When is impedance matching critical?

One of the questions I asked myself in my previous post was when does it become critical to have a impedance-matched traces? Today I came across an interesting presentation by Rick Hartley, then a Senior Principal Engineer at L-3 Avionics Systems, now Principal Engineer at RHartley Enterprises.

In his presentation, Rick Hartley states that impedance matching becomes critical when the trace is 1/16th the wavelength of the signal in the propagation material. Here's the relevant slide, giving the formulas.

In my case, I'm working with signals of roughly 2.45 GHz. The PCB material has a stated dielectric constant of 4.4, but at these frequencies I believe the effective dielectric constant may be around 3.91. Cranking these numbers through a calculator gives a signal critical length of 3.87 mm.

With an actual trace length of about 2.54 mm, the trace in question appears to be shorter than the signal critical length. Perhaps it's not an impedance mismatch causing my problems?

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To confirm I'm not using my vector network analyzer improperly — always a risk when using a new piece of equipment — I decided to experiment with some commercial antennas. First I tried connecting my VNA to an air-band (108 to 137 MHz) "rubber ducky" antenna from a handheld transceiver. I figured it would be smart to start at a lower frequency, in case this VNA has a problem at the high end. This test showed a nice dip in the return loss ("LOGMAG" format in the LiteVNA) centered near the middle of the voice communications frequencies. So far, so good.

Next I tried an antenna taken from an old 802.11bg WiFi router. It showed a -35 dB or better return loss near the low end of the 2.40 - 2.50 GHz ISM band, which is what I would expect to see. This suggests that I'm using the VNA correctly. My boards operate in the same ISM frequency band so my tests should be valid.

I have a NanoVNA test board, which is designed to make it easy to experiment with filter circuits. I mounted one of the Johanson 2450AT43A100 chip antennas I used for my boards vertically onto this test board. While not ideal, I hoped this would give a better test result than soldering the end of a cut coax cable to one of my boards. I wouldn't expect a -35 dB return loss, as the chip antenna is only specified to give a -9.5 dB return loss.

But when I tested it, I saw negligible return loss in the 2.40 - 2.50 GHz ISM band (only 1.42 dB at 2.45 GHz). I had to broaden the scan well above the 2.50 GHz to see any significant return loss: the dip shown peaks at -4.5 dB at about 2.9 GHz.

This antenna is supposed to be naturally tuned to 2.45 GHz when fed with a 50 ohm source. Maybe this odd configuration requires a bit of tuning to get a good match? I'm really a novice at RF, and 2.45 GHz is not an easy place to start.

Johanson makes (or made) a reference board for this chip, but I can't find anyone who stocks it. I guess the next step is to build some test boards myself using their descriptions.