Designing PCB Spiral Inductors: When & How

Why Planar Spirals Matter

Planar spiral inductors are everywhere in modern RF and analog PCB design. They're compact, easy to integrate into your layout, and don't require discrete components. You see them in matching networks, LC filters, impedance matching stages, and local bias inductors on high-frequency boards. But here's the thing: most engineers either treat them as magic or ignore their parasitics entirely, and both approaches lead to circuits that don't work the way the simulation predicted.

The real problem is that a planar spiral isn't a simple lumped inductor. It has parasitic capacitance, resistance, and its self-resonant frequency can be embarrassingly close to your operating frequency. If you don't understand what's happening, you'll waste days debugging a layout that looked fine in simulation.

The Two Models: Mohan and Wheeler

There are multiple ways to estimate the inductance of a planar spiral, and you'll see two names pop up constantly: Mohan and Wheeler. They're both empirical models, and they give slightly different answers. That's not a bug—it's just how the math works out.

The Wheeler model is older and simpler. It uses the average diameter of the spiral and applies a correction factor based on the geometry. It's fast to calculate by hand, which is why you still see it referenced in old textbooks.

The Mohan model is more accurate, especially for spirals with higher fill ratios (more turns packed into the same area). It accounts for the current distribution more carefully and includes corrections for the trace width and spacing. For modern, tightly-wound spirals, Mohan tends to be closer to measured reality.

Here's the key: neither model is "correct." They're both approximations. The actual inductance depends on the dielectric constant of your substrate, the copper thickness, and the layer stackup. But for a quick design check, Mohan will get you within 10–15% of measured value on a typical FR-4 board, and Wheeler will get you close enough for a sanity check.

The Fill Ratio and Why It Matters

The fill ratio $\rho$ is the ratio of the outer diameter to the inner diameter. A tight spiral with a small inner diameter has a high fill ratio. A loose spiral with a large inner diameter has a low fill ratio.

This number tells you something important: how much of the available space you're using. A fill ratio of 2.0 means the outer diameter is twice the inner diameter. A fill ratio of 10.0 means it's ten times larger.

Why does this matter? Because the inductance per unit area increases with fill ratio, but the parasitic capacitance also increases. You're not getting free lunch. As you pack more turns into the same footprint, you're also creating more capacitance between adjacent traces, which lowers your self-resonant frequency. There's a sweet spot for your application, and it depends on what frequency you're actually trying to work at.

A Real Example: 2.4 GHz Matching Network

Let's say you're designing a small-signal amplifier that needs input matching at 2.4 GHz. You want an inductor in series with the input, and you're planning to use a planar spiral on a standard 1 oz copper FR-4 board.

Your target inductance is 1.2 nH. Your PCB has 2 mils of trace width available (that's tight but doable with modern fab houses), and you want to keep the spiral small—maybe 1 mm outer diameter.

Let's work through this with the calculator. We'll try:

• Outer Diameter: 1.0 mm
• Inner Diameter: 0.3 mm
• Number of Turns: 2
• Trace Width: 0.05 mm (2 mils)
• Trace Spacing: 0.05 mm (2 mils)
• Shape: Circular (Shape = 3)

Running this through the Mohan model, you get an inductance of roughly 1.18 nH. That's spot on. The Wheeler model might give you 1.25 nH—close enough for government work.

But here's where most engineers stop, and that's where they get into trouble. Look at the other outputs:

• Total Trace Length: About 6.3 mm
• DC Resistance (1 oz Cu): About 0.012 Ω
• Q at 100 MHz: About 780
• Estimated SRF: About 28 GHz

Wait. 28 GHz? That seems way higher than your operating frequency. Actually, that's good news—it means the spiral won't self-resonate and mess up your impedance at 2.4 GHz. But here's the catch: that SRF estimate is very rough. It assumes the parasitic capacitance is small, which it is at this scale, but in reality, you'll see some capacitive effects starting around 5–10 GHz depending on the substrate.

The DC resistance of 0.012 Ω is negligible, so Q at 100 MHz is huge. But at 2.4 GHz? The skin effect kicks in, and your resistance climbs. A rough estimate is that the resistance scales with the square root of frequency, so at 2.4 GHz you're looking at maybe 0.08–0.1 Ω, which brings your Q down to maybe 90–100. Still decent, but not the 780 you see in the calculator output.

The Geometry Trade-Off

Now let's say your layout is tight and you can't fit a 1 mm spiral. You need something smaller. Let's try:

• Outer Diameter: 0.6 mm
• Inner Diameter: 0.2 mm
• Number of Turns: 1.5 (okay, you can't actually have 1.5 turns, so this is a theoretical exercise)
• Trace Width: 0.05 mm
• Trace Spacing: 0.05 mm
• Shape: Circular

Now your inductance drops to about 0.45 nH. That's way too low. To get back to 1.2 nH, you'd need to increase the number of turns, which increases the fill ratio and brings down the SRF. Or you increase the outer diameter. There's no free lunch.

The shape of the spiral also matters. A square spiral packs more turns into a given area than a circular one, so you get higher inductance for the same footprint. Hexagonal and octagonal shapes are compromises. Most of the time, square spirals are the practical choice on PCB because they align nicely with your grid-based layout.

Common Mistakes and Gotchas

Mistake 1: Ignoring the SRF. Engineers design a spiral inductor at 1 GHz, measure it, and find that the impedance starts going capacitive above 500 MHz. They didn't account for the parasitic capacitance. The calculator gives you an estimate of SRF, but treat it as a rough ballpark, not gospel. Always measure or simulate the actual impedance if you're working above a few hundred megahertz. Mistake 2: Forgetting about the substrate. The inductance values you get from the calculator assume a specific substrate (usually FR-4 with a certain thickness and dielectric constant). If you're on a different material—alumina, Rogers, or even a different thickness of FR-4—your actual inductance will shift. The model is semi-empirical, not physics-based, so it doesn't adapt automatically. Check your fab's stackup and adjust your expectations. Mistake 3: Underestimating the DC resistance impact at high Q. The Q factor shown at 100 MHz assumes DC resistance only. At RF frequencies, the skin effect dominates, and the resistance climbs. For a 2 mil trace at 2.4 GHz, you're not getting a Q of 780. You're getting maybe 50–100. This matters if you're relying on high Q for filter selectivity. Mistake 4: Not accounting for coupling to nearby traces. A planar spiral is a loop, and it radiates and couples to everything around it. If you route a high-speed clock line underneath or next to your spiral, you'll get crosstalk and EMI. The calculator doesn't know about your layout—it only calculates the spiral itself. Keep other traces away from the spiral, especially if they're switching at high frequency. Mistake 5: Treating the inner diameter as a free parameter. A small inner diameter gives you a tighter spiral and higher inductance per unit area. But it also makes the spiral harder to fabricate, especially with tight trace spacing. Most PCB fabs have a minimum feature size, and if you go below it, they'll either enlarge your traces automatically (which changes the inductance) or reject your design. Check your fab's design rules before you commit to a spiral with 0.1 mm inner diameter.

When to Use Planar Spirals vs. Discrete Inductors

Planar spirals are great for inductances in the range of 0.5 nH to maybe 50 nH, depending on your board size and frequency. Below 0.5 nH, you're fighting parasitic capacitance and the SRF gets too close to your operating frequency. Above 50 nH, the spiral gets so large that it's cheaper and easier to use a discrete chip inductor.

At RF frequencies (above 1 GHz), planar spirals are usually better than discrete inductors because they have lower parasitic capacitance and can be optimized for your specific impedance and Q requirements. At audio and low-frequency analog (below 100 MHz), discrete inductors are often simpler and more predictable.

There's also the question of current handling. A planar spiral with 2 mil traces can handle maybe 50–100 mA before the DC resistance becomes significant. If you need to handle amps, you need either a much wider trace (which changes the inductance) or a discrete component.

Practical Design Tips

Start with the calculator to get a ballpark value, then build in some margin. If you need 1.2 nH and the calculator says 1.2 nH, design for 1.0 nH and plan to trim it in layout or simulation. You can always add a small series capacitor to fine-tune the resonant frequency if you're building an LC tank.

Simulate your spiral in your favorite EM simulator (Ansys HFSS, Keysight ADS, or even free tools like OpenEMS) before you commit to fabrication. The calculator is a starting point, not the final answer. Real-world effects like the dielectric loss of your substrate, the copper roughness, and the presence of nearby ground planes will shift the inductance and Q.

If you're building a filter or matching network, account for the series resistance of the spiral. It acts like a resistor in series with your inductor, and it kills Q. For a 2 GHz circuit with a 2 mil spiral, expect Q values in the range of 20–50, not 200.

Keep the spiral away from the board edge and away from other traces that carry high-frequency signals. Use a ground plane underneath if possible—it reduces the loop area and improves the Q, but it also reduces the inductance slightly. This is another reason to simulate before you build.

Try It Out

The best way to understand planar spirals is to play with the numbers. Open the Planar Spiral Inductor Calculator and try a few different geometries. See how the inductance changes when you increase the number of turns. Watch the SRF drop as you pack more turns into the same area. Notice how the fill ratio affects the inductance per unit area.

Then grab an EM simulator or a network analyzer, build a test spiral on a small PCB, and measure it. Compare your measurement to the calculator output and the Mohan and Wheeler models. You'll learn more from one real measurement than from a dozen theoretical exercises.

Planar spirals aren't magic, and they're not that complicated once you understand the trade-offs. They're just another tool in your RF design toolkit, and like any tool, they work best when you understand their limitations.