tank circuit design

[W1RKW]

Is there an ideal ratio between capacitance and inductance for resonant C/L circuits?  If so, what is the relationship between the two? One can get a wide range of resonance points with various value of L and C so is there a sweet spot so to speak? The reason I ask I want to build a tuned loop antenna.

[W3RSW]

Yes there is.
ARRL handbook had a log/log chart with suggested cap values vs. a final tank load derived function for HF hambands at a certain Q.  I didn't see a formula but believe it may have been empirically derived.
- it was for link coupled output circuits but amazingly close for a PI net tune cap anyway at modern PI net input impedances And consequently just as useful for receiver LC circuits. At the very light load values on left side of chart your approaching receiver circuit values.

As you probably already know:
Think of it this way.  As you approach higher freqs., the residual capacitance of wiring and the variable cap itself of 3 to 20 pf ( depending on construction) becomes more and more significant thus limiting variability spread.

As you approach lower freqs. You simply need a lot of capacitance to even achieve resonance.

So typically, LF uses caps approaching thousands of picofarads; MF such as broadcast band uses caps of the common 365 to 500pf variety; shortwave uses 100 to 150pf , higher freq shortwave uses 30 to 50pf,  VHF starts getting into piston caps or very few plates of 3 to 30 pf.  You soon run into quarter wave lines, etc. required at UHF.  Values given match all the capacitance in an LC circuit, all the wiring, padding, vernier, and even capacitance of the coil windings.

[DMOD]

Much depends on your source R and load R and Q.

Try the spreadsheet below:

[KZ5A]

The trade-off for tank circuit "Q" is basically higher Q gives better suppression of harmonics at the cost of higher circulating currents in the coil, and thus more IR loss.  The typical Q is 12 for single ended amps or 6 for push-pull amps (because P-P stages have inherent 2nd harmonic suppression).

Also higher Q requires more capacitance and less inductance.

Besides the spreadsheet already mentioned the is a good (free) Windows program from WA2WHV called "pi.exe" on the internet at http://www.qsl.net/wa2whv/radiocalcs.shtml.

73 Jack KZ5A

[Steve - K4HX]

The Q of many tuned loops is far higher than 12. If only used for receiving, losses don't matter that much.