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8.3.3.2.2 FIR Section

The second section of the digital filter is an FIR low-pass filter. Data are supplied to this section from the sinc filter. The FIR stage is segmented into four subsections, as shown in Figure 46.

Figure 46. FIR Filter

The first two subsections are half-band filters with fixed decimation ratios of two. The third subsection of the FIR filter decimates by four (fixed), and the fourth subsection decimates by two (fixed). The overall decimation ratio of the entire FIR section is 32. Two coefficient sets are used for the third and fourth subsections, sets for linear phase mode and minimum phase mode (programmable). Table 10 lists the data rate programming and overall decimation ratio of the FIR stage. See Table 11 for the FIR filter coefficients.

Table 10. FIR Filter Data Rates

DR[2:0] REGISTER	OVERALL DECIMATION RATIO (COMBINED SINC + FIR)		FIR DATA RATE (SPS)
DR[2:0] REGISTER	HIGH-RESOLUTION MODE	LOW-POWER MODE	FIR DATA RATE (SPS)
000	4096	2048	250
001	2048	1024	500
010	1024	512	1000
011	512	256	2000
100	256	128	4000

Table 11. FIR Stage Coefficients

COEFFICIENT	SECTION 1	SECTION 2	SECTION 3		SECTION 4
	LINEAR PHASE SCALING = 1 / 512	LINEAR PHASE SCALING = 1 / 8388608	SCALING = 1 / 134217728		SCALING = 1 / 134217728
	LINEAR PHASE SCALING = 1 / 512	LINEAR PHASE SCALING = 1 / 8388608	LINEAR PHASE	MINIMUM PHASE	LINEAR PHASE	MINIMUM PHASE
b₀	3	–10944	0	819	–132	11767
b₁	0	0	0	8211	–432	133882
b₂	–25	103807	–73	44880	–75	769961
b₃	0	0	–874	174712	2481	2940447
b₄	150	–507903	–4648	536821	6692	8262605
b₅	256	0	–16147	1372637	7419	17902757
b₆	150	2512192	–41280	3012996	–266	30428735
b₇	0	4194304	–80934	5788605	–10663	40215494
b₈	–25	2512192	–120064	9852286	–8280	39260213
b₉	0	0	–118690	14957445	10620	23325925
b₁₀	3	–507903	–18203	20301435	22008	–1757787
b₁₁		0	224751	24569234	348	–21028126
b₁₂		103807	580196	26260385	–34123	–21293602
b₁₃		0	893263	24247577	–25549	–3886901
b₁₄		–10944	891396	18356231	33460	14396783
b₁₅			293598	9668991	61387	16314388
b₁₆			–987253	327749	–7546	1518875
b₁₇			–2635779	–7171917	–94192	–12979500
b₁₈			–3860322	–10926627	–50629	–11506007
b₁₉			–3572512	–10379094	101135	2769794
b₂₀			–822573	–6505618	134826	12195551
b₂₁			4669054	–1333678	–56626	6103823
b₂₂			12153698	2972773	–220104	–6709466
b₂₃			19911100	5006366	–56082	–9882714
b₂₄			25779390	4566808	263758	–353347
b₂₅			27966862	2505652	231231	8629331
b₂₆			25779390	126331	–215231	5597927
b₂₇			19911100	–1496514	–430178	–4389168
b₂₈			12153698	–1933830	34715	–7594158
b₂₉			4669054	–1410695	580424	–428064
b₃₀			–822573	–502731	283878	6566217
b₃₁			–3572512	245330	–588382	4024593
b₃₂			–3860322	565174	–693209	–3679749
b₃₃			–2635779	492084	366118	–5572954
b₃₄			–987253	231656	1084786	332589
b₃₅			293598	–9196	132893	5136333
b₃₆			891396	–125456	–1300087	2351253
b₃₇			893263	–122207	–878642	–3357202
b₃₈			580196	–61813	1162189	–3767666
b₃₉			224751	–4445	1741565	1087392
b₄₀			–18203	22484	–522533	3847821
b₄₁			–118690	22245	–2490395	919792
b₄₂			–120064	10775	–688945	–2918303
b₄₃			–80934	940	2811738	–2193542
b₄₄			–41280	–2953	2425494	1493873
b₄₅			–16147	–2599	–2338095	2595051
b₄₆			–4648	–1052	–4511116	–79991
b₄₇			–874	–43	641555	–2260106
b₄₈			–73	214	6661730	–963855
b₄₉			0	132	2950811	1482337
b₅₀			0	33	–8538057	1480417
b₅₁			0	0	–10537298	–586408
b₅₂					9818477	–1497356
b₅₃					41426374	–168417
b₅₄					56835776	1166800
b₅₅					41426374	644405
b₅₆					9818477	–675082
b₅₇					–10537298	–806095
b₅₈					–8538057	211391
b₅₉					2950811	740896
b₆₀					6661730	141976
b₆₁					641555	–527673
b₆₂					–4511116	–327618
b₆₃					–2338095	278227
b₆₄					2425494	363809
b₆₅					2811738	–70646
b₆₆					–688945	–304819
b₆₇					–2490395	–63159
b₆₈					–522533	205798
b₆₉					1741565	124363
b₇₀					1162189	–107173
b₇₁					–878642	–131357
b₇₂					–1300087	31104
b₇₃					132893	107182
b₇₄					1084786	15644
b₇₅					366118	–71728
b₇₆					–693209	–36319
b₇₇					–588382	38331
b₇₈					283878	38783
b₇₉					580424	–13557
b₈₀					34715	–31453
b₈₁					–430178	–1230
b₈₂					–215231	20983
b₈₃					231231	7729
b₈₄					263758	–11463
b₈₅					–56082	–8791
b₈₆					–220104	4659
b₈₇					–56626	7126
b₈₈					134826	–732
b₈₉					101135	–4687
b₉₀					–50629	–976
b₉₁					–94192	2551
b₉₂					–7546	1339
b₉₃					61387	–1103
b₉₄					33460	–1085
b₉₅					–25549	314
b₉₆					–34123	681
b₉₇					348	16
b₉₈					22008	–349
b₉₉					10620	–96
b₁₀₀					–8280	144
b₁₀₁					–10663	78
b₁₀₂					–266	–46
b₁₀₃					7419	–42
b₁₀₄					6692	9
b₁₀₅					2481	16
b₁₀₆					–75	0
b₁₀₇					–432	–4
b₁₀₈					–132	0
b₁₀₉					0	0

As shown in Figure 47, the frequency response of the FIR filter is minimum ripple, flat to 0.375 of the data rate (±0.003 dB pass-band ripple until 0.375 · f_DATA) and is fully attenuated at the Nyquist frequency. Figure 48 shows the transition from pass band to stop band.

Figure 47. FIR Pass-Band Magnitude Response

Figure 48. FIR Transition Band Magnitude Response

Although not shown in Figure 48, the pass-band response repeats at multiples of the modulator frequency (N · f_MOD – f₀ and N · f_MOD + f₀, where N = 1, 2, and so on, and f₀ = pass band). These image frequencies, if present in the signal and not filtered before the analog-to-digital conversion process, fold back (or alias) into the pass band and cause errors. A low-pass signal filter reduces the amplitude of the aliasing frequencies. Often, the RC low-pass filter provided by the PGA output resistance and the external capacitor connected to CAPP and CAPN provide sufficient anti-alias attenuation.