AD9548SLASHPCBZ datasheet(108/112 Pages) AD

108 / 112 page

AD9548

Rev. 0 | Page 108 of 112

If x is an integer, then y = x. Otherwise, y is the nearest integer to x.

For example, round(2.1) = 2, round(2.5) = 3, and round(−3.1) = −3.

The ceil() function

y = ceil(x)

If x is an integer, then y = x. Otherwise, y is the next integer to the

right on the number line. For example, ceil(2.8) = 3, whereas

ceil(−2.8) = −2.

The min() function

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

where x0 through xn is a list of real numbers, and the value of 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, and the value of y is

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

number line.

The log2() function

)

(

)

(

)

(

log

where ln() is the natural log function and x is a positive, nonzero

number.

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

following results:

012735446

98672

−

50373

−

002015399

These values are floating point numbers that must be quantized

according to the bit widths of the linear and exponential

components 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 AD9548

registers as positive values. The AD9548 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 is

contained in the Calculation of the α Register Values section to

the Calculation of the δ Register Values section.

CALCULATION OF THE

α REGISTER VALUES

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

, and α3 according to

quantized

−

≈

where α0, α1, α2, and α3 are the register values. α2 provides front-

end gain and α3 provides back-end gain, and 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:

)

)),

(

(log

ceil

(

2 α

−

[

] )0

)

max(

min

(

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

calculation of α2 is to be done before α3. Calculation of α2 is a

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

)

)),

(

(log

ceil

(

2 α

α >

[

] )0

)

max(

min

(

)

(

≥

)

(

−

≥

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

)

(

round

−

[

])

max(

535

min

0 =

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 = 53,416.332099584, so α0 = 53,416

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

the desired value of 0.012735446:

0127356682

53416

≈

−

quantized

CALCULATION OF THE

β REGISTER VALUES

The quantized β coefficient consists of two components, β0 and β1

according to

)

(

−

≈

−

quantized

where β0 and β1 are the register values. Calculation of β1 is a two-

step process that leads to the calculation of β0, which is also a two-

step process.

))

(

(log

ceil

−

[

])

max(

min

1 =

)

(

round

[

])

max(

071

131

min

0 =

Using the example value of −β = 6.98672 × 10−5 yields

x = 13, so β1 = 13

y = 75,019.3347657728, so β0 = 75,019

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