[hpsdr] Proposal for Loop Antenna Project

[Guido]

On 7/2/07, Philip Covington <p.covington at gmail.com> wrote:

> If you limit it to a RX antenna then the digitally switched capacitor
> idea should work well - I'd think a sequence binary weighted capacitor
> values and some analog switches would work.Â


A digital switched capacitor is a nice and practical idea. But what happens
with tuning preciseness and the quadratic behavior of LC networks, when
covering a large bandwidth with a loop?

What I mean is this:

Lets tune in 10kHz steps over various bands. The loop tunes at:Â  f = 1 /
2pi*sqrt(LC), where L is constant i.e 1uH.
So,

at 30.000Mhz, C must be   28.144pF,
at 30.010Mhz, C must be   28.126pF,  so the least significant binary step
of C is ~0.018pF at 30Mhz);

at 3.000Mhz, C must be 2814.477pFÂ  (C must be increased 100 times!)
at 3.010Mhz, C must be 2795.807pF, so the least significant binary step of C
is still ~18pF at 3Mhz).

Conclusion: higher band require 1000x more preciseness to tune the loop in
10kHz steps like in the lower bands.
Should we lower the Q for the higher bands, to keep the bandwidth large
enough?

Conclusion2: changing frequency does not scale linear, but quadratic
for a 3-30Mhz coverage, we require to have (2814p-28p/0.018p)=154778 steps
or 18 switched capacitors,
(in contrast to(30M-3M/10k=)2700 steps for a linear case: if the resonance
equation was linear)

Any comments, ideas?
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