Diode Wave Shaping
(Sawtooth to Sinusoid)
To obtain a sinusoidal output waveform the triangular waveform will be 'shaped' appropriately. Even a
relatively simple diode shaping produces a surprisingly low-distortion output. A non-critical piecewiselinear approximation to the sinusoid is illustrated to the
right. (Only a quarter cycle is shown; application to the
remaining portions of the period follows on application of
the symmetry of the sinusoid.) The triangular waveform is
assumed to have a relative amplitude of 1.5; the sinusoid
will have a unit amplitude. For 0˚ to 30˚ the 'sinusoid' will
follow the triangle ramp. For 30˚ to 60˚ the slope of the
waveform will be reduced so that the 'sinusoid' rises to only
0.866, and for the remaining 30˚ the slope changes to rise
to unit amplitude.
The diode circuit drawn below is used to describe how the
desired shaping is obtained; only the positive half-cycle is
described explicitly. The input voltage is the triangular
waveform. For simplicity the diode junction voltage drop
is ignored. While the diodes are reverse-biased neither
shunt branch conducts, and Vo = V, i.e., the output voltage
follows the ramp.
Suppose V1 < V2 is 0.5 volt. Then when the input voltage
reaches 0.5 volt D1 begins to conduct. The output voltage is
given by
and setting Vo = 0.866 when V=1 requires R1 = 2.73Ω.
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= 0.42Ω
A completed circuit realization is
drawn to the right. The first pair
of diode branches from the left
provides the shaping for the
positive half-cycle.
The second set of branches is
the dual of the first set; the breakpoints are set to account for the negative half-cycle. Note that what is
involved 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 convenient
values, and when a voltage divider network replaces the batteries. When the circuit resistances are suitably
scaled ‘real’ diodes may be used in place of the idealized models, and a voltage divider network used to
supply the bias voltages. The divider resistances should be small compared to the diode branch resistances
to minimize interaction. An illustrative network is drawn below (Schematics drawing); resistance values
have been scaled by a (more or less arbitrary) factor of 47, and adjusted to standard 10% values. The
circuit response to the design triangular waveform is shown in the Probe plot. For comparison a 250 Hz
sinusoidal waveform with unit amplitude also is drawn. And in addition an expanded detail near the peak
of the sinusoid is provided.
A Fourier analysis computer a total harmonic distortion of 1.6% out to 20 harmonics.
Diode Wave Shaping
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M H MILLER
Diode Wave Shaping
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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 increased
number of secants. An improvement is often obtained by varying the bias supply voltage (V4) to force
agreement between the approximation and the sine at a second point (in addition to the agreement for zero
input), on the expectation that a general continuity in nature also will improve agreement at other points.
Diode Wave Shaping
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M H MILLER