# Closed form equivalent circuit of microstrip gap (slot)?

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#### div

##### Member level 3 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.

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

##### Member level 3 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
ISBNs: 0-471-38877-7 (Hardback);
________

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

Regards
Div

#### div

##### Member level 3 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

##### Full Member level 2 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: Two models to test #### yingyang

##### Full Member level 2 slot

you may also like to look at microstriplines and slotlines by K. C. Gupta. Hi yingyang
gap2.pdf is the model from the book you are talking about (2nd edition)

#### div

##### Member level 3 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

##### Full Member level 2 thanks

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