Diode Wave Shaping(Sawtooth to Sinusoid)
To obtain a sinusoidal output waveform the triangular waveform
will be 'shaped' appropriately. Even arelatively simple diode
shaping produces a surprisingly low-distortion output. A
non-critical piecewise-linear approximation to the sinusoid is
illustrated to theright. (Only a quarter cycle is shown;
application to theremaining portions of the period follows on
application ofthe symmetry of the sinusoid.) The triangular
waveform isassumed to have a relative amplitude of 1.5; the
sinusoidwill have a unit amplitude. For 0 to 30 the 'sinusoid'
willfollow the triangle ramp. For 30 to 60 the slope of thewaveform
will be reduced so that the 'sinusoid' rises to only0.866, and for
the remaining 30 the slope changes to riseto unit amplitude.
The diode circuit drawn below is used to describe how thedesired
shaping is obtained; only the positive half-cycle isdescribed
explicitly. The input voltage is the triangularwaveform. For
simplicity the diode junction voltage dropis ignored. While the
diodes are reverse-biased neithershunt branch conducts, and Vo = V,
i.e., the output voltage
follows the ramp.Suppose V1 < V2 is 0.5 volt. Then when the
input voltagereaches 0.5 volt D1 begins to conduct. The output
voltage isgiven by
and setting Vo = 0.866 when V=1 requires R1 = 2.73W.
Similarly set Vo = 1 volt when V = 1.5V (with V2 = 0.866
volt)calculate. Note that D1 is conducting in this interval.
Calculate R2= 0.42W
A completed circuit realization isdrawn to the right. The first
pairof diode branches from the leftprovides the shaping for
thepositive half-cycle.
The second set of branches isthe dual of the first set; the
breakpoints are set to account for the negative half-cycle. Note
that what isinvolved simply is a reversal of the diode and bias
voltage polarities.
The diode shaping circuit becomes more practical when the
resistances are scaled to more convenientvalues, and when a voltage
divider network replaces the batteries. When the circuit
resistances are suitablyscaled real diodes may be used in place of
the idealized models, and a voltage divider network used tosupply
the bias voltages. The divider resistances should be small compared
to the diode branch resistancesto minimize interaction. An
illustrative network is drawn below (Schematics drawing);
resistance valueshave been scaled by a (more or less arbitrary)
factor of 47, and adjusted to standard 10% values. Thecircuit
response to the design triangular waveform is shown in the Probe
plot. For comparison a 250 Hzsinusoidal waveform with unit
amplitude also is drawn. And in addition an expanded detail near
the peakof the sinusoid is provided.
A Fourier analysis computer a total harmonic distortion of 1.6%
out to 20 harmonics.
Diode Wave Shaping 3 M H MILLER
The period of the input waveform das decreased to 0.1msecond,
and the conversion recomputed as shown:
Total harmonic distortion increased to 1.8%.
Improvements in the approximation can be made by a more
thoughtful choice as well as an increasednumber of secants. An
improvement is often obtained by varying the bias supply voltage
(V4) to forceagreement between the approximation and the sine at a
second point (in addition to the agreement for zeroinput), on the
expectation that a general continuity in nature also will improve
agreement at other points.
