-fly alteration of parameters –provides a simple and effective
facility to attune micro stepping to a given type of two-phase stepper motor. Enhanced micro stepping
requires accurate current control. So, stepper motor driver chips with enabled and well tuned fast decay
operational mode– as our TMC288 / TMC289 smart power drivers provide –are necessary to be used.
Non-Linearities resulting from magnetic field configuration determined by shapes of pole shoes,
ferromagnetic characteristics, and other stepper motor characteristics effect non-linearity in micro
stepping of real stepper motors. The non-linearity of micro stepping causes micro step positioning
displacements, vibrations and noise, which can be reduced dramatically with an adapted micro step table.
Nevertheless sine cosine micro stepping is a good first order approach for microstepping. The micro step
enhancement possible with the TMC428 bases on replacement of the look-up table initialization function
sin(
j
) used for sine cosine micro stepping by a function with the shape parameter
s
. A quarter sine wave
period is the basic approach for initialization of the micro step look up table . A quarter of a trapezoidal
function or a quarter of a triangular function is chosen depending on the shape parameter
s
for a given
stepper motor type.
.
2
0
0
+
0
0
)
(
0
)
(
0
)
(
)
(
hom
_
_
p
j
s
s
j
s
j
s
j
j
s
<
≤
≤
≤
<
=
>
=
and
with
for
for
for
f
f
f
f
b
r
circle
circle
circle
box
The look-up table (
f
(
j
) ) of the TMC428 enfolds a quarter period (0
=
j
<
p
/2) only. This quarter period is
expanded to a full period (0
=
j
< 2
p
) and the phase shifted companion function value (
f
(
j
-
p
/2
)) is
added automatically by the TMC428 during operation. So, for reach function value (
f
(
j
)) one
automatically gets a pair of function values {
f
(
j
);
f
(
j
-
p
/2
)} respectively {sin(
j
); cos(
j
)}. This automatic
expansion of the TMC428– primary proposed for sine cosine microstepping (
f
(
j
) = sin(
j
)) –also works
fine with other micro step controlling functions
f
s
.
x
0
4
p
2
p
0
p
p
2
4
3
p
)
(
j
f
j
box
rom
cce
1
1
1
2
p
y
up to 64 micro steps
1 full step
u o6 mcoseswhnaqarn
1flse
2
Figure 16 - micro step enhancemant by introduction of a shape function f
s
(
j
)