# Pi-matching impedance calculation for LoRa 868Mhz RFM95

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:

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?"
• Did you read this , hoperf.com/data/upload/back/20181122/ANTENNAS_MODULE.pdf Commented Jun 1, 2022 at 13:44
• If the source is 50Ω and the antenna is 50Ω, then no matching required, they're already matched. Commented Jun 1, 2022 at 14:31

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: -

$$\R_X\$$ would be the output impedance of the left hand L-pad or the input impedance of the right-hand L-pad. Of course, when placed back-to-back they fully interlock as matching impedances AND, $$\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: -

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

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.

• 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. Commented Jun 1, 2022 at 10:28
• It sounds like you don't need matching because they are inherently matched @VirtApp Commented Jun 1, 2022 at 10:39