The upper part of the figure illustrates the major functional blocks of a direction-sensitive analog tachometer circuit based on the use of an unexcited two-phase brushless dc motor as a rotation transducer. The primary advantages of this circuit over many older tachometer circuits include the following:

  • Its output inherently varies linearly with the rate of rotation of the shaft.
  • Unlike some tachometer circuits that rely on differentiation of voltages with respect to time, this circuit relies on integration, which results in signals that are less noisy.
  • There is no need for an additional shaft-angle sensor, nor is there any need to supply electrical excitation to a shaft-angle sensor.
  • There is no need for mechanical brushes (which tend to act as sources of electrical noise).
  • The underlying concept and electrical design are relatively simple.
These Analog Tachometer Circuits perform straightforward operations on the back-emf outputs of a brushless dc motor to generate voltages proportional to the rate of rotation of the shaft.

This circuit processes the back-electromagnetic force (back-emf) outputs of the two motor phases into a voltage directly proportional to the instantaneous rate (sign · magnitude) of rotation of the shaft. The processing in this circuit effects a straightforward combination of mathematical operations leading to a final operation based on the well known trigonometric identity (sin x)2 + (cos x)2 = 1 for any value of x. The principle of operation of this circuit is closely related to that of the tachometer circuit described in "Tachometer Derived From Brushless Shaft-Angle Resolver" (MFS- 28845), NASA Tech Briefs, Vol. 19, No. 3 (March 1995), page 39. However, the present circuit is simpler in some respects because there is no need for sinusoidal excitation of shaft-angle resolver windings.

The two back-emf signals are kθ̇sin θ for phase A and kθ̇cos θ for phase B, where k is a constant that depends on the electromagnetic characteristics of the motor, θ is the instantaneous shaft angle, and the overdot signifies differentiation with respect to time. Note that θ̇ is the quantity that one seeks to measure.

Each back-emf signal is fed to one of two inputs of a multiplier circuit of gain k2 dedicated to its respective phase. Each of these signals is also integrated with a suitable time constant and gain to obtain a voltage of k1sin θ for phase A and –k1cos θ for phase B (where k1 is a constant that incorporates the combined effects of the gain and the time constant). The output of the integrator for phase B is inverted to obtain a voltage k1cos θ. Each of these signals is fed to the other input terminal of the multiplier circuit for its respective phase.

NASA Tech Briefs Magazine

This article first appeared in the November, 2007 issue of NASA Tech Briefs Magazine.

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