I'm not an expert in RF, but I'm interested in understanding how to calculate an RF matching circuit for my RFM95W 868M LoRa node that indicates pin ANT terminated in a matched 50 ohm impedance matching.

At the output of the matching circuit, I want to connect a wire antenna or an RP-SMA connector like this.

I've readed around and I've found this tool that can be used to calculate the RF matching circuit.

This is how I've placed my frequency (F=868) reference, my source resistance (RS=50) and my load resistance (RL=50.) The output is the following:

enter image description here

I have two main questions:

  1. Let's suppose that the calculation are okay, which commercial parts/values I can use?
  2. The Q factor can be 3? Must it be higher? Lower? Is there a "rule of thumb?"

1 Answer 1


This is how i've placed my Frequency (F=868) reference, my Source resistance \$\color{red}{\text{(RS=50)}}\$ and my Load Resistance \$\color{red}{\text{(RL=50)}}\$

Your source and load impedances are identical so, you have no need to match them. The pi network will give you some filtering benefits but that's a different question.

The Q factor can be 3? Must it be higher? Lower? Is there a "rule of thumb?"

Here's where there's a bit of controversy as to what Q factor actually means. This document (entitled Quality Factor, Bandwidth, and Harmonic Attenuation of Pi Networks) discusses what the so-called Q factor is in pi filters and concludes that it can mean different things to different people.

Significantly, the on-line calculators that invoke Q factor as a parameter don't appear to justify what it means or how to use it. Think about a pi filter of equal input and output impedance; the circuit gain has to be unity hence, Q factor should be unity basically because: -

$$Q = A_V = \sqrt{\dfrac{R_L}{R_{IN}}}$$

On my basic website I don't use Q factor because of the ambiguity stated above. I derive the pi network as two back-to-back L-pads like this: -

enter image description here

\$R_X\$ would be the output impedance of the left hand L-pad or the input impedance of the right-hand L-pad. Of course, when placed back-to-back they fully interlock as matching impedances AND, \$R_X\$ is unambiguous in that respect. For instance, if I use my calculator at 868 MHz I get the same results as the calculator you used when \$R_X\$ is 5 Ω: -

enter image description here

And, if I vary \$R_X\$ you can see it is peakier in the response as \$R_X\$ gets lower: -

enter image description here

Incidentally, the graph above is when \$R_{IN}\$ = 50 Ω and \$R_L\$ = 300 Ω. So, decide yourself whether you want to use Q or want to use \$R_X\$. As a last resort, you can always simulate the circuit to look at the frequency response.

  • \$\begingroup\$ RS and RL = 50 Ohm maybe are placed wrong...i mean the source resistance needs to be 50 ohm as specified in the datasheet and the antenna may be matched to be at 50 ohm; idk, i feel a little bit confused on that. \$\endgroup\$
    – VirtApp
    Jun 1, 2022 at 10:28
  • \$\begingroup\$ It sounds like you don't need matching because they are inherently matched @VirtApp \$\endgroup\$
    – Andy aka
    Jun 1, 2022 at 10:39

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