Differential impedance microstrip line

[mirror_pole]

Hallo guys, i have a question regarding the differential impedance of a microstrip line. I watched a Video where someone said that Z,diff=2×(Z0-Z,coupling), where Z0 is the impedance of a Single line to GND and Z,coupling the impedance between the Signal lines. What i dont get is, why does Z,coupling decreases when the distance between the Signal lines increases? My First Intuition was exactly the way around, as i thought of a capacitive coupling between them. So from my thought, if i increase the distance i reduce the capacitance and therefore increase the impedance. What is my mistake?

 

[PlanarMetamaterials]

I assume you mean a differential pair, which may also be referred to as conductor-backed coplanar stripline.
Your intuition is in general correct. I'm not sure where that equation comes from, but I don't think it's too useful. For small gap sizes, the impedance response is dominated by the capacitive coupling between the strips, which serves to reduce impedance with reduced gap width.

 

[mirror_pole]

Hey,

Thanks for the answer. Well i got it from this Video

. Minute 9 he is talking about what happens if you increase the distance between the Signal lines.

 

[FvM]

The usual term for "Zcoupling" is mutual impedance. It's a formal quantity rather than a real impedance. See e.g. http://emlab.uiuc.edu/ece451/appnotes/CoupledTL.pdf

 

[mirror_pole]

This equation makes much more sense : \[ Z_d=\sqrt{\frac{L_S-L_M}{C_S+2C_M}} \]

. So if the distance of the Signal lines decreases the mutual cap increases and therefore the differential impedance decreases? Does the mutual inductance decrease with lower distance? In this case the numertor will also increase but i guess the denominator will increase more because of the Factor 2 for the mutual cap.

--- Updated Jul 18, 2023 ---

This equation makes much more sense : \[ Z_d=\sqrt{\frac{L_S-L_M}{C_S+2C_M}} \]

. So if the distance of the Signal lines decreases the mutual cap increases and therefore the differential impedance decreases? Does the mutual inductance decrease with lower distance? In this case the numertor will also increase but i guess the denominator will increase more because of the Factor 2 for the mutual cap.

I think i got it now, didnt check the whole file..equation is actually the odd Mode impedance and differential impedance is just 2 times the odd Mode one. Mutual inductance also increases with lower distance, which makes sense actually since the magnetic flux also increases. Interestingly the mutual inductance is much bigger then mutual capacitance. Both are also dependant of the hight above the ground plane..thx FvM for providing this file again.