This example shows how to measure performance characteristics of a pulse width modulated sinusoid. The example contains a model which you can modify to view the effects of parameter changes on rise time, fall time, overshoot, undershoot, pulse width, pulse period, and duty cycle measurements. The example also shows an example of a rising edge trigger and is set up to perform basic statistical operations (mean, median, RMS, maximum, minimum) and measure the frequency and period of the pulse period via cursors and peak finding.
The example model contains several measurements and their corresponding setups.
The first section shows how to use a trigger to stabilize a noisy sinusoid in the display. You can see how the sinusoid is constructed by double-clicking on the Noisy Sinusoid block.
The sinusoidal signal is fed into a Time Scope block with triggers enabled.
You can experiment with the trigger position by dragging the markers around the display. You can trigger upon rising or falling edges. This example includes 0.1 V of hysteresis to help stabilize the sinusoid in the presence of noise. The hysteresis ensures that the signal traverses at least 0.1 V below the trigger level before registering a positive-going transition.
If you close the triggers, you will see that the sinusoid no longer stays fixed in the screen. You can bring the triggers back by clicking on the trigger icon.
In this example, a pulse width modulated source is connected to several time scopes that contain measurements.
You can view the source by clicking on it:
The model constructs sinusoidal pulse width modulation by applying a bias to the desired sine wave and subsequently subtracting a periodic sawtooth wave. The resulting waveform is then fed into a comparator to form the shape of the pulse. Noise is then added to the signal and then sent to a filter with an underdamped response.
You can modify the amount of additive noise on the input by clicking on the Random Source and modifying the variance of the Gaussian distribution.
You can similarly modify the response of the filter by changing its coefficients.
You can view some basic information about the rising and falling transitions of the waveform by viewing the Transitions panel of the Bilevel Measurements dialog.
Viewing the results, you can see that the pulse has a high voltage level of +1 V and a low voltage level of -1 V.
The example above captures two rising (positive) edges and two falling (negative) edges with rise times and fall times of around 340 ns. If you zoom into just one edge of the waveform you can see the measurements for just that edge.
Note that the edges of the pulses are fairly steep, having a slew rate of about 4 V/us. An underdampened filter was used to achieve this rate. Changing the filter to be overdamped would decrease the rate at which the edge of each pulse could transition between pulse levels. The output of an underdampened filter exhibits significant ringing immediately after changing between low and high states. To quantify this ringing behavior, you can use the measurements in the Overshoots / Undershoots panel.
The Bilevel Measurements dialog also contains measurements that relate to an under-damped environment. You can view the transition aberrations by opening the Overshoots / Undershoots panel:
The average overshoot of the rising edges is about 42%. The undershoot is 34%. Large overshoots can sometimes damage logic devices which are designed to accept only a small voltage range. Large undershoots can cause devices to detect incorrect logic states. In this example the transitions settle on average within 7.3 microseconds.
You can reduce the amount of ringing by experimenting with the filter coefficients at the output of the modulated source.
You can also view how the pulse width and duty cycle vary as functions of time by opening the Cycles panel in the Bilevel Measurements dialog:
This example shows three positive-polarity pulses but only two negative-polarity pulses. The pulse frequency is 10 kHz. You can observe the encoded sinusoid by watching how the duty cycle and pulse width change over time.
Alternatively, you can measure the amplitudes and the times of significant peaks by invoking the Peak Finder dialog.
The voltage at the tip of each overshoot is about 1.8 V and the next largest ringing component of the first pulse is at 1.14 V.
Expand the settings panel to change the number of peaks shown. You can also filter based on height or distance between peaks. You can also change the text annotation shown in the display.
You can measure the relative distances between events of the waveform by using cursor measurements. Here the cursors are at the start of each pulse and confirm that the pulse period is 10 kHz.
Experiment with the settings to move the cursors anywhere on the screen or measure the locations of other signals. You can move the cursors with the arrow keys and also snap them to either the nearest data point or screen pixel.
You can view basic signal statistics of the captured wave with the Signals Statistics measurement dialog.
You can observe the minimum and maximum values of the displayed signal and other signal metrics, such as the peak-to-peak, mean, median, and RMS values.
IEEE Std. 181-2003 IEEE Standard on Transitions, Pulse, and Related Waveforms