Microstrip Impedance
Z₀ and effective εr for a surface trace over a ground plane (Hammerstad).
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The engineering
The everyday controlled-impedance line: half the field in the board, half in the air, hence the *effective* εr between the two. On 1.6 mm FR-4 (εr ≈ 4.4), 50 Ω wants a trace roughly 3 mm wide — which is why RF boards use thinner dielectrics.
Accuracy is a few percent, ignoring trace thickness and solder mask; your fab's field solver gets the last word, this card gets you to the neighborhood.
Where this math comes from
Microstrip came out of ITT's labs (Grieg and Engelmann, 1952) as the printed alternative to coax, but was too lossy and dispersive to trust until the analysis caught up. Harold Wheeler's 1965 conformal-mapping papers made it computable; Hammerstad's 1975 closed-form fits — refined with Jensen in 1980 — are what every calculator, this one included, actually evaluates.
The stripline/microstrip family is why 'transmission line' stopped meaning something you buy on a spool and started meaning something you draw in CAD.
- 1952Grieg & Engelmann (ITT)Microstrip introduced.
- 1965Harold WheelerConformal-mapping analysis of strip lines.
- 1975Erik HammerstadClosed-form design equations — the ones in this card.
See the full timeline of the math behind every calculator →
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