TLC32047C Datasheet, PDF (33/61 Pages) Texas Instruments – Wide-Band Analog Interface Circuit

Table 2–5. (sin x)/x Roll-Off Error
fs (Hz)
7200
8000
9600
14400
16000
19200
25000
Error = 20 log
sin π f/fs
π f/fs
f = 3000 Hz
(dB)
– 2.64
– 2.11
– 1.44
– 0.63
– 0.50
– 0.35
– 0.21
The actual AIC (sin x)/x roll-off is slightly less than the figures above because the AIC has less than 100%
duty cycle hold interval.
2.27 Correction Filter
To externally compensate for the (sin x)/x roll-off of the AIC, a first-order correction filter can be implemented
as shown in Figure 2– 8.
u _{(i + 1)}
X
+
Σ
+
y(i _{+ 1)}
(1 – p1) p2
X
Z–1
p1
Figure 2–8. First-Order Correction Filter
The difference equation for this correction filter is:
y_{(i + 1)} = p2 ⋅ (1 – p1) ⋅ u_{(i + 1)} + p1 ⋅ y_(i)
(4)
where the constant p1 determines the pole locations.
The resulting squared magnitude transfer function is:
| H (f) | ² =
(p2)² ⋅ (1–p1)²
1 – 2 ⋅ p1 ⋅ cos (2π f/f_s) + (p1)²
(5)
2.28 Correction Results
Table 2-6 shows the optimum p values and the corresponding correction results for 8000-Hz and 9600-Hz
sampling rates (see Figures 5 – 8, 5 –9, and 5 –10).
2–15