First up, the equation posted up by vfone is only an approximation. It is commonly used but there are more accurate equations than this for a capacitive tap impedance match.
Second, the app note can't possibly be peaked to work at 45MHz with the values shown even with 280nH. It won't tune down to 45MHz. Therefore it relies on the self capacitance of the device itself.
If you want to match 50R to your 1500R Philips part at 38MHz then you are also going to also have to take into account the parallel resistance of the inductor due to finite Q.
Therefore you will probably have to match to something like 1100R rather than 1500R.
From your range of coils available the only one that comes close is the 220nH one. Using this in a capacitive tap to match to 1100R at 38MHz requires
C1 = 100pF
C2 = 360pF
L1 = 220nH (assuming Q= 100 approx and this might be hard to realise)
In practice you will have to tune the 220nH inductor down to maybe 210nH to account for the 3pF of the Philips part and centre the response on 38MHz.
This will just about meet your 2MHz BW requirement although it will show about -1.5dB of droop at 37 and 39MHz.
The match will be quite poor at 37 and 38MHz. You really need to redesign using a bigger inductor if this is a problem. eg:
C1 = 56pF
C2 = 200pF
L1 = 390nH (assuming Q= 60 approx and this should be typical with a tunable coil)
This will give a wider bandwidth
In practice you will have to tune the 390nH inductor down to maybe 360nH to account for the 3pF of the Philips part.
Note: The very first impedance matching program I ever wrote for a computer was for a capacitive tap network and this was a very long time ago :lol:
---------- Post added at 23:06 ---------- Previous post was at 21:28 ----------
If you resort to an L match you could use C1 as 12pF and L1 as 1.2uH (C2 not fitted)
This would give a reasonable match and good bandwidth.
If you can tune the 1.2uH down to 1.1uH and increase C1 to 14pF then the match gets better.