AK1590 Datasheet, PDF (11/36 Pages) Asahi Kasei Microsystems – 1GHz Delta-Sigma Fractional-N Frequency Synthesizer

[AK1590]
8. Block Functional Descriptions
1. Frequency Setup
AK1590 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 = FPFD × (Integer + Numerator / 2¹⁸)
Integer = ROUND (Target Frequency / FPFD)
Numerator = ROUND {(Target Frequency – Integer × FPFD) / (FPFD / 2¹⁸)}
Note) ROUND: Rounded off to the nearest integer
FPFD : Phase Frequency Detector comparative Frequency (= [REFIN] input frequency / R divider ratio)
 Calculation examples
Example 1) The numerator is positive; when the target frequency is 950.0375MHz and FPFD is 1MHz.
Integer = 950.0375MHz / 1MHz = 950.0375
It is rounded off to 950 (decimal) = 3B6 (hexadecimal) = 0011 1011 0110 (binary)
Numerator = (950.0375MHz - 950 × 1MHz) / (1MHz / 2¹⁸) = 9830.4
It is rounded off to 9830 (decimal) = 2666 (hexadecimal) = 10 0110 0110 0110 (binary)
Frequency setting =1MHz × (950 + 9830 / 2¹⁸) = 950.0374985MHz
(In this case the frequency error is 1.5Hz.)
Example 2) The numerator is negative; when the target frequency is 950.550MHz and FPFD is 1MHz.
Integer = 950.550MHz / 1MHz = 950.550
It is rounded off to 951 (decimal) = 3B7 (hexadecimal) = 0011 1011 0111 (binary)
Numerator = (950.550MHz - 951 × 1MHz) / (1MHz / 2¹⁸) = -117964.8
It is rounded off to -117965 (decimal), which is reduced 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 × (951 + (-117965/2¹⁸)) = 950.5499992MHz
(In this case the frequency error 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)
MS1478-E-01
11
2013/2