Electronics > RF, Microwave, Ham Radio

Copper-tape microstrip prototyping on a PCB of unknown dielectric substrate

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**szoftveres**:

It was fun doing it, so wrote up the process:

First we need to determine the Er of the substrate. We have a 1/4" wide copper tape and a 1.4mm thick single-sided PCB with a ~35um thick copper layer on it to work with:

After building a transmission line with this copper strip of known width on the PCB of known thickness, we need to determine its characteristic impedance; we can use the 1/4 wave impedance transformer method for this: a 1/4 wave impedance transformer terminated by 50ohm on one side looks purely resistive on its other side at the frequency where it's behaving as a 1/4 wave impedance transformer, and the impedance it's showing (measured by VNA) is based on how it's reflecting the 50ohm termination back, based on its own characteristic impedance. The characteristic impedance of the transmission line can then be derived from the impedances at its two sides: Zt = sqrt(Z1 * Z2), where Z1 is the termination impedance (50ohm) and Z2 is the measured impedance (16ohm) at its other side.

The resulting characteristic impedance of the transmission line is 28.28ohms, which checks out, as the trace is quite wide and impedace gets lower with more capacitance (Z = sqrt(L/C)).

Next, we can use an online microstrip calculator tool to come up with an Er for the substrate, knowing that building a 1/4" wide trace on a 1.4mm thick piece of it results in a 28.28ohm transmission line:

The resulting Er is around 4.3, which also checks out; it's a common number for FR4 substrates. We can use the same tool to come up with a width for the final, 50ohm transmission line:

The resulting width is 2.72mm.

We can verify the new 2.72mm wide transmission line, by again using the 1/4 wave impedance transformer method. The new, 50 ohm terminated 1/4 wave impedance transformer is showing impedances between 44ohm and 50ohm, corresponding to 47-50ohm transmission line characteristic impedance.

**DavidAzulay5000**:

**joeqsmith**:

About 50 minutes into the review, I show several copper-tape experiments. Nothing too complex. Just needed some props to show the VNA making some higher frequency measurements.

**joeqsmith**:

You may want to have a look at this channel as well.

**szoftveres**:

Now that this thread turned into a collection of Youtube videos, let me also post one that actually inspired the idea in the original post of measuring the Er of the substrate (as opposed to just assuming Er=4.5):

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