AD9548 datasheet(109/111 Pages) AD

109 / 111 page

Data Sheet

AD9548

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

x =

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,

α2, and α3 according to

quantized

−

≈

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

front-end gain, 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

(

)

(

y ≥

)

(

−

≥

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

22 ≈

−

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

2 β

−

[

])

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

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

to the desired value of 6.98672x10−5:

986688823

019

−

≈

quantized

Rev. G | Page 109 of 111

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