■ The LCD interface board showing the fine pitch
connector and copper traces.
fast as the highest frequency being analyzed. This
sampling frequency is called the Nyquist limit after
an early developer of sampling theory. One of the
anomalies of the FFT is that input frequencies
above one half the sampling frequency will be
“mirrored” into the lower frequency range of the
results. For instance, if the sampling frequency is
40 kHz, the highest input frequency that should
be applied is 20 kHz. However, if a signal of 21
kHz is applied, it will be displayed as if it were 19
kHz. This is one of the limitations of this system.
There are two ways of getting around this: (1)
insert a low pass filter with a sharp cutoff at the
highest frequency of interest; or (2) sample at a
higher rate than necessary. The disadvantage of the
low pass filter is that it should be programmable.
The disadvantage of the high sampling rate is
lower resolution. The resolution of the system can be
calculated as follows: Resolution = Sample
Frequency/(2*Sample Size). The factor of 2 is due to the
FFT algorithm that I am using.
I have decided to include an active low pass filter
(Figure 4) with a cutoff frequency of 22 kHz. The filter is a
four pole Sallen-Key design and can easily be bypassed if
you do not want to include it. The design I used was
found at http://beis.de/Elektronik/Filter/ActiveLPFilter.
html. This site allows you to modify the characteristics of
the filter on-line and calculates new values for you. I have
no idea how sensitive the filter characteristics are relative
to the component values. However, I did measure the
response of the filter in the circuit and it is quite good:
at 20 kHz it has about 1.2 db loss; at 24 kHz it is about
4 db. I suggest that you use a sampling frequency of
about 45 kHz if you are going to analyze signals with
frequency components up to 20 kHz. This should allow
the filter to remove most — if not all — of the higher
frequency artifacts. Another limitation of the system is the
display frequency resolution; 100 columns are used for
the FFT display. Based on the formula above for resolution,
at a sample frequency of 45 kHz and a sample size of
512, the resolution is 43. 9 Hz. Since the data is displayed
in 100 columns, that essentially means that the total span
of frequencies displayed must be a multiple of 100 43. 9
or 4390 Hz. In practical terms, this says that if you tell the
system that you want an upper frequency of 10 kHz
displayed, you will actually get 4390* 3 or 13.2 kHz.
My original design had the analog circuits on the
same board as the processor. I decided to move them to a
separate board for two reasons: (1) to keep digital noise
■ FIGURE 7.
An overview of
August 2008 49