Microstripline calculator - Synthesis & Analysis

Microstripline Synthesis & Analysis

Frequency MHz

Electrical length deg

Dielectric relative permittivity (ε_r)

Dielectric height (h ) μm

Conductor thickness (t ) μm

Buried depth (b) μm

Conductor width (w ) ≈ μm

Impedance (Z₀) Ω

Impedance (Z_0,buried ) ≈ Ω

Effective relative permittivity ≈

Capacitance ≈ pF/m

Inductance ≈ nH/m

Velocity of propagation ≈

Physical length ≈ mm

Rightangle bend compensation (r_c) ≈

Open end effect length (Δ_ℓ ) ≈ μm

Side gap (s) μm

Differential impedance (Z_diff) ≈ Ω

Note: The practical ranges for Z₀ and Z_diff 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, ϵ_r=4.7, W = 2740, H = 1635 : Z₀ ≃ 63.303 Ω
w = 200, h = 200, t = 35, b = 55, ϵ_r=4.7, W = 2740, H = 1635 : Z₀ ≃ 58.388 Ω

[画像: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

• Effect of the top coat on Planar Transmission Lines
• Conductor-backed Coplanar Waveguide Analysis
• for the HP 42S - Synthesize/Analyze microstrip transmission line
• for the HP 32sII - Synthesize/Analyze microstrip transmission line
• for the HP 15C - Synthesize/Analyze microstrip transmission line
• Ostrowski's method
• Online-calculator - Inductance of a straight conductor of thin flat section