Pulses and Pulse Waveforms
Pulses and pulse generating circuits are important aspects of electronics. The diagram shows a typical
pulse waveform.
There are a number of important parameters to identify and define for a pulse. We will not be
concerned with Overshoot, Droop, and Undershoot.
Rise Time - tR
The rise time of a pulse waveform is defined as the time it takes for the pulse to rise from 10% to 90% of
its final value.
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In the diagram above estimate the rise time.
Rise time = 90% time - 10 % time = 2.3 sec - 0.1 sec = 2.2 sec
Fall Time - tf
The fall time of a pulse waveform is similarly defined as the time it takes for the pulse to drop from 90%
to 10% of its initial value. In general there is no relationship between the values of rise time and fall
time.
Pulse Width
This is a measure of the time that a pulse is in the High voltage state. Pulse width is commonly
measured between the 50% points of the waveform.
What Causes Rise Times (and Fall Times)?
When a DC voltage is connected a RC circuit the capacitor in the circuit charges. The VIN voltage shown,
can assumed to be a pulse with a zero rise time. The VOUT voltage across the capacitor displays a nonzero rise time as a result – the capacitor takes time to charge.
Calculating the Rise Time for an RC Circuit
VC = E (1 - e-t/RC )
The charging equation for a capacitor is give as
This equation can be re-arranged to solve for the variable t.
t = - RC ln (1 - VC/E)
derivation not shown
The times to reach 10 % and 90% can be calculated as shown
t90% = - RC ln (1 - .9E/E) = 2.30 RC
t10% = - RC ln (1 - .1E/E) = 0.10 RC
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Rise time tR = t90% - t10% = 2.30 RC – 0.10 RC = 2.2 RC
Rise Time of an Oscilloscope
Oscilloscopes have an input resistance RIN and an input capacitance CIN. These parameters cause the
oscilloscope to behave like a low pass filter with a corner frequency fC determined by RIN and CIN.
For the scopes that are used in the lab the values of RIN and CIN are 1 MΩ and 30 pF.
The oscilloscope will accurately display signals that have a frequency less than the corner frequency and
will not accurately display signals greater than the corner frequency.
As a result of this RC circuit the oscilloscope will cause a “perfect” waveform to now display a rise time.
The amount of rise time is
where BW is the bandwidth of the scope
tr = 0.35/BW
oscope
Derivation
fC = BW = 1/2πRC
So RC = 1/2πBW
tR = 2.2RC = 2.2/2πBW = 0.35/BW
Example
A scope with a 100 MHz bandwidth will have an inherent rise time of 0.35/100 MHz = 3.5 ηs. This is a
limiting value for the scope in its ability to measure rise times.
This then raises an important question. When a waveform, with a measurable rise time, is viewed on a
scope the rise time seen is actually a combination of the rise time of the original waveform and the rise
time contributed by scope itself. The actual rise time of a wave form measured on a scope and can be
corrected for the effect of the scope.
tR,actual – this is the actual rise time of the waveform
tr,meas – is the measured rise time on the scope
tr,scope – is the rise time of the scope used to correct the measurement
The formula to correct a rise time measurement is
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Examples
Calculate the actual rise time for a pulse waveform where a rise time of 15 ηsec and is measured on a
100 MHz scope. Repeat for a 5 ηsec rise time waveform.
1. tr,scope = 3.5 ηs.
tr,actual = sqrt(15 ηsec2 - 3.5 ηs2) = 14.6 ηsec
2. tr,scope = 3.5 ηs.
tr,actual = sqrt(5 ηsec2 - 3.5 ηs2) = 3.6 ηsec
Rise Time Specifications for Electronic Test Equipment
Devices that produce very short rise time waveforms (or the wave forms themselves) are commonly
referred to as “fast” devices or “fast” waveforms.
Function Generators
The function generators you use in the lab have two waveform outputs that can produce pulses – the
Main output and the TTL or SYN output.
Main Output – this output produces sine waves, triangular waves and square waves at varying
frequencies, amplitudes, offset voltages and duty cycles. For square waves the rise times are in the
order of 30 – 100 ηsec.
TTL/SYNC Output – this output produces TTL level (0 to +5V) square waves at varying frequencies. The
rise times are in the order of 5 – 10 ηsec.
Pulse Generators
If faster rise times are required then a pulse generator is used. Pulse generators can have rise times less
than 1 ηsec.
Propagation Delay
Pulse signals that appear at the input of a circuit do not move through the circuit output in zero time.
The time for a circuit is referred to as Propagation delay. There are two values for these Propagation
delays called tp,HL and tp,LH . The first, tp,HL, refers to the time delay for the output signal to change from
a High level to a Low level and it is measured between the 50% points of the input and output
waveforms. The second delay, tp,LH, is measured in a similar manner. In general there is no relationship
between tp,HL and tp,LH .
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Application Note
Written by David Lloyd
Computer Engineering Program
Humber College
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