MCP6271R Microchip Technology Inc., MCP6271R Datasheet - Page 35

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

Riding The Crest Factor Wave
By Bonnie C. Baker, Microchip Technology Inc.
Crest factor is a unit-less figure of merit that engineers use to
describe a signal. You can use crest factors to describe the
purity of voltage, current or power waveforms. This figure of merit
can describe power signals, machine vibration, or half-wave lamp
dimmers, to name a few. In these applications, it is not enough
just to know the average power (or voltage or current) but you
also need to know the equipment-design, peak-value guidelines
in order to accommodate maximum allowable excursions. Within
these disciplines, the crest factor is equal to the ratio of the
peak value to the rms value. (Crest Factor = V(peak) / V(rms);
V(rms) is the statistical standard deviation of the signal.)
A perfect sine wave with an amplitude peak of one volt has an
rms value of 0.707V or 1/√2 V. The crest factor for this signal
is equal to 1.414 or /√2. A sine wave that has a crest factor
greater than 1.414 is less than perfect, showing additional noise,
distortion or spikes. Unfortunately, non-periodic events will not
appear in a Fast Fourier Transform (FFT). The crest factor will be
higher than ideal if low-level noise or spikes exist.
There is another way to use crest factors in your system if you
are not sure about the magnitude of the signal but would like to
know the signal boundaries over time. You can take the above
formula and rewrite it to solve for the signal peak value; V(peak)
= Crest factor * V(rms) or V(peak-to-peak) = 2 * Crest factor *
V(rms). This formula structure is extremely useful if you have
a general idea about the type of signal that you are working
with. For instance, crest factors are well defined for signals
that form a gaussian or normal distribution across multiple
samples. A gaussian distribution of noise is generated by analog
systems that are void of internal switching circuitry. The common
elements that generate gaussian noise are amplifier circuits,
resistors, voltage references, D/A converters and ADCs. These
devices generate non-periodic events riding on top of the signal
of interest. Again, an FFT analysis will not produce an accurate
indication of analog system noise.
When you compute the rms value of your system you must take
multiple, periodic samples of a DC signal. Once you have these
samples, you can calculate the rms value (see Figure 1). At
this point, you need to determine how often you will accept an
occurrence that exceeds the expected output value (see Table 1).
From the list of devices above, the sigma-delta ADC holds my
interest the most. This is because the sigma-delta converter
replaces an entire discrete analog system. The sigma-delta
converter oversamples an analog signal and produces a stream
of single bits. Then the converter employs digital filtering to
calculate the one-bit conversion results to a higher resolution.
In this process, gaussian noise is a by-product. The range of the
converter’s resolution change can be from one bit to 24 bits (or
more). The accuracy (which is different than resolution, Ref 1)
can be higher than 22 bits (rms) in this type of system. From
these “noisy” results, you need to determine the acceptable
system accuracy. With a crest factor, you are armed to effectively
estimate the accuracy of your system (see Table 1).
Miscellaneous Articles
Figure 1: The standard deviation (rms) of several samples (>1024)
of a DC signal is enough data to describe the system’s future
performance (per Table 1).
Table 1: Noise volts (peak-to-peak) in a signal is equal to Noise
volts (rms) * 2 * CF. The Noise bits (peak-to-peak) is equal to Noise
in bits (rms) – BCF. From the selected rest factor, you can predict
the probability of an occurrence that exceeds defined peak-to-peak
limits.
Crest Factor
(CF)
2.6
3.3
3.9
4.4
4.9
Analog and Interface Guide – Volume 2
Crest Factor in Bits
(BCF, bits)
2.38
2.72
2.94
3.13
3.29
Peaks are Exceeded
Occurrences Where
Percentage of
0.0001%
0.001%
0.01%
0.1%
1%
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