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

- To: femm@yahoogroups.com
- Subject: Re: Self and mutual inductances of coupled microstrip lines in RF frequency range
- From: "Samuel" <sdaylis@hotmail.com>
- Date: Fri, 22 Nov 2002 18:29:03 -0000
- In-reply-to: <3DDC6249.6020102@ieee.org>
- User-agent: eGroups-EW/0.82

    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

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  - Re: [femm] Self and mutual inductances of coupled microstrip lines in RF frequency range
    - From: David Meeker <dmeeker@ieee.org>

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