... | @@ -3,7 +3,40 @@ This image shows a high-level block diagram of the microstepper. |
... | @@ -3,7 +3,40 @@ This image shows a high-level block diagram of the microstepper. |
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Frequency resolution
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Frequency resolution
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--------------------
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--------------------
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try wiki math:
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This is a basic derivation of the frequency-resolution of the microstepper. This assumes a 100 MHz reference-frequency (from maser), and a 100 MHz OCXO frequency. Other configurations are certainly possible and could be explored.
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The phase-detector PD forces both generated IFs to be equal. The reference-IF $`IF_A`$ is directly mixed down from the fererence frequency $`f_R`$, while the fine-resolution-IF $`IF_B`$ is produced by dividing DDS1.
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```math
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IF_A=f_R - {{f_{DDS1}}\over{4}}
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```
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```math
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```math
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a^2+b^2=c^2
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IF_B={{f_{DDS2}}\over{2^{2}2^{10}}}
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```
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When both DDSs are clocked at $`f_{SYSCLK}=10\cdot f_{OCXO}`$ the DDS frequencies are given by
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```math
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f_{DDS}={{f_{SYSCLK} \cdot FTW}\over{2^{48}}} = {{10f_{OCXO} \cdot FTW}\over{2^{48}}}
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```
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If we now equate $`IF_A=IF_B`$ and insert the DDS frequencies $`f_{DDS1}(FTW_1)`$ and $`f_{DDS2}(FTW_2)`$ we get for the fractional frequency of the microstepper output (left as an exercise to the reader!)
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```math
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{f_{OCXO}\over{f_R}} - 1 = { {2^{48} \cdot 2^2}\over{ 10 (FTW_1 + { {FTW_2}\over{ 2^{10}}}) }}-1
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```
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DDS1 can be used for coarse frequency adjustments. Around a fractional frequency of zero, changing FTW1 by 2 steps changes the output frequency by 1.8e-14 as follows:
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```
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uStep output fractional frequency y
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FTW2 = 112589990684262 (constant)
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FTW1 dFTW1 y
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112480039521475 -10 8.88e-14
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112480039521477 -8 7.11e-14
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112480039521479 -6 5.33e-14
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112480039521481 -4 3.55e-14
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112480039521483 -2 1.78e-14
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112480039521485 0 5.2e-18
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112480039521487 2 -1.78e-14
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112480039521489 4 -3.55e-14
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112480039521491 6 -5.33e-14
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112480039521493 8 -7.1e-14
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112480039521495 10 -8.88e-14
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y change due to 2 steps in FTW1: -1.8e-14
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``` |
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``` |
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\ No newline at end of file |