Cirrus Logic AN330 REV2 - Manual (Page 2)

2 AN330REV2
AN330
of the codes ( [(2.04 / 8) • 1048576] = 267387 ) of the converter as the load on the load cell goes from zero to full
scale.
But how many of these codes are really usable, since there is noise in the system? Using the specifications for the
various elements of the circuit, an estimate of the performance of the system can be derived. The means by which
the estimate is derived will be presented and then the circuit will be tested to confirm that the derivation is valid.
The op amp is configured for the inverting gain configuration. The positive terminal of the bridge is connected to the
positive terminal of the op amp to establish the common mode voltage for the op amp as an inverting amplifier. The
effective resistance of each of the output terminals of the bridge is about 175 ohms each (two 350 ohm resistors in
parallel). The spot noise of this resistance is about 1.7 nV /
√
Hz. The op amp spot noise is 6 nV /
√
Hz. The amount
of noise (33.8 nV /
√
Hz) from the 71.5 k
Ω resistor will be divided down by 175 / (71500 +175) to become
0.08 nV /
√
Hz at the input of the op amp. If these noise sources are summed in rms fashion, the result is
√(
1.7
2
+ 1.7
2
+ 0.08
2
+ 6
2
) = 6.46 nV /
√
Hz. It is apparent that the op amp is the dominate source of noise. The
effect of the noise of the ADC has not been included at this point. The amplifier will amplify the noise at its input by
the noise gain of the amplifier which is 409 (noise gain of an inverting amplifier is 1 + its forward gain of 408). But
the bandwidth is limited by the 0.47
μF and the 71.5K due to its 4.73 Hz corner frequency. This analysis will ignore
the fact that the capacitor may be ±20% tolerance. So the op amp noise referred to the input of the ADC will be about
6.46 nV /
√
Hz • 409 = 2642 nV / √
Hz or 2.642 microvolts /
√
Hz across the noise bandwidth of the analog filter.
Figure 2.
This noise is that of the front end components only and does not include the noise of the ADC. The noise from the
amplifier will be reduced by the RC filter corner at 4.73 Hz at a rate of about 6 dB / octave. The noise bandwidth of
a single-pole filter is 1.57 times the -3 dB corner frequency, so the effective noise bandwidth for the amplifier is
7.43 Hz. A frequency of 7.5 Hz will be used for the bandwidth of the input noise and in the derivation that follows.
It is difficult to estimate spot noise (per
√
Hz noise) characteristics of a delta-sigma ADC because to do so requires
that the user understand the particular noise behavior of the converter for the particular configuration in which the
converter is used. The spot noise can change whenever the sample rate or master clock rate is changed. And it may
change if the magnitude of the voltage reference is changed. Sometimes, A/D converter vendors will supply noise
plots but they may not be at the operating conditions selected by the user. It is beneficial to actually capture data
and analyze the spectrum under the intended operating conditions. Figure 3 illustrates how the spot noise charac-
teristics of two different ADCs can be quite different. The left portion of the figure illustrates the noise spectrum of
a specific delta-sigma ADC along with the magnitude characteristic of its digital filter (a Sinc
3
filter). As the frequency
increases, the filter attenuation increases, and therefore, the noise decreases across the spectrum as the frequency
approaches one half the converter sample rate as shown in the Figure 3.
0 7.5 53.5
Frequency (Hz)
M
a
gn
it
ud
e
Op A mp Spot N oise
Op A m p Spot N oise = 2642 nV / √HZ
0