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# Grounded coplanar waveguide vs. microstrip

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#### dspdev

##### Newbie level 1
Hello,

Consider a grounded coplanar waveguide (GCWG) implemented on some PCB. When increasing the spacing between signal trace and upper ground, the effect of the upper ground gets lower and the GCWG slowly turns into a microstrip line. So far my thoughts. I tried a few calculations using wcalc-1.1 and the calculator found on microwaves101.com. Starting point was the geometry of a PCB microstrip line. When taking this geometry and calculating the impedance of a GCWG with increasing spacing to the top ground plane, the impedance gets much higher than those of the microstrip line (= GCWG with infinite spacing?).

Can somebody explain me why this happens? Maybe the calculators only work for small spacings?

Original intention was to tune a PCB trace from the micrstrip's 77.7 Ohms towards 50Ohms by placing ground next to the signal trace.

Here are some of my calculations done with wcalc-1.1
a) inputs to wcalc, where
w is trace width in meters
s is spacing between signal trace and upper ground plane in meters
h is height of the substrate in meters
l is trace length in meters
tmet is thickness of the signal trace in meters
rho is the conductance of the signal trace (copper)
rough is surface roughness
er is the dielectric constant of the substrate
tand is substrate loss
GND flag for telling whether bottom ground plane is included (1=GCWG, 0=CWG)
f is the signal frequency in Hz
microstrip_calc 0.00015 0.00024 0.05 0.00005 1.72e-8 0.00001 4.3 0.01 4e8
coplanar_calc 0.00015 1.0e-1 0.00024 0.05 0.00005 1.72e-8 0.00001 4.3 0.01 1 4e8
coplanar_calc 0.00015 1.0e-2 0.00024 0.05 0.00005 1.72e-8 0.00001 4.3 0.01 1 4e8
coplanar_calc 0.00015 1.0e-3 0.00024 0.05 0.00005 1.72e-8 0.00001 4.3 0.01 1 4e8
coplanar_calc 0.00015 1.0e-4 0.00024 0.05 0.00005 1.72e-8 0.00001 4.3 0.01 1 4e8
coplanar_calc 0.00015 1.0e-5 0.00024 0.05 0.00005 1.72e-8 0.00001 4.3 0.01 1 4e8
coplanar_calc 0.00015 1.0e-6 0.00024 0.05 0.00005 1.72e-8 0.00001 4.3 0.01 1 4e8
coplanar_calc 0.00015 1.0e-7 0.00024 0.05 0.00005 1.72e-8 0.00001 4.3 0.01 1 4e8
b) Results:
microstrip line
79.7586

GCWG
wcalc microwaves101's calculator
106.641 div_by_0
101.979 div_by_0
93.676 181.27
72.7772 82.52
42.534 44.03
27.9331 28.51

I ran these cases with Rogers trace impedance tool (MWI-2010). It looks like it performs better, but still does not quite match the microstrip calculation when the spacing is large.

Using your numbers, Rogers MWI predicts the microstrip impedance is 84.7 ohms.
GCPW, Spacing
100 mm = 90.8 ohms
10 mm = 90.8 ohm
1 mm = 90.1 ohm
0.1 mm = 72.8 ohm
0.01 mm = 41.3 ohm
0.001 mm = 26.7

https://www.rogerscorp.com/designtools/index.aspx

Go to the microwave impedance calculator. You'll have to register an account to download, but it's free. It's also preloaded with Rogers materials, but it does allow to customize the properties.

One nice feature of the MWI is that it documents the references it uses. At the top of the program, see the tab for Information > References.

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