Specifications

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SLWS142J − JANUARY 2003 − REVISED AUGUST 2007
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13.13 Overall Gain in Receive Mode
The overall gain in the receive mode is a function of zero padding (rinf_zpad), the CIC decimation (cic_dec), the cic
shift settings (cic_shift and cic_rshift), the sum of the programmable filter taps (PFIR_SUM), the filter output shift
(fir_shift) and the final gain in the agc circuit (G). The cmd5016 program, described later in the data sheet, sets the
cic_shift, cic_rshift, fir_shift, and G to their optimum levels for a targeted overall gain using the overall_gain keyword.
The calculated gain is done to limit the gain between stages, as well as provide an overall gain.
The overall gain is:
DDC_gain = zpad_gain x mix_gain x cic_gain x rshift_gain x fir_gain x agc_gain
Where the individual gains are:
zpad_gain = 1 / (rinf_zpad+1)
mix_gain = 1/2
cic_gain = cic_dec
5
x 2
(cic_shift−39)
rshift_gain = 2
(cic_rshift−1)
fir_gain = PFIR_SUM x 2
(fir_shift−21)
agc_gain = G / 4096
The restrictions on the gain settings are:
1. To prevent overflow in the CIC, cic_shift must be set such that:
zpad_gain x mix_gain x cic_gain ≤ 1
2. If rinf_zpad is greater than cic_dec, then cic_shift must be set such that:
(1/cic_dec) x mix_gain x cic_gain ≤ 1
3. For symmetric filters the maximum amplitude allowed into the fir is one-half, so cic_shift must be set such that:
zpad_gain x mix_gain x cic_gain x rshift_gain ≤ 1/2
4. The cic_rshift control is set to 1 (this control is only used to extend the allowable cic_dec range, and must be used
with care).
The fir_gain and agc_gain are used to adjust the overall gain to match the user’s desired gain (overall_gain). The
fir_shift control should be set such that:
zpad_gain x mix_gain x cic_gain x rshift_gain x fir_gain ≤ overall_gain
and the final agc_gain is set to give the desired overall_gain.
This equation gives unity gain for dc or complex data inputs. For real inputs, such as from an ADC, the DDC_gain
is typically set to 2 (6 dB). The gain of 2 compensates for the loss of 6 dB when tuning a signal to dc and filtering
out the negative image. Mathematically this is illustrated by using a an example input signal s(t) modulated up to a
frequency of ”ω”. The input is defined as:
d(t) = s(t) x cos(ωt) = s(t) x (e
jωt
+ e
−jωt
) / 2