Multifunction Generation with Logarithmic Pulse Width/Pulse Height Modulation

A new method for the generation of the multifunction operation W = sign(X).Z(X/Y)
m
is treated in this paper. The method is based on logarithmic function generation by means of logarithmic pulse width modulation, which is pulse width modulation with an exponential carrier signal (Ye
-α
X
t
). Demodulation is done by feeding the pulse width modulated signal into an integrator which has a logarithmic pulse width modulator in its feedback path. This feedback pulse width modulator has an exponential carrier signal of the form Ze
-α
W
t
. Moreover, this logarithmic pulse width modulator in the feedback path also performs the antilog operation. Hence, multifunction operation is accomplished based on the log-antilog principle. The exponent m is equal to the ratio of the inverse of the time constants of the exponential carrier signals for the input and feedback modulators (m = α
w
/α
x
).Hence, the exponent m can easily be adjusted. Experiments on the analog computer showed that an accuracy of 0.2% of a 1 V full scale was easily obtainable. The frequency response and the signal-to-noise ratio of the system was determined through simulation on a digital computer.