Embedded Software and Motor Control Libraries for PXR40xx

Function GFLIB_AtanYXShifted_F16
• error contributed by higher order harmonics appearing in the input signals
• computational error of the multiplication due to the finite length of registers
• error of the phase shift Δθ representation in the finite precision arithmetic and in the
values
• error due to differences in signal amplitudes
It should be noted that the function requires both signals to have the same amplitude. To
minimize the output error, the amplitude of both signals should be as close to 1.0 as much
as possible.
The function has been tested to be reliable at a phase shift in the range of [-165, -15] and
[15, 165] degrees for perfectly sinusoidal input signals. Beyond this range, the function
operates correctly, however, the output error can be beyond the guaranteed value. In a
real application, an error, contributed by an AD conversion and by higher order
harmonics of the input signals, should be also taken into account.
Note
The function calls the GFLIB_AtanYX_F16 function. The
function may become numerically unstable for a phase shift
approaching -180, 0 or 180 degrees. The function accuracy is
guaranteed for a phase shift in the range of [-165, -15] and [15,
165] degrees at perfect input signals.
4.38.5 Re-entrancy
The function is re-entrant.
4.38.6 Code Example
#include "gflib.h"
tFrac16 f16InY;
tFrac16 f16InX;
tFrac16 f16Ang;
GFLIB_ATANYXSHIFTED_T_F16 Param;
void main(void)
{
//dtheta = 69.33deg, thetaoffset = 10deg
//CY = (1 - 2^-15)/(2*cos((69.33/2)/180*pi))= 0.60789036201452440
//CX = (1 - 2^-15)/(2*sin((69.33/2)/180*pi))= 0.87905201358520957
//NY = 0 (abs(CY) < 1)
//NX = 0 (abs(CX) < 1)
//KY = 0.60789/2^0 = 0.60789036201452440
//KX = 0.87905/2^0 = 0.87905201358520957
//THETAADJ = 10/180 = 0.05555555555
Param.f16Ky = FRAC16 (0.60789036201452440);
Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0
262 Freescale Semiconductor, Inc.