Delete comment from: Ken Shirriff's blog
Thank you for this amazing blog and especially for this post, that brought me back to a time when I was familiar with telecommunications stuff.
I was intrigued by the frequency ratios of the transponder and would like to share an alternative theory as to why the funny ratio 240/221 comes up.
I tried to figure out what a transponder with ratio 12/11 would look like and if the carrier recovery and downlink frequency generator could be accommodated by a single mixer architecture, which would be the real advantage.
I reckon that the critical part would be the narrowband filter, which runs around 9 MHz in the original: the higher the center frequency, the higher the cost. Another constraint may come from the frequency multipliers, that call for a low factor for low cost.
After playing around with the numbers, one solution consists of a narrow band filter at 8.3 MHz, i.e. the uplink frequency is scaled down by 1/(1+12*21)=1/(11*23)=1/253, a PLL with a multiplying factor of 12 (that might be implemented by one stage PLL and some frequency multipliers), giving a frequency of about 100 MHz at the input of a x21 frequency multiplier for the LO (2098.1 MHz) and a x23 frequency multiplier for a downlink frequency of 12/11 times the uplink frequency of 2106.4 MHz.
Actually this corresponds to a downlink/uplink ratio of 12*23/11*23 = 276/253 which is quite like 240/221.
This design has still the disadvantage of having two RF frequency multipliers with input at 100 MHz and factors above 20, which might be awkward to implement.
The original design has a double mixer, first one balanced, and leaves more room to choose PLL and frequency multiplier factors, while keeping the center frequency of the narrowband filter low enough. The factor 240/221 might be the result of design constraints of the individual components.
Apr 26, 2022, 6:24:13 PM
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