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3.5 1 1 1 1 1 Rating 3.50 (4 Votes)

pcb spiral inductor

PCB coilsFlat PCB coils are most often used in the VHF and UHF bands to reduce the size of the device. Usually they are produced with round, square or meander form of turns, although it can be in the form of a polygon. With the advent technology of multilayer PCB the multi-layer coil appears. The use of a magnetic core is ineffective because such a core is far away from the turns of the coil and can change its inductance by 3 - 5 %, which in most cases is not enough. Therefore, printed inductors are used in most cases when the adjustment is not required and the value of the inductance units does not exceed microhenry. Q-factor of PCB inductors is generally lower then Q-factor of the inductors having a coil of wire and less than that of the cylindrical microstrip coils. The self capacitance of the printed inductors depends on the width of the spiral turns, the gap between them and the PCB material and can reach 3 to 5 pF, which is pretty high at such frequencies. All I have said is not in favor of flat PCB coils, however, the compact design along with the use of SMD components often plays a decisive role in use such inductors.

On our site you can use the online calculator to calculate the coils on PCB.PCB coil formula

To compute inductance of PCB inductors we can use three pretty accurate methods.



1.The first approximation is based on a modification of an expression developed by H.A.Wheeler for the planar spiral inductors:

PCB inductor Wheeler formula [1]

The coefficients K1 and K2 are layout dependent and are shown in following table:

Table I
LayoutK1K2
Square 2.34 2.75
Hexagonal 2.33 3.82
Octagonal 2.25 3.55

 


2.The second is a monomial expression derived from fitting to a large database of inductors (and the exact inductance values):

PCB inductor monomial formula [2]

where g = s - W  gap between turns and the coefficients β and αi are layout dependent and given in the following table:

Table II
Layoutβα1α2α3α4α5
 Square  1.62·10-3  -1.21  -0.147  2.40  1.78  -0.03
 Hexagonal  1.28·10-3  -1.24  -0.174  2.47  1.77 -0.049
 Octagonal  1.33·10-3  -1.12  -0.163  2.43  1.75  -0.049

 This formula is used in Coil32 for square PCB coil calculation.


3.The third is derived from electromagnetic principles by approximating the sides of the spirals as current-sheets:

PCB inductor current sheet formula [3]

where

  • L- inductance (nH);
  • D - outer diameter of coil (mm);
  • d - inner diameter of coil (mm);
  • N - number of turns;
  • Davg - average diameter of coil (mm);
  • φ - fill factor;
  • ci - factors from Table III (layuot depending):
Table III
Layoutc1c2c3c4
Square   1.27  2.07  0.18  0.13
 Hexagonal  1.09  2.23  0.00  0.17
 Octagonal  1.07  2.29  0.00  0.19
 Circle  1.00  2.46 0.00  0.20

 For PCB inductor with round turns Coil32 uses the third method. The rearranged formula [3] is shown as:Although the accuracy of this expression worsens as the ratio s/W becomes large, it exhibits a maximum error of 8% for s ≈ 3W. Note that typical practical integrated spiral inductors are built with w ≤ s. For highest Q-factor the optimum ratio d/D = 0.4 for circle coil and optimum d/D = 0.362 for square coil. The program automatically set inner diameter value for this ratio. In the calculation, we define the outer diameter of the coil and its layout. If the result of the calculation obtained unacceptable sizes of printed trace, the outer diameter we can modify and recalculate the coil again.


In all expressions Davg factor is average diameter of the coil and φ is the filling factor that represents how hollow the inductor is. Theese factors are defined as:

eq406eq407

  • Davg - average diameter of coil;
  • φ - fill factor;
  • D - outer diameter of coil;
  • d - inner diameter of coil;

All dimentions in meter, inductance in henry. All three expressions are accurate, with typical errors of 2–3%, and very simple, and are therefore excellent candidates for use in design and synthesis PCB inductors.


Inductor as a straight microstrip calculates by the following expression:straight micristrip trace inductoreq404

  • L - inductance (μH)
  • l -trace length (mm)
  • b - trace width (mm)

Such inductive elements are often used in filters UHF band. Because of what the self-capacitance of such inductive element is quite large, it is necessary to keep in mind that the more correct to represent it in the form of a segment of a transmission line with distributed parameters. However, for approximate calculations, this model is quite acceptable if this element works at frequencies much lower the self-resonance.

Plugin meandr_PCB allows to calculate PCB inductors with meander layout of turns.

References:

 

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