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C2000 Clarke Transformation

Convert balanced three-phase quantities to balanced two-phase quadrature quantities


Embedded Coder® Support Package for Texas Instruments™ C2000™ Processors/ Optimization/ C28x DMC

Embedded Coder Support Package for Texas Instruments C2000 F28M3x Concerto™ Processors Processors/ Optimization/ C28x DMC


This block converts balanced three-phase quantities into balanced two-phase quadrature quantities. The transformation implements these equations


and is illustrated in the following figure.

The inputs to this block are the phase a (As) and phase b (Bs) components of the balanced three-phase quantities and the outputs are the direct axis (Alpha) component and the quadrature axis (Beta) of the transformed signal.

The instantaneous outputs are defined by the following equations and are shown in the following figure:


The variables used in the preceding equations and figures correspond to the variables on the block as shown in the following table:

 Equation VariablesBlock Variables


  • To generate optimized code from this block, enable the TI C28x or TI C28x (ISO) CRL.

  • The implementation of this block does not call the corresponding Texas Instruments library function during code generation. The TI function uses a global Q setting and the MathWorks® code used by this block dynamically adjusts the Q format based on the block input. See Using the IQmath Library for more information.


For detailed information on the DMC library, see C/F 28xx Digital Motor Control Library, Literature Number SPRC080, available at the Texas Instruments Web site.