sizing a DC bias RF choke for a differential antenna + PA

Question

Trying to figure an antenna for the Si4012 RF chip. Page 26 of https://www.silabs.com/documents/public/application-notes/AN639.pdf talks about feeding the two sides of the loop antenna through two pull-up inductors (LP and LM) which it fails to provide any values for.

I have read here that I should

Select a sufficiently high inductance value. (Z = 2 * pi * f * L) Select an impedance (Z) that is much larger than the load resistance.

This usually translates into "make it tenfold"

In my design, |Z_load| is somewhere between 500 and 600 ohm (PA and adapted differential antenna). Wouldn't it be required to pick an inductor having its impedance in the 5k - 6k ohm interval in order to actually be effective at blocking the fundamental + first few armonics ? -

• Meaning 2.2 uH with a SRF of more than 1736 MHz in order to cut out everything to and including the 3rd armonic. The trouble is I am unable to find on the market such a large inductor at that kind of SRF. They usually go to 100+ MHz SRF at 2.2 uH. Perhaps I am miscalculating something ?

Answer 1

1. Since the impedance is differential, you actually only need half the impedance on each side.

2. You don't need to "cut" harmonic power in these inductors - in fact, you want to absorb harmonics. Therefore an SRF above the fundamental is acceptable.

3. The third harmonic is 3x the fundamental, not 4x. (The first harmonic is the fundamental) Just FYI - it does not matter in this case!

4. Small PCB loop antennas are already lossy, so you don't need "tenfold" reactance or a super Q for, say, less than 1dB of additional loss. Without calculating, I would guesstimate 5x to be workable. (It will slightly "pull" your antennna's center frequency though.)

5. Based on the above, an RF inductor like the 470nH from Johanson is a workable candidate: