11.1. DIGITAL OSCILLOSCOPES
Today, the most prominent basic tool for electrical analysis is the digital oscilloscope. The
instrument operates by waiting for a trigger event and then recording voltage and time
information after the trigger event. Typically, the trigger event is a rising or falling voltage
transition past a specified voltage. The instrument typically operates in real-time and/or
equivalent-time mode. In real-time operation, the instrument takes consecutive samples of
the voltage waveform after the trigger event and constructs the signal accordingly. If the
sample rate is not sufficiently fast, the waveform will not be constructed accurately. The
sample rate of the instrument strongly affects the quality of the reconstructed waveform in
real-time operation. In equivalent-time operation, the instrument assumes that a periodic
waveform is under measurement and constructs a displayed waveform from samples taken
at varying delays from different triggering events. Basically, in this mode the waveform is
constructed as a combination of different periods of the periodic waveform. Real-time and
equivalent-time operation are explained further later in this chapter. The analog bandwidth of
the instrument also affects the quality of the reconstructed waveform. The analog bandwidth
gives information on how high frequencies are attenuated when entering the instrument. The
bandwidth typically reported for an oscilloscope is the frequency at which the input will be
attenuated by 3 dB. If the bandwidth of the oscilloscope is not sufficiently high to capture all
significant frequency components of a signal, the measured waveform will not be
constructed accurately.
11.1.1. Bandwidth
The input bandwidth to a scope is similar to an RC circuit, where the R and the C represent
the input capacitance and impedance. Subsequently, as derived in
Appendix C
, the
frequency spectrum of an edge passing through an RC circuit is related to the subsequent
rise or fall time by
equation (11.1)
. The rise time in
equation (11.1)
is the fastest rise time
that can be passed without distortion, assuming the corresponding bandwidth. Since spectral
content and rise or fall time are related to each other as shown in
equation (11.1)
, it is easy
to see that the input bandwidth of the scope can filter out high-frequency components of the
signal rise time and degrade the signal edge. For example, if the system rise time is 100 ps
but the bandwidth of the probe is 2.5 GHz and the input to the scope is 1.5 GHz, the rise
time constructed by the oscilloscope will be 290 ps as calculated using the root mean square,
as shown in
equation (11.2)
. The terms T
scope
and T
probe
in
equation (11.2)
are the rise and
fall times calculated with
equation (11.1)
from the respective bandwidths of the scope and
probe.
Equation (11.1)
is valid for rise and fall times measured between 10 and 90% of the
amplitude. For different definitions of the rise and fall times (i.e., 20 to 80%), different
equations will result.
(11.1)
(11.2)
where T
measured
is the rise or fall time measured by the scope, T
scope
and T
probe
are the
minimum rise and fall times that the input of the scope or probe will pass as solved by
equation (11.1)
, and T
signal
is the actual edge rate.
As illustrated in
Figure 11.1
, the time interval measurement (i.e., flight time) is a function of
voltage because the measurement is taken at or near the threshold voltage of the receiving
buffers (for this case the 50% amplitude point). The key item to understand is that if the
scope degrades the signal rise time significantly, flight times and flight-time skews will not be