Datasheet

Data Sheet AD9547
Rev. E | Page 103 of 104
Calculation of the β Register Values
The quantized β coefficient consists of two components, β
0
and
β
1
, according to
−β ≈ β
quantized
= β
0
× 2
−(17 + β
1
)
where β
0
and β
1
are the register values.
Calculation of β
1
is a two-step process that leads to the
calculation of β
0
, which is also a two-step process.
x = −ceil(log
2
(
β
))
β
1
= min[31, max(0, x)]
y = round(
β
× 2
17 + β
1
)
β
0
= min[131071, max(1, y)]
Using the example value of −β = 6.98672 × 10
−5
yields
x = 13, so β
1
= 13
y = 75019.3347657728, so β
0
= 75019
This leads to the following quantized value, which is very close
to the desired value of 6.98672 × 10
−5
:
β
quantized
= 75019 × 2
−30
≈ 6.986688823 × 10
−5
Calculation of the γ Register Values
The quantized γ coefficient consists of two components, γ
0
and
γ
1
, according to
−γ ≈ γ
quantized
= γ
0
× 2
−(17 + γ
1
)
where γ
0
and γ
1
are the register values.
Calculation of γ
1
is a two-step process that leads to the
calculation of γ
0
, which is also a two-step process.
x = −ceil(log
2
(
γ
))
y
1
= min[31, max(0, x)]
y = round(
γ
× 2
17 + γ
1
)
γ
0
= min[131071, max(1, y)]
Using the example value of −γ = 7.50373 × 10
−5
yields
x = 13, so γ
1
= 13
y = 80570.6873700352, so γ
0
= 80571
This leads to the following quantized value, which is very close
to the desired value of 7.50373 × 10
−5
:
γ
quantized
= 80571 × 2
−30
≈ 7.503759116 × 10
−5
Calculation of the δ Register Values
The quantized δ coefficient consists of two components, δ
0
and
δ
1
, according to
δ ≈ δ
quantized
= δ
0
× 2
−(15 + δ
1
)
where δ
0
and δ
1
are the register values.
Calculation of δ
1
is a two-step process that leads to the
calculation of δ
0
, which is also a two-step process.
x = −ceil(log
2
(δ))
δ
1
= min[31, max(0, x)]
y = round(δ × 2
15 + δ
1
)
δ
0
= min[32767, max(1, y)]
Using the example value of δ = 0.002015399, the preceding
formulas yield
x = 8, so δ
1
= 8
y = 16906.392174592, so δ
0
= 16906
This leads to the following quantized value, which is very close
to the desired value of 0.002015399:
δ
quantized
= 16906 × 2
−23
≈ 0.002015352249