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Pulse Width Modulated Waveforms
Dynamically Stepping Duty Cycle From 1% To 99%
LAB
in PDF format
The LeCroy LW420 Arbitrary Waveform generator is an ideal source of pulse width modulated
(PWM) signals commonly used in power, industrial control, and automotive
electronics systems. The 1 Megabyte memory supports long test waveforms where the duty
cycle of a pulsed waveform can be varied over a wide range without loss of signal
continuity. Consider the following example:
Create
a 10 KHz pulse waveform where the duty cycle steps from 1% to 99% at a rate of 1 % per
pulse period.
This waveform is easily created in the LW420 using equations
to describe the required linear stepped pulse width modulation. The 1 % to 99% duty cycle
range requires the use of two different equations which are shown in figure 1:
X1 = SIN ( 2 * PI * 10k * T ) - creates a 10 kHz
sine wave
X2 = T - 1 - 1 * FLOOR ( T/100 ) - Time variable
with a
stepped ramp delay
X3 = SIN ( 2 * PI * 10k * X2) - Delayed sine wave
X4 = PULSE ( X3 , X1 ) - Pulse with 1% < duty
cycle < 49%
X5 = 1 - PULSE ( X3 , - X1 ) - Pulse with 50%
<duty cycle< 99%
Figure 1 - Lines X4 and X5 describe the PWM waveform
Figure 2 - The PULSE function converts sine
waves into a periodic pulse width modulated pulse train
The waveform is created using the PULSE function with the
sine wave arguments (in lines X1 and X3) as shown in figure 2. The sinewave described by
line X3 is delayed in time, starting at 1 s and increasing by 1 for each cycle of the sine
wave. The pulse waveform begins when the sinewave in X1 goes positive and ends when X3
goes positive.
The test waveform is formed in two parts. One, line X4,
creates a waveform PWM_1 with a duty cycle that steps from 1 % to 49% in 4.9 ms. In the
second waveform PWM_2 created using the equation on line X5 the duty cycle varies from 50%
to 99% in 4.9 ms. The two waveforms are concatenated using the LW420 waveform sequence PWM
shown in figure 3.
Figure 3 - The waveform sequence PWM
Figure 4 - The completed waveform as measured
on a 9354AL
The waveform sequence produces a continuous waveform that
steps through 98 cycles of the pulse period increasing the duty cycle smoothly from 1% to
99%. The entire waveform, as captured on a LeCroy 9354AL oscilloscope is shown in figure
4.
In addition to the acquired waveform (Ch2) three zoom traces
show the pulse width at the beginning middle and end of the waveform while the local time
over threshold parameter shows the range of pulse widths encountered.
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