Keithley 194 Instruction Manual page 48

OPERATION
If the sampling frequency is not at least twice the frequency
being sampled, a phenomenon known as &sing results.
When aliasing occurs, the sampled information will not
contain data on the original waveform, but instead a new
signal with a frequency equal to the difference between
the sampling frequency and the original applied signal.
For example, if a 1OOkHz signal is sampled at a 1lOkHz rate,
a new signal of 1OkHz will be the one actually seen in the
resulting data. If the signal and sampling frequencies are
exactly the same, a DC signal level will result, since the
difference between the two signals is zero. Thus, it is im-
perative that the minimum 2:l ratio of sampling frequen-
cy to measured frequency be maintained if accurate results
are to be expected.
Once we have established our minimum sampling fre-
quency based on the above criteria, we can then go ahead
and choose the correct sample and rate parameters for a
given situation. For example, assume that we are measur-
ing a 20kHz sine wave. We would then press the RATE
key and then key in the desired sampling frequency.
Although a 40kHz frequency sampling frequency would
be adequate, we might want to play it safe and choose a
50kHz sampling frequency for this measurement. Once
the rate parameter is established, we can choose a sam-
pling duration or number of samples to measure based on
how many cycles, or how much of a single cycle WC wish
to sample. For example, if we wished to sample one com-
plete cycle of the 20kHz waveform, the measurement dura-
tion would be li20kHz = 50~s~. Aside from which range
to use, the only other consideration for a basic measure-
ment would be the trigger method, as described in
paragraph 3.6.
Thus far in our discussion, we have assumed that all
signals arc sinusoidal in nature. In the real world, of
course, many complex waveforms exist. These complex
waveforms can be broken down into a fundamental
sinusoidal waveform and a number of harmonics in ac-
cordance with the Fourier series. While detailed Fourier
analysis is beyond the scope of this discussion, you should
be aware that such harmonics do exist.
From this discussion, we can see that it may necessary to
choose a sampling frequency substantially above the fun-
damental frequency of a non-sinusoidal waveform to en-
sure good results. For example, when sampling a 10kHz
rectangular waveform it would be a good idea to choose
a sampling frequency of 200kHz since a substantial por-
tion of the ninth harmonic (YOkHz) is present, and the
sampling rate must be at least twice as high as the highest
frequency.
Another consideration when selecting the sampling rate
is the overall resolution and accuracy of the measurement.
For sampling rates 1OOkHz and below,, the AID converter
operates with &bit resolution (assuming the number of
samples is ~32,768), meaning that it digitizes the signal
into 21L, or 65,536 steps. Above lOOkHz, the A/D converter
has only R-bit resolution, so it can resolve only 2", or 256
steps. The A/D resolution has a direct effect on display
resolution as well as the ultimate accuracy of the measure-
ment. At 1OOkHz and below, display resolution is 4% digits,
while the usable resolution is reduced to 2?0 digits ,~bow
lOOkfIr (the unit will still display 4% digits, howc\~r, ab<~vt~
100kHr). Consequently, instrument accuracy is not a go<~l
with sampling rates above 1OOkHz as it is below that valw
(refer to the specifications at the front of this manuI~l iol
actual figures). Thus, if accuracy is ot paramount impw
tance, you should select a sxnpling rate of 1OOkHz or less
and ~32,768 samples, unless other factors such 1)s
measurement speed override this consideration
3.6 TRIGGERING
A triger stimulus is used to initiate .) M~~lel I'll mel~suw
ment sequence. The duration of that seqwnc~' dnd the
number of samples taken during the sequence will depend
on previously selected rate and sample parameters.
TRIGGER BUTTONS
The unit can be triggered with the front panel 'I'l~I~~C~ER
button, the input signal, from a pulse applied to the ex-
ternal trigger input jack, or from the other channel (the
instrument can also be triggered over the IEEE-488 bus,
as discussed in Section 4). When triggering from the ill-
put signal, you can define slope and triger level
parameters. From the front panel, these modes xc' prw
grammed with the various trigger buttons. as described
in the following paragraphs.
3-9