AK1541_17 Datasheet, PDF (11/37 Pages) Asahi Kasei Microsystems – 20 to 600Mhz Delta-Sigma Fractional-N Frequency Synthesizer

[AK1541]
8. Block Functional Descriptions
1. Frequency Setup
The AK1541 is a Fractional-N type synthesizer that takes 2¹⁸ as the denominator, which calculates the integer and
numerator to be set using the following formulas:
Frequency setting = Ref Frequency x (Integer + Numerator / 2¹⁸)
Integer = ROUND (Target Frequency / FPFD)
Numerator = ROUND {(Target Frequency – Integer x FPFD) / (FPFD / 2¹⁸)}
Note) ROUND: Rounded off to the nearest value
FPFD : Phase Frequency Detector comparative Frequency([REFIN] pin input frequency/R divider ratio)
 Calculation examples
Example 1) The numerator is positive when the target frequency is 465.0375MHz and the Phase Frequency Detector
comparative Frequency is 1MHz.
Integer = 465.0375MHz / 1MHz = 465.0375
It is rounded off to 465 (decimal) = 1d1 (hexadecimal) = 1 1101 0001 (binary)
Numerator = (465.0375MHz - 465 x 1MHz) / (1MHz / 2¹⁸) = 9830.4
It is rounded off to 9830 (decimal) = 2666 (hexadecimal) = 10 0110 0110 0110 (binary)
Frequency setting =1MHz x (465 + 9830 / 2¹⁸) = 465.0374985MHz
(In this case the error between the calculated frequency and the target frequency is 1.5Hz.)
Example 2) The numerator is negative when the target frequency is 468.550MHz and the Phase Frequency Detector
comparative Frequency is 1MHz.
Integer = 468.550MHz / 1MHz = 468.550
It is rounded off to 469 (decimal) = 1d5 (hexadecimal) = 1 1101 0101 (binary)
Numerator = (468.550MHz - 465 x 1MHz) / (1MHz / 2¹⁸) = -117964.8
It is rounded off to -117965 (decimal), which is deduced from 2¹⁸ to be converted into binary for 2's complementary
expression.
2¹⁸ - 117965 (decimal) = 144179 (decimal) = 23333 (hexadecimal) = 10 0011 0011 0011 0011 (binary)
Frequency setting =1MHz x (469 + (-117965/2¹⁸)) = 468.5499992MHz
(In this case the error between the calculated frequency and the target frequency is 0.8Hz.)
 Calculation of 2’s complement representation
1) Positive number: Binary expression (Unmanipulated)
exp. 100 (decimal) = 64 (hexadecimal) = 110 0100
(binary)
2) Negative number: 2¹⁸ minus this number in binary expression
exp. –100 (decimal)
2¹⁸ - 100 = 262044 (decimal) = 3FF9C (hexadecimal) = 11 1111 1111 1001 1100 (binary)
MS1043-E-05
11
2013/03