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PCB Inductor – Definition and Methods of Computing Inductance Value

An inductor is a passive component that operates via opposing sudden changes in current flow. It does so by temporarily reducing the spikes or current surge by storing the energy in the electromagnetic field before releasing it into the electronic circuit. A common inductor example is the PCB inductor. In today’s article, we’ll define a PCB inductor and then teach you a few methods of computing the inductance value. 

What is a PCB inductor?

Flat PCB coils are electronic components used by circuit designers to reduce the size of electronic devices, such as in UHF and VHF bands. 

Radio frequency PCB coils

(Radio frequency PCB coils)

Often, they come in the forms of polygons, meander turns, squares, or rounds in a circuit board. In addition, now we have multilayer coils due to the copper layers in multilayer PCB technology. 

How do you Compute the PCB Inductors?

Usually, there are four known ways of computing inductance of PCB inductors, but we will major in the first three. Additionally, they have a 2-3% typical error and are very easy to use in the synthesis and design of PCB inductors. 

  • Based on a modification of an expression developed by H.A.Wheeler for the planar spiral inductors
Planar magnetic core assembly

Planar magnetic core assembly

Source; Wikimedia 

It is the first approximation method and includes the formula below;

Whereby;

  • φ = Fill factor (expression [4])
  • Davg – average diameter of coil (µm) (expression [4])
  • N = Number of turns
  • µ0 = 4π × 10-7 = magnetic constant
  • L = inductance (µH)

Additionally, we have our layout-dependent coefficients K2 and K1 displayed in the following table:

  • A monomial expression derived from fitting to a large database of inductors

The second method has the following formula;

Whereby;

A table summarizing the layout dependent on coefficients β and αI

  • Derived from electromagnetic principles by approximating the sides of the spirals as current-sheets

The formula in the last method is;

Whereby;

  • φ = Fill factor (expression [4])
  • Davg = Average diameter of coil (µm) (expression [4])
  • N = Number of turns
  • µ0 = 4π*10-7 – magnetic constant
  • L = inductance (µH)

Layout table on ci-factors

  • In the last step, where we have an inductor acting as a straight microstrip, we calculate using the following formula;

Whereby;

b = trace width in mm

I = trace length in mm

L = inductance in μH

The inductive element in this method suits the filters of the UHF band. What’s more, when using the formula, remember to represent it as a transmission line segment with distributed parameter since its self-capacitance is large. 

However, you can still use the method at a range of frequencies lower than the self-resonant frequency. 

Conclusion

As we conclude, we hope that you’ve grasped several techniques for calculating a PCB series inductor. You can contact us if you need assistance with any of the concepts. 

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Hommer Zhao
Hi, I am Hommer, the founder of WellPCB. So far, we have more than 4,000 customers worldwide. If you have any questions, you can feel free to contact me. I really appreciate any help you can provide.

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