TLC32046CFN Datasheet, PDF (29/56 Pages) Texas Instruments – Wide-Band Analog Interface Circuit

Table 2–5. (sin x)/x Roll-Off Error
fs (Hz)
Error = 20 log
sin π f/fs
π f/fs
f = 3000 Hz
(dB)
7200
– 2.64
8000
– 2.11
9600
– 1.44
14400
– 0.63
16000
– 0.50
19200
– 0.35
25000
– 0.21
The actual AIC (sin x)/x roll-off is slightly less than the figures in Table 2–5 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
=
1–2
V
(p2)² V (1–p1)²
p1 V cos (2p 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