Tachometers Derived From a Brushless DC Motor

Marshall Space Flight Center, Alabama

Thursday, November 01 2007 The multiplier circuit for phase A thus generates an output signal proportional to both of its inputs; namely k₃ θ. (sin θ)², where k₃ = k₁k₂. In a similar manner, the multiplier circuit for phase B generates an output signal of k₃ θ. (cos θ)². These signals are fed to an adder circuit. By virtue of the identity (sin θ)² + (cos θ)² = 1, the output of the adder is simply k₃θ. .

The lower part of the figure illustrates the major functional blocks of a direction- insensitive analog tachometer that, except for its lack of directionality, offers the same advantages as does the analog tachometer described above. However, this circuit is conceptually simpler in that it does not contain integrators.

This circuit processes the back-emf outputs of the two motor phases into a voltage directly proportional to magnitude of the instantaneous rate of rotation of the shaft. As in the circuit described above, the processing in this circuit effects a straightforward combination of mathematical operations leading to a final operation based on the identity (sin x)² + (cos x)² = 1 for any value of x.

Further as in the circuit described above, the two back-emf signals are k θ. sin θ for phase A and k θ . cos θ for phase B, where k is a constant that depends on the electromagnetic characteristics of the motor. In the present case, the quantity that one seeks to measure is ⎪θ. ⎪.

Each back-emf signal is fed to a dedicated squaring circuit. The outputs of the squaring circuits for phases A and B are thus proportional to (θ. sin θ)² and (θ. cos θ)². The outputs of the squaring circuits are fed to an adder. By virtue of the identity (sin θ)² + (cos θ)² = 1 the output of the adder is proportional to θ. ²; this output is fed to a square-root circuit to obtain a final output proportional to ⎪θ. ⎪.

This work was done by David E. Howard and Dennis A. Smith of Marshall Space Flight Center.

This invention has been patented by NASA (U.S. Patent No. 6,084,398). Inquiries concerning nonexclusive or exclusive license for its commercial development should be addressed to Sammy Nabors, MSFC Commercialization Assistance Lead, at This e-mail address is being protected from spambots. You need JavaScript enabled to view it . Refer to MFS-31142/3.