360 Appendix E High Resolution Digitizing With the 3458A
An inescapable reality in any measurement is the attendant noise with increasing
bandwidth. The effects of random measurement noise can be reduced by
averaging the measurements. Caused by Johnson noise and other circuit related
noise as well as noise on the input signal, the removal of this noise always costs
measurement time. A measure of the quality of a digitizing instrument, called the
“effective bits” of resolution, combines noise with ADC linearity to show the
usable resolution of the digitizer:
effective bits = N -log
2
(rms error (actual)/rms error (ideal))
The rms error (actual) is the error measured relative to the best-fit perfect sine
wave. The rms error (ideal) is the theoretical error from a perfect N bit ADC. For
low resolution instruments, the effective bits is a true measure quality; for high
resolution instruments, the noise associated with any measurement swamps the
actual performance of the ADC. If, however, a large number of samples is taken
or, equivalently, the samples are averaged, the noise can be reduced to the point
where actual quantization and non-linearity errors are evident in the Fourier
transform of the sampled data. This effect is shown in Figure 62. The third
harmonic of the input signal is actually an integral non-linearity. Averaging ten
samples does not remove its level, whereas the noise floor drops 10 dB.
Figure 61. With static
DC input levels, the
analog-to-digital
converter may exhibit
an ideal transfer
function as shown in
12a. With a dynamic
input, however, errors
shown in 12b may
appear.
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