Anti-Aliasing Filter - Ametek 7230 Instruction Manual

Chapter 3, TECHNICAL DESCRIPTION

3.3.05 Anti-Aliasing Filter

3-6
DR(in dB)
Applying this formula to the model 7230 at the maximum value of INPUT LIMIT
(2.5 V) and the smallest available value of FULL-SCALE SENSITIVITY (10 nV),
gives a maximum available dynamic reserve of about 165 dB. Figures of this
magnitude are available from any DSP lock-in amplifier but are based only on
arithmetical identities and do not give any indication of how the instrument actually
performs. In fact, all current DSP lock-in amplifiers become too noisy and inaccurate
for most purposes at reserves of greater than about 100 dB.
The signal then passes through an anti-aliasing filter to remove unwanted frequencies
which would cause a spurious output from the main ADC as a result of the sampling
process.
Consider the situation when the lock-in amplifier is measuring a sinusoidal signal of
frequency f Hz, which is sampled by the main ADC at a sampling frequency
signal
f Hz. In order to ensure correct operation of the instrument the output values
sampling
representing the f frequency must be uniquely generated by the signal to be
signal
measured, and not by any other process.
However, if the input to the ADC has, in addition, an unwanted sinusoidal signal
with frequency f Hz, where f
1
will appear in the output as a sampled-data sinusoid with frequency less than half the
sampling frequency, f
alias
indistinguishable from the output generated when a genuine signal at frequency f
is sampled. Hence if the frequency of the unwanted signal were such that the alias
signal frequency produced from it was close to, or equal to, that of the wanted signal
then it is clear that a spurious output would result.
For example, at the sampling frequency of 1.0 MHz then half the sampling frequency
is 500 kHz. If a signal of 40 kHz accompanied by an interfering signal of 950 kHz
was then applied, the output of the ADC would include a sampled-data sinusoid of
40 kHz (the required signal) and, applying the above formula, an alias signal of
50 kHz (i.e. |950 kHz - 1000 kHz|). If the signal frequency were now increased
towards 50 kHz then the output of the lock-in amplifier would increasingly be
affected by the presence of the alias signal and the accuracy of the measurement
would deteriorate.
To overcome this problem the signal is fed through the anti-aliasing filter which
restricts the signal bandwidth to 400 kHz The filter is a conventional elliptic-type,
low-pass, stage, giving the lowest possible noise bandwidth.
It should be noted that the dynamic range of a lock-in amplifier is normally so high
that practical anti-alias filters are not capable of completely removing the effect of a
full-scale alias. For instance, even if the filter gives 100 dB attenuation, an alias at
the input limit and at the reference frequency will give a one percent output error
when the dynamic reserve is set to 60 dB, or a ten percent error when the dynamic
reserve is set to 80 dB.
In a typical low-level signal recovery situation, many unwanted inputs need to be
dealt with and it is normal practice to make small adjustments to the reference
frequency until a clear point on the frequency spectrum is reached. In this context an
unwanted alias is treated as just another interfering signal and its frequency is
 
20 log(DR(as a ratio
is greater than half the sampling frequency, then this
1
= |f - nf |, where n is an integer. This alias signal is
1 sampling
))
alias