MCP6271R Microchip Technology Inc., MCP6271R Datasheet - Page 30

• Manufacturer Part Number: MCP6271R
• Description: 170 ?a, 2 Mhz Rail-to-rail Op Amp
• Manufacturer: Microchip Technology Inc.

Turning Nyquist Upside Down By Undersampling
By Bonnie C. Baker, Microchip Technology Inc.
Bravo to Harry Nyquist and Claude Shannon. According to
these two gentlemen, in the 1920s, the well-known Nyquist
theorem was created stating, “when sampling a signal at
discrete intervals, the sampling must be greater than twice the
highest frequency of the input signal.” This is done so that you
can reconstruct the original signal perfectly from the sampled
version.
Their theorem has held up well through the ages. In my
discussions with engineers, I use the Nyquist theorem to explain
the accuracy of sampling systems where the bandwidth of the
signal of interest is less than twice the sampling frequency of
the converter. The sampling systems I describe use a low-pass,
anti-aliasing filter before the ADC. This is usually an engineer’s
initial exposure to the Nyquist theorem, where signals with
frequencies greater than ½ of the sampling rate of a converter
will come back to haunt you. The experts fondly call this a “fold-
back” phenomena
maximum-input frequency, the digitizing system will produce a
mixture of in-band and out-of-band data. Once this fold-back of
signal information has occurred, there is no going back in terms
of retrieving the original signal that is below ½ of the sampling
frequency. So, my advice for this type of system is to always
place a low-pass, anti-aliasing filter before your ADC.
That is all well and good, but let’s try to turn the Nyquist theorem
upside down. We can use this theorem in an alternate manner by
intentionally forcing a system configuration that aliases or folds
back higher-frequency signals that occur above the sampling
rate of the converter. This is known as undersampling. Some
synonyms for undersampling are bandpass sampling or super-
Nyquist sampling. Applications, such as wireless communication
receivers, radar instrumentation, infrared instrumentation or
video, are well suited for this use of the Nyquist theorem.
In these systems, the bandwidth of the signal of interest (Δf
is centered at a higher frequency than the sampling frequency
(f
carrier signal (f
filter that acts like an anti-aliasing filter in this system. It is not
unusual to implement a simple second-order filter (one zero and
one pole) for this purpose. The order and response of this filter is
user defined. If you design in a higher order filter, the bandwidth
of Δf
28
Analog and Interface Guide – Volume 2
SAMPLE
Analog-to-Digital Converters
SIG
) of the converter. Δf
is smaller.
CAR
). Δf
(1)
. If the sample rate is less than twice the
SIG
is limited by an analog bandpass
SIG
is also riding on a high-frequency
SIG
)
Two formulas will help you determine the sampling frequency of
your system. The first equation is f
complements the Nyquist theorem directly. The second formula is
f
down. You will use this second formula twice as you zero in on
the actual sampling frequency.
With the first formula above, the sampling frequency should be
equal to twice Δf
sample frequency and a predetermined carrier frequency, you can
calculate the quantity of Z in the second formula. The value of
Z is usually not a whole number and should be rounded down.
With this new value of Z, you should use the second formula to
recalculate a value for f
An example may clarify any questions that you have. For instance,
if a system has a signal that has a 3.5 MHz bandwidth (Δf
that is centered at a 70 MHz carrier frequency (f
can calculate the sampling frequency as 7 Msps (f
#1). With this number for f
equal to 20.5 (formula #2). Rounding down, Z is equal to 20
making the actual sampling frequency (f
7.18 MHz.
Beyond the selection of your sampling clock, there are several
important issues to think about with your undersampling
application. You should select an ADC with an input stage that
can accept signals with frequencies above the converter’s
sampling rate. An undersampling converter’s product data sheet
will specify this. Jitter and phase noise of the converter’s sample
clock (f
also require a high-quality crystal oscillator.
This column gives you a short tour of undersampling theory. If
you need more information, refer to the references below.
References
20, 2003.
ISBN0-506-7841.
www.pentek.com/applications
SAMPLE
“Filtering? Before or after?”, Bonnie C. Baker, EDN, February
“The Data Conversion Handbook”, Walt Kester, Elsevier,
“Putting Undersampling to Work”, Pentek, Inc.
SAMPLE
= 4 f
CAR
) can degrade the system performance. You may
/ (2 *Z –1), where Z is a whole number rounded
SIG
. Then, by using this calculated value for the
SAMPLE
SAMPLE
.
, the calculated value for Z is
SAMPLE
SAMPLE
> 2(Δf
) equal to
SIG
CAR
). This formula
SAMPLE
), initially you
, formula
SIG
)