Closed form equivalent circuit of microstrip gap (slot)?

[div]

Hi there:

I am looking for some closed form
equation of microstrip gap.

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It can be modeled as
a Pi network with three Caps.
Two C1 as shunt cap to model the fringing field
and C2 as the cap cross the gap.

I read some paper about using integration
equation, variational method ... to solve
the problem.
But as a l@zy guy as I always am, I am wondering
is there any closed form equation for C1 & C2 as a functionof
1)distance of gap
2) hight of dielectic
3) width of the edge
4) dielectric constant ( if we still call it constant) or permittivity.
5) thickness of metal
6) you name it.

Regards
Div

 

[div]

I find the equations.

Hi:

After I post the last message,
I find it by myself.
The book in which the equations
is given is
______
Microstrip Filters for RF/Microwave Applications.
Jia-Sheng Hong, M. J. Lancaster
Copyright © 2001 John Wiley & Sons, Inc.
ISBNs: 0-471-38877-7 (Hardback);
________


Thanks for viewing the post.
But if you know different/more-accurate equations,
please also show the reference.

Regards
Div

 

[div]

THe problem with closed form equation

Well.
I used the equation to calculate C1 and C2
but I got a negative value of capacitor.

So I am still on the way to find a better
closed form equation of equivalent circuit.

Div

 

[yingyang]

equivalent circuit for slot

You have to take note of the validity of the model defined. They are usually accurate for certain dimension constraint.


:lol: :lol:

 

[Chinaski]

Two models to test

 

[yingyang]

slot

you may also like to look at microstriplines and slotlines by K. C. Gupta.

 

[Chinaski]

Hi yingyang
gap2.pdf is the model from the book you are talking about (2nd edition)

 

[div]

My matlab file

Hi:

I attach my matlab file which
implent the equation from
the book.

You will find a negative capacitor
value by using the equation.
Any idea?

Regards
Div

________

mil=2.54e-5;

% s is distance of the gap, W is the width of the mline
s=50*mil;
W=100*mil;
h=1*mil;
Er=4;

if (s/W <0.1 | s/W>1)
fprintf('There is sth. wrong!\n');
break;
else
mo=W/h*(0.619*log(W/h)-0.3853);
ko=4.26-1.453*log(W/h);
end

if (0.1<= s/W & s/W<=0.3)
me=0.8675;
ke=2.043*power(W/h,0.12);
else
me=1.565/power(W/h,0.16)-1;
ke=1.97-0.03/(W/h);
end

%Co=power(Er/9.6,0.8)*power(s/W,mo)*exp(ko)*W;
%Ce=12*power(Er/9.6,0.9)*power(s/W,me)*exp(ke)*W;

Co=1.1*power(Er/9.6,0.8)*power(s/W,mo)*exp(ko)*W;
Ce=1.167*power(Er/9.6,0.9)*power(s/W,me)*exp(ke)*W;

Cp=0.5*Ce
Cg=0.5*Co-0.25*Ce

 

[cawan]

thanks