Re: Self and mutual inductances of coupled microstrip lines in RF frequency range

["Samuel" <sdaylis@xxxxxxxxxxx>]

Hello,

Sorry, I used my friend's e-mail address in the previous mail, now I 
have my own :-)
Thanks Dave for detailed explanation. Enforcing zero net circuit 
current on the "passive" 
line really changed everything. Here is what I'm getting now directly 
from Dave's structures:
------------------------------------------
Single Line 

F L,nH/m

0	559	
1 MHz	559
100 MHz	557
1 GHz	539
---------------------------------------------------------------------
Coupled lines

F	L11	L21,1st method L21, 2nd method

0	559	267	352	
1 MHz	559	269	352
100 MHz	549	270	344
1 GHz	513	281	315
----------------------------------------------------------------------
In this table 1st method is integral of A21 over strip 2 with I2=0
divided by cross-section; 2nd method is diference between
cases I1=1A, I2=0 and I1=I2=1A (both cases use Int{A11*J1} over
the area of the strip #1), done according to Dave's suggestion.	


My favorite electrostatic solver is LINPAR ( A. Djordjevic et 
al,"Linpar for Windows", Software and Manual, Artech House, 1996), 
specialized 
software that analyzes coupled microstrip lines. I've been using it 
for years, its very robust. I trust it even up to 40 GHz. It 
calculates 

L-matrix from capacitance C-matrix as: 

[L] = 1/[C_0]/v_light^2

where [C_0] capacitance matrix of conductors placed in air, v_light 
is 
the speed of light. [C] is found from charge distribution which, in 
its turn is obtained from solution of integral equation by method of 
moments.

To my knowledge, Linpar is very accurate in getting [L] at f~=0 for 
our simple example. Note that these inductances are:

----------------------------------------------
Single line L = 536 nH/m
coupled lines L11 = 503 nH/m, L21 = 295 nH/m
----------------------------------------------

FEMM results at f=0 are 4% off for a single line (well, its 
acceptable at least).

What kills me in FEMM results for coupled lines is that L11 at f=0 is 
exactly the same as L for a single line! Linpar gives L11=503 against 

single line L=536. It's normal because lines are only 10 microns 
apart. So L11 from FEMM is 11% off LINPAR; L21 from FEMM is 9.5% off; 
L21 is underestimated in FEMM.

I applied alternative method of L21 evaluation that Dave advised in 
his response (applied I1=1A,I2=1A, estimated Int{A11*J1}/I1^2; 
applied I1=1A,I2=0, estimated Int{A11*J1}/I1^2; subtracted results ) 
and found that L21 is very overestimated (see table above).

The bottom line: what is going wrong at f=0? Why L11 for coupled 
lines is the same as L for a single line? Is there any hope to get 
correct mutual inductances even at low frequencies?

Thanks for your input,

Samuel