SBASB74 October 2024 ADS127L21B
PRODUCTION DATA
The bilinear transform converts the continuous time function HA (s) to the discrete time function HA (z). From an analytical perspective, the bilinear transform substitutes a function of z for s in HA (s) to produce HA (z).
Equation 23 shows the A-weighting transfer function of the ANSI standard. The denominator pole frequencies are in Hz.
Equation 24 shows the S-plane conversion of Equation 23 by multiplying the frequency terms by 2π to convert to angular frequency (radians/s).
The bilinear transform substitutes the variable s in HA (s) with Equation 25, to produce HA (z) of each separated denominator term.
where:
In the z-plane transformation, frequency error occurs when the poles are close to the ADC Nyquist frequency (fDATA / 2). As such, the error of the pole closest to the Nyquist frequency at 12,194Hz is compensated by a new equation for variable s, replacing Equation 25. Equation 26 shows the new equation for variable s.
where:
HA (z) is found by collecting like powers of variable z then multiplying through by z–1 / z–1 to yield the HA (z) function in the biquad form of Equation 27.
Table 9-6 shows the biquad coefficient values in decimal and 2.30 hex format for the IIR filter design. The gain coefficients including g5 are 1.0 (40000000h). The coefficient upload procedure is described in the IIR Filter Stage section.
COEFFICIENT(1) | BIQUAD 1 | BIQUAD 2 | BIQUAD 3 | BIQUAD 4 |
---|---|---|---|---|
bx0 | 0.997417013 | 0.993278382 | 0.955663664 | 0.481661428 |
3FD5AE2Bh | 3F91DF7Eh | 3D2997EEh | 1ED38A74h | |
bx1 | –1.994834026 | –0.99327838 | –0.955663664 | 0.161859553 |
8054A3AAh | C06E2082h | C2D66812h | 0A5BE82Ch | |
bx2 | 0.997417013 | 0.00000000 | 0.00000000 | 0.00000000 |
3FD5AE2Bh | 00000000h | 00000000h | 00000000h | |
ax1 | –1.99483069 | –0.986556766 | –0.911327329 | –0.395604811 |
8054B1ACh | C0DC4103h | C5ACD023h | E6AE6929h | |
ax2 | 0.994837367 | 0.00000000 | 0.00000000 | 0.039125792 |
3FAB6A59h | 00000000 | 00000000h | 02810977h | |
gx | 1.00000000 | 1.00000000 | 1.00000000 | 1.00000000 |
40000000h | 40000000h | 40000000h | 40000000h |