Datasheet

SNR = 20log
System
-
-SNR
Amp+Filter
10
10
-SNR
ADC
10
+ 10
HDx = 20log
System
-
-HDx
Amp+Filter
20
10
-HDx
ADC
20
+ 10
PGA870
www.ti.com SBOS436A –DECEMBER 2009–REVISED FEBRUARY 2011
e
NAmpout
is the output noise density of the PGA870 (30 nV/√Hz), ENB is the brick-wall equivalent noise bandwidth
of the filter, and V
O
is the amplifier output signal. For example, with a first-order (N = 1) bandpass or low-pass
filter with 30-MHz cutoff, the ENB is 1.57 • f
–3dB
= 1.57 • 30 MHz = 47.1 MHz. For second-order (N = 2) filters, the
ENB is 1.22 • f
–3dB
.
As the filter order increases, the ENB approaches f
–3dB
(for N = 3, ENB = 1.15 • f
–3dB
, and for N = 4, ENB = 1.13 •
f
–3dB
). Both V
O
and e
Filterout
are in RMS voltages. For example, with a 2-V
PP
(0.707-V
RMS
) output signal and
30-MHz first-order filter, the SNR of the amplifier and filter is 70.7 dB with e
Filterout
= 30 nV/√Hz • √47.1 MHz= 206
μV
RMS
.
The signal-to-noise ratio (SNR) of the amplifier, filter, and ADC add in RMS fashion as shown in Equation 3
(SNR values in dB):
(3)
Using this equation, one can see that if the SNR of the amplifier + filter equals the SNR of the ADC, the
combined SNR is 3 dB lower (that is, worse). For minimal impact (less than 1 dB) on the ADC SNR, the SNR of
the amplifier and filter together should be ≥ 10 dB better than the ADC SNR. The combined SNR calculated in
this manner is accurate to within ±1 dB of actual implementation.
SFDR Considerations
The SFDR of the amplifier is usually set by second-order or third-order harmonic distortion for single-tone inputs,
and by second-order or third-order intermodulation distortion for two-tone inputs. Harmonics and second-order
intermodulation distortion can be filtered to some degree by the filter, but third-order intermodulation spurious
cannot be filtered. The ADC generates the same distortion products as the amplifier; however, as a result of the
sampling and clock feedthrough, additional spurs (not linearly related to the input signal) are also added.
When the spurs from the amplifier and filter together are known, each individual spur can be directly added to the
same spur from the ADC as shown in Equation 4 to estimate the combined spur (spur amplitudes in dBc):
(4)
Note that Equation 4 assumes the spurs are in phase, but generally provides a good estimate of the final
combined distortion.
For example, if the spur of the amplifier + filter equals the spur of the ADC, the combined spur is 6 dB higher. To
minimize the amplifier contribution (less than 1 dB) to the overall system distortion, it is important that the spur
from the amplifier + filter be ~15 dB better than the converter. The combined spur calculated in this manner is
usually accurate to within ±6 dB of actual implementation, but higher variations have been observed, especially
in second-order harmonic performance as a result of phase shift in the filter.
The worst-case spur calculation above assumes that the amplifier/filter spur of interest is in phase with the
corresponding spur in the ADC, such that the two spur amplitudes can be added linearly. There are two phase
shift mechanisms that cause the measured distortion performance of the amplifier-ADC chain to deviate from the
expected performance calculated using Equation 4: common-mode phase shift and differential phase shift.
Common-mode phase shift is the phase shift seen equally in both branches of the differential signal path,
including the filter. This common-mode phase shift nullifies the basic assumption that the amplifier/filter and ADC
spur sources are in phase. This phase shift can lead to better performance than predicted as the spurs are
phase shifted, and there is the potential for cancellation as the phase shift reaches 180°. However, there is a
significant challenge when designing an amplifier-ADC interface circuit to take advantage of common-mode
phase shift for cancellation: the phase characteristic of the ADC spur sources are unknown, and therefore the
necessary phase shift in the filter and signal path for cancellation is unknown.
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