Re: LF: LF EbNaut test from JN80 on 137370

[Paul Nicholson <vlf0403@abelian.org>]

If the signal is on the high side of the oscillator,
Q should lead I after the mixer,

 s(t) = sin(wc * t);   // Signal, wc = 2 * pi * Fc

 i(t) = sin(wc * t) * cos( wo * t);  // LO, wo = 2 * pi * Fo
 q(t) = sin(wc * t) * sin( wo * t);

expands to

 i(t) = 1/2 * { sin((wc+wo)*t) + sin((wc-wo)*t) }
 q(t) = 1/2 * { cos((wc-wo)*t) - cos((wc+wo)*t) }

which after LPF to remove the wc+wo component leaves

 i(t) ~= 1/2 * sin((wc-wo)*t)
 q(t) ~= 1/2 * cos((wc-wo)*t)

which has q(t) leading i(t) by 90 degrees.

The above are the polarities used by vlfrx-tools and ebnaut.

On the scope, signal at 77500 Hz and LO at 77490 Hz looks like

 http://abelian.org/vlf/tmp/151213a.gif

with Q (the 2nd channel) peaking 90 deg before I.

--
Paul Nicholson
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