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The LO2 frequency used to track a spectral line at a given frequency Frest centered in the IF band (350
) is
![\begin{displaymath}
Flo2 = \frac{ Frest \times Doppler + S \times 350 + M \times L \times Eps }
{ M \times H + S }
\end{displaymath}](img9.png) |
(6) |
and, from eq. (5), the image rest frequency at the band center is
![\begin{displaymath}
F_{I} = \frac{ (M \times H-S) \times Flo2
- M \times L \times Eps + S \times 350}
{Doppler}
\end{displaymath}](img10.png) |
(7) |
A little algebra follows
cm and result in
![\begin{displaymath}
F_{I} = \frac{M \times H-S}{M \times H+S} \times Frest
+ \...
...H \times 350 - L \times Eps)}
{(M \times H+S) \times Doppler}
\end{displaymath}](img15.png) |
(8) |
This result is not independent of the Doppler effect. Accordingly, it the
doppler tracking is not exact for the image frequency. and for 2 different
values,
and
, corresponding to different velocities
and
,
we obtain (assuming no change of
)
![\begin{displaymath}
\delta F_{I} = \frac{D2-D1}{ D2 \times D1} \times
\frac{ ...
...imes M \times ( H \times 350 - L \times Eps) }
{M \times H+S}
\end{displaymath}](img21.png) |
(9) |
or, assuming
and
, and with
,
, the frequency
shift in MHz is
![\begin{displaymath}
\delta F_{I} = \frac{\delta V}{c} \times 700
\end{displaymath}](img25.png) |
(10) |
or, in velocity (in km.s
)
![\begin{displaymath}
\delta V_{I} = \delta V \frac{700}{F_I}
\end{displaymath}](img27.png) |
(11) |
Next: Consequences
Up: Image Frequency Doppler Tracking
Previous: Image Frequency Doppler Tracking
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Gildas manager
2014-07-01