AD9547SLASHPCBZ datasheet(100/104 Pages) AD

100 / 104 page

AD9547

Rev. 0 | Page 100 of 104

The min() function

y = min(x0, x1, ... xn)

where:

x0 through xn is a list of real numbers.

y is the number in the list that is the farthest to the left on the

number line.

The max() function

y = max(x0, x1, ... xn)

where:

x0 through xn is a list of real numbers.

y is the number in the list that is the farthest to the right on the

number line.

The log2() function

log2(x) =

)

(

)

(

where: ln() is the natural log function.

x is a positive, nonzero number.

Assume that the coefficient calculations for α, β, γ, and δ above

yield the following results:

α = 0.012735446

β = −6.98672 × 10−5

γ = −7.50373 × 10−5

δ = 0.002015399

These values are floating point numbers that must be quantized

according to the bit widths of the linear and exponential com-

ponents of the coefficients as they appear in the register map.

Note that the calculations that follow indicate a positive value

for the register entries of β and γ. The reason is that β and γ,

which are supposed to be negative values, are stored in the

AD9547 registers as positive values. The AD9547 converts the

stored values to negative numbers within its signal processing

core. A detailed description of the register value computations

for α, β, γ, and δ follows.

Calculation of the α Register Values

The quantized α coefficient consists of four components: α0, α1,

α2, and α3, according to

α ≈ αquantized = α0 × 216 − α1 + α2 + α3

where:

α0, α1, α2, and α3 are the register values.

α2 provides front-end gain.

α3 provides back-end gain.

α1 shifts the binary decimal point of α0 to the left to accommodate

small values of α.

Calculation of α1 is a two-step process, as follows:

w = if(α <1, −ceil(log2(α)), 0)

α1 = if(α <1, min[63, max(0, w)], 0)

If gain is necessary (that is, α > 1), then it is beneficial to apply

most or all of it to the front-end gain (α2) implying that the cal-

culation of α2 is to be done before that of α3. Calculation of α2

is a three-step process that leads directly to the calculation of α3.

x = if(α > 1, ceil(log2(α)), 0)

y = if(α > 1, min[22, max(0, x)], 0)

α2 = if(y ≥ 8, 7, y)

α3 = if(y ≥ 8, y – 7, 0)

Calculation of α0 is a two-step process, as follows:

z = round(α × 216 + α1 − α2 − α3)

α0 = min[65535, max(1, z)

Using the example value of α = 0.012735446 yields

w = 6, so α1 = 6

x = 0 and y = 0, so α2 = 0 and α3 = 0

z = 53416.332099584, so α0 = 53416

This leads to the following quantized value, which is very close

to the desired value of 0.012735446:

αquantized = 53416 × 2−22 ≈ 0.01273566821

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