Hardware Reference
In-Depth Information
It is worth noting that most manufacturers define the bandwidth of an instru-
ment as the frequency at which a sine wave input signal will be fall to 0.707 of
its true amplitude (i.e. the
−
3 dB point). To put this into context, at the cut-off
frequency the displayed trace will be in error by a whopping 29%!
Resolution and accuracy
The relationship between resolution and signal accuracy (not bandwidth) is
simply that the more bits used in the conversion process the more discrete
voltage levels can be resolved by the DSO. The relationship is as follows:
x
=
2
n
where
x
is the number of discrete voltage levels and
n
is the number of bits.
Thus, each time we use an additional bit in the conversion process we double
the resolution of the DSO, as shown in the table below:
Number of bits (
n
)
Number of discrete voltage levels (
x
)
8
256
10
1024
12
4096
16
65 536
A DSO stores its captured waveform samples in a buffer memory. Hence, for
a given sampling rate, the size of this memory buffer will determine for how
long the DSO can capture a signal before its buffer memory becomes full.
The relationship between sampling rate and buffer memory capacity is impor-
tant. A DSO with a high sampling rate but small memory will only be able to
use its full sampling rate on the top few timebase ranges.
To put this into context, it is worth considering a simple example. Assume
that we need to display 10 000 cycles of a 10 MHz square wave. This signal will
occur in a time frame of 1 ms. If we are applying the five times rule we would
need a bandwidth of at least 50 MHz to display this signal accurately.
To reconstruct the square wave we would need a minimum of about five
samples per cycle so a minimum sampling rate would be 5
10 MHz
=
50 MB
samples per second. To capture data at the rate of 50 MB samples per second
for a time interval of 1 ms requires a memory that can store 50 000 samples. If
each sample uses 16 bits we would require 100 KB of extremely fast memory!
The
measurement resolution
or
measurement accuracy
of a DSO (in terms of
the smallest voltage change that can be measured) depends on the actual range
that is selected. So, for example, on the 1 V range an 8-bit DSO is able to detect
a voltage change of one in two hundred and fifty-sixth of a volt or 1/256 V or
about 4 mV. For most measurement applications this will prove to be perfectly
adequate as it amounts to an accuracy of about 0.4% of full scale.
Low-cost DSO
Low-cost DSO are primarily designed for low-frequency signals (typically sig-
nals up to around 20 kHz) and are usually able to sample their signals at rates of
