Microstrip Width for 50 Ohm on a 1.6 mm FR-4 Board
On FR-4 (er 4.4) a microstrip line reaches 50 ohm at a width-to-height ratio of about 1.9, which is about 3 mm on a 1.6 mm board. Wider strips lower the impedance and narrower strips raise it.
For practitioners
A microstrip line is a copper strip of width W on a dielectric of height h, over a ground plane. The field runs through the dielectric and through the air above it. Three numbers set the characteristic impedance: the ratio W/h, the substrate permittivity and, through the air share of the field, the geometry again. This article shows how they combine and works one example on a 1.6 mm FR-4 board.
What sets the impedance
The characteristic impedance of any line is set by its inductance and capacitance per unit length:
For a microstrip line the geometry changes both terms. The strip and the ground plane form a capacitor. A wider strip faces more ground plane, so C' rises. A thicker substrate moves the strip away from the ground plane, so C' falls. Inductance moves the opposite way, and the impedance follows the ratio.
The result is one rule. For a given substrate height, the characteristic impedance falls as the strip gets wider. For a given width, a taller substrate raises it. Only the ratio W/h matters for the shape of the field. Scaling both dimensions by the same factor leaves the impedance unchanged, which is why the formulas below use W/h and not W and h separately.
Effective permittivity
The field does not sit entirely in the substrate. Part of it is in air. A single number, the effective permittivity, stands for the blend. It lies between 1 and the substrate permittivity.
Two limits show this. A very wide strip pushes most of the field into the dielectric, so the effective permittivity approaches the substrate value. A very narrow strip spreads the field more into the air, so it moves toward the middle of the range.
The Hammerstad-Jensen form for W/h of 1 or more is:
The impedance then follows from the effective permittivity and the ratio:
For narrow strips with W/h below 1, the textbook form is different:
The wide-strip expression is the one used for 50 ohm on FR-4, because the answer lands above W/h = 1.
How the impedance changes with W/h
On FR-4 with a relative permittivity of 4.4, the impedance passes 50 ohm at a width-to-height ratio of about 1.9. Below that ratio the line is above 50 ohm. Above it the line is below 50 ohm.
Two points on a 1.6 mm board show the trend. A 1 mm strip is about 87.5 ohm. A 3 mm strip is about 50.8 ohm. Making the strip three times wider cuts the impedance by roughly 37 ohm. The curve is steep for narrow strips and flattens as the strip widens, so a given change in width matters most for thin lines.
Worked example: 1.6 mm FR-4
Given: h = 1.6 mm and a relative permittivity of 4.4. The target is 50 ohm.
- The 50 ohm crossing is at W/h of about 1.9. The width is W = 1.9 × 1.6 mm ≈ 3.0 mm.
- Check with a 3 mm strip. W/h = 3 / 1.6 = 1.875.
- Effective permittivity: 12h/W = 6.4, so 1 + 6.4 = 7.4 and its square root is about 2.720. Then ε_eff = 2.7 + 1.7 / 2.720 ≈ 3.32.
- Denominator bracket: 1.875 + 1.393 + 0.667 × ln(3.319) = 1.875 + 1.393 + 0.667 × 1.200 ≈ 4.07.
- Impedance: 120π is about 376.99. The square root of 3.32 is about 1.823. So Z₀ ≈ 376.99 / (1.823 × 4.07) ≈ 50.8 ohm.
The check agrees with the 3 mm figure above. The 3 mm strip sits about 0.8 ohm above 50 ohm, so the exact 50 ohm width is slightly more than 3 mm, consistent with the 1.9 ratio.
The effective permittivity of 3.32 is well inside the allowed range: above 1 and below 4.4.
Limits of the formula
The formula assumes a single, known permittivity. Real FR-4 does not offer one.
- The permittivity varies with the material.
- It varies with the glass weave.
- It varies with the frequency.
A permittivity change moves the result. A higher permittivity lowers the impedance for the same width. So the formula is a starting point.
For a controlled-impedance order, do not send only a width. Specify the stack-up and the target impedance, and let the fabricator confirm the width for their material.
To run other widths and heights, use the Microstrip Impedance and Width Calculator.
In plain words · for students and beginners
Microstrip impedance in plain words
An everyday picture
Think of a garden hose lying over the ground. The hose is the signal strip and the ground is the ground plane. A wide, flat hose has lots of room for water to flow, so it resists less. A narrow hose resists more. Raise the hose high above the ground and the flow is harder to control.
Impedance works a little like that. It is the "resistance" a signal sees as it travels along the line. A wider strip lowers it. A taller board raises it.
Where the picture breaks down: water only flows inside a hose, but the signal's electric field is not trapped inside the board. Some of it sits in the air above the strip. That is why the board's permittivity (how much the material stores electric field) is only part of the story.
The same example in simple steps
The board is 1.6 mm thick FR-4, and we want 50 ohm.
- Find the ratio. For FR-4 the 50 ohm point is when width divided by height is about 1.9.
- Multiply. 1.9 × 1.6 mm is about 3 mm.
- Check. A 3 mm strip works out to about 50.8 ohm, which is close.
- Compare. A thin 1 mm strip is about 87.5 ohm, far too high.
The curve shows the same story. Impedance drops quickly as the strip widens, then more slowly.
Mistakes beginners make
- Using the width alone. The height matters just as much. A 3 mm strip on a thinner board has a much higher ratio and a lower impedance.
- Treating the board permittivity as exact. Real FR-4 varies with material, glass weave and frequency, so the answer is a starting point.
- Forgetting the air. The field is partly in air, so the effective permittivity is lower than the board's value.
- Ordering by width only. Ask the fabricator for controlled impedance and give the stack-up.
Remember
- Wider strip, lower impedance. Taller board, higher impedance.
- On FR-4 (permittivity 4.4), 50 ohm is at width divided by height of about 1.9, which is about 3 mm on 1.6 mm.
- A formula is a starting point. Specify the stack-up when you order.
Related pages on RF View
Frequently asked questions
What width is a 50 ohm microstrip on 1.6 mm FR-4?
With a relative permittivity of 4.4, the impedance passes 50 ohm at a width-to-height ratio of about 1.9. On a 1.6 mm board that is about 3 mm. A 3 mm strip computes to about 50.8 ohm.
Does a wider microstrip line have higher or lower impedance?
Lower. For a given substrate height, a wider strip has more capacitance to the ground plane, and the characteristic impedance falls.
Why is the effective permittivity of a microstrip line lower than the substrate permittivity?
Part of the field runs through the air above the strip. The effective permittivity is therefore a blend that lies between 1 and the substrate permittivity.
Can I trust a formula for FR-4 impedance?
Treat it as a starting point. The permittivity of real FR-4 varies with the material, the glass weave and the frequency, so a controlled-impedance order should specify the stack-up.