Re: 50 ohm on FR4

On Sun, 2 Feb 2025 13:02:16 -0500, bitrex <user@example.net> wrote:

On 2/2/2025 12:42 PM, Cursitor Doom wrote:

On Sun, 2 Feb 2025 12:00:24 -0500, "Edward Rawde"
<invalid@invalid.invalid> wrote:
 

"Cursitor Doom" <cd@notformail.com> wrote in message news:pssupj9omf6d3ao3jpilfjmhkommdf0m6e@4ax.com...

Grok reckons to make a 50 ohm tx line on FR4 I would need  a Trace
Width of approximately 2.73 mm and a Trace Spacing of at least 2.73
mm. Does that sound about right?

>
It doesn't seem to match anything I can get from the site below with 2oz copper and er=4
Does Grok know the difference between stripline and microstrip?
>
https://www.elektroda.com/calculators/pcb-impedance-calculator-microstrip
>

 
Thank you, Edward. Well, to be fair to Grok, it did spell out a lot of
qualifiers relating to the precise structure of the FR4 substrate
which I did not include in the OP. So that could well have something
to do with it. Grok also felt that performing such calcs was somewhat
out of its comfort zone and referred me to specific websites for these
calculations. However, I just wanted a quick and dirty figure as I'm
not attempting metrology-level measurements in this instance and will
not be venturing beyond VHF.

>
>
The pen-and-paper method given in Pozar's "Microwave Engineering" is to
guesstimate whether W/d is >= or <= 2, use the second part of equation
3.197 to find A and B, use the first part to see if the guess is
satisfied, use 3.195 to find the effective dielectric constant, and
verify with 3.196.
>
<https://imgur.com/a/Dr23fNi>
>
Or use the calculator included in KiCad..I get more like 3.1 mm for a
width with the parameters given

Thanks, Bitrex, that certainly helps.
Here's the full reply Grok wrote (although I suspect some of the
equations won't render correctly  so go by the text primarily)

**************************************************

To design a 50 ohm microstrip transmission line on FR4, you'll need to
consider several parameters:

    Dielectric Constant (er):
        FR4 typically has a dielectric constant (er) around 4.4 at 1
MHz, but this can vary slightly with frequency. For microstrip
calculations, you might use a value closer to 4.0 or 4.2 for higher
frequencies.
    Thickness of the Substrate (h):
        This is the thickness of the FR4 board. Common thicknesses are
1.6 mm (0.063 inches) or 0.8 mm (0.031 inches).
    Trace Thickness (t):
        Typically, copper thickness might be 35 µm (1 oz), 70 µm (2
oz), or 105 µm (3 oz) for PCB manufacturing.
    Trace Width (W):
        The width of the trace is what we're primarily solving for to
achieve 50 ohms impedance.


Using these parameters, you can use formulas or online calculators for
microstrip impedance. Here's a simplified approach:

    Formula for Microstrip Impedance:

    
    Z0˜87?r+1.41ln?(5.98h0.8W+t)

     Where:
        Z0
         is the characteristic impedance (50 ohms in this case)
        ?r
         is the effective dielectric constant
        h
         is the board thickness
        W
         is the trace width
        t
         is the trace thickness


For a rough estimate with:

    ?r=4.2
    h=1.6
     mm
    t=35
     µm (1 oz copper)


Solving for W:

50˜874.2+1.41ln?(5.98×1.60.8W+0.035)
50˜872.54ln?(9.5680.8W+0.035)
50˜34.25ln?(9.5680.8W+0.035)
5034.25˜ln?(9.5680.8W+0.035)
1.46˜ln?(9.5680.8W+0.035)
e1.46˜9.5680.8W+0.035
4.305˜9.5680.8W+0.035
0.8W+0.035˜9.5684.305
0.8W+0.035˜2.222
0.8W˜2.187
W˜2.734 mm
So, for a 50 ohm microstrip line on FR4 with these specifications, the
trace width would be approximately 2.73 mm.

However, these calculations can be quite sensitive to manufacturing
tolerances and material variations. It's recommended to use a precise
microstrip calculator or simulation software for exact dimensions, and
possibly to verify with a test board or adjust based on actual
measurements if possible.

*******************************************************

It's good that it shows its methodology for arriving at this figure,
IMO.