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How to calculate impedance matching for STM32WLE5 RF network?

Associate III

I am attempting to compute an impedance matching network by following the guidelines outlined in the ST Application Note - AN5457.

However, on page 24, the formula and calculations appear unclear to me due to the presence of a negative value under the square root.




Even though the provided example calculation values for L1 (4.45 nH) and C1 (5.53 pF) are intended for a 14 dB power setup at 868 MHz, they don't correspond with the component values found in the High band-low power reference design, MB1720.


For instance, L6 on reference design includes a 0 Ohm resistor, not 4.45hH inductor as calculated in application note, similarly and for C6 in reference is 0.7 pF vs 5.5pF in AN. 

What further distracts me is that these values are allocated to a high-power reference design - 22 dB components too.
Kindly advice how matching network is calculated? Does reference design show wrong component values or Application Note calculations are misleading?

ST Employee

Hi @Levan,

Sorry for the late answer.

Thank you for your interest in our products.

There is no problem with the formula. It's a complex number. You must take the absolute value of this complex number. The bars represent the absolute value - or the modulus - of this number. 

Note the comment in parentheses:


By the way, there is a typo in the parentheses. I'll ask for the correction.

Concerning your question about the board. Sometimes with the board parasitics, you can directly use/combine the values of the first LC (L6 and C20 from the picture you posted) matching components in the next LC pair (L4 and C11) with some shunt capacitor (C20) to adapt the frequency response.

The formulas and calculations you find in this AN are for an ideal case, it means whitout board parasitics. The formulas will give you a good starting point, but you still need to solder these values onto your board and check if they need to be fine tuned. Keep in mind that these values depend on the PCB.

I hope it answer your question.

Best regards,