What is the role of frequency synthesizer stages in a receiver and transmitter?

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The discussion focuses on the concept of "tuning resolution" in receivers, particularly in the context of the R-1051 model, which has variations offering 500 Hz and 100 Hz tuning resolutions. Tuning resolution refers to the discrete frequency steps a digital receiver can achieve. The R-1051 features a modular design with exceptional frequency stability, utilizing a 5.0 MHz internal frequency standard and a phase-locked synthesizer. Additionally, the frequency synthesizer stages play a crucial role in the matched transmitter, highlighting the interconnectedness of these components in radio technology. Overall, tuning resolution is essential for understanding the performance capabilities of receivers and transmitters.
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I've checked the Internet and this forum, and while I notice the term, "tuning resolution" used in different contexts, I can't find a definition. Can anyone provide a clear and concise definition or explanation?
 
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We used it to describe the 'tuning' increments or discrete frequency steps of a digital receiver.

For an old receiver like the R-1051 there were several models
Some had 500hz "tuning resolution"
other models had 100hz "tuning resolution"
http://www.radiomuseum.org/r/military_radio_receiver_r_1051urr.html
The receiver joins quite exceptional performances to a marvelous modular execution, with the RF unit containing the several tuning turrets, the external one is motor driven. The exceptional frequency stability is based upon an internal 5.0 MHz frequency standard reference (An external standard may be selected) and a synthesizer, phase locked to the reference, also containing an error canceling loop. Various revisions built in the years, with increasing tuning resolution. Depending upon the revision, varies the quantity of semiconductors (Transistors and even ICs) used.

http://www.navy-radio.com/rcvrs/r1051.htm
 
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