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Microstripline
Synthesis and analysis



Takayuki HOSODA
Sep. 14, 2011

Microstripline Synthesis & Analysis

Frequency    MHz
Electrical length    deg
Dielectric relative permittivity (εr)   
Dielectric height (h )   μm
Conductor thickness (t )    μm
Buried depth (b)     μm
Conductor width (w ) ≈     μm
Impedance (Z0)    Ω
Impedance (Z0,buried ) ≈     Ω
Effective relative permittivity ≈     
Capacitance ≈     pF/m
Inductance ≈     nH/m
Velocity of propagation ≈     
Physical length ≈     mm
Rightangle bend compensation (rc) ≈     
Open end effect length (Δℓ ) ≈     μm
Side gap (s)     μm
Differential impedance (Zdiff) ≈     Ω
Note: The practical ranges for Z0 and Zdiff are from 20 Ω to about 150 Ω, with possible erros of up to ± 10%.
ustrip-3.2.js (Javascript program and Input form used in this page.)

Formulas used

Micro strip line impedance
Micro-strip-line characteristic impedance
where,
w_\mathrm{eff} & \simeq & w + t \frac{1 + \displaystyle\frac{1}{\varepsilon_\mathrm{r}}}{2 \pi}\left(1 + \ln \left( \frac{4}{ \sqrt{\left(\displaystyle\frac{t}{h}\right)^2 +\left(\displaystyle\frac{1}{\pi}\frac{1}{\displaystyle\frac{w}{t} + 1.1}\right)^2} } \right)\right)

Open end effect length
Open end effect length
Rightangle bend compensation. Valid for w / h ≥ 0.25, ϵr ≤ 24, ± 4 % accuracy.
R_\mathrm{miter} & = & 0.52 + 0.65 \ e^{\displaystyle\left(\frac{-1.35\ w}{h} \right)}
Buried microstrip line
Z_\mathrm{0,buried} &=& Z_0 \sqrt{\frac{ \varepsilon_\mathrm{eff}}{\varepsilon_\mathrm{eff,buried}}}\\ \varepsilon_\mathrm{eff,buried} &=& \varepsilon_\mathrm{eff} \ e^{\displaystyle\left( 2b / h \right)} + \varepsilon_r \left(1 - e^{\displaystyle\left(-2 b / h \right)}\right)
Differencial impedance of side coupled microstrip line
Z_\mathrm{diff} $ \simeq $ Z_0 \left(1 - 0.48\ e^{\left(\displaystyle\frac{-0.96 s}{h}\right)} \right)

APPENDIX

Example of field solver results (simulation box width W = 12 h + 4 t + 2 s + w, box height H = 8 h + t) Length unit in [ grid ].

w = 200, h = 200, t = 35, b = 0, ϵr=4.7, W = 2740, H = 1635 : Z0 ≃ 63.303 Ω
w = 200, h = 200, t = 35, b = 55, ϵr=4.7, W = 2740, H = 1635 : Z0 ≃ 58.388 Ω

microstripline with solder resist
Pseudo color visualization of absolute value of the electric field.

REFERENCE

  1. H. A. Wheeler, "Transmission-line properties of a strip on a dielectric sheet on a plane",
    IEEE Trans. Microwave Theory Tech., vol. MTT-25, pp.631-647, Aug. 1977.

  2. R. J. Douville and D. S. James, "Experimental study of symmetric microstrip bends and their compensation",
    IEEE Trans. Microwave Theory Tech., vol. MTT-26, pp. 175-182, Mar. 1978

  3. James A. Mears, "Transmission Line RAPIDESIGNER Operation and Applications Guide",
    National Semiconductor Application Note, AN-905, May.1996

  4. Brian C. Wadell, "Transmission Line Design Handbook", Artech House, Inc., 1991, ISBN 0-89006-436-9

SEE ALSO

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