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Appendix A
Practical Information on Inductors
A.1 Air Core Inductors
An approximate formula for the inductance of a close-wound single-layer coil with nonmagnetic core (e.g., air) is
L =
(rN )^2 9 r + 10l
(A.1)
where L = inductance in μH
N = number of turns
r = radius of coil (inches)
l = length of coil (inches)
Formula A.1 is accurate to within 1% if l > 0. 8 r, i.e., if the coil is not too short.
A.2 Toroidal Inductors
We will make extensive use of toroidal inductors which are inductors formed by winding a coil of wire around a donut-shaped (toroidal) core. An important advantage of this type of inductor is its self-shielding property. Due to the relatively high magnetic permeability of the core material (compared to air), the magnetic fields are essentially confined to the core. This means that the coil inductance will be unaffected by its physical orientation and also that negligible mutual coupling will exist between toroidal coils in close proximity. Circuit design can be greatly simplified if mutual coupling effects can be neglected. Mutual coupling can also cause serious problems in tuned amplifiers, since coupling between coils in the input and output circuits can cause the circuit to oscillate.
The core material for a toroidal inductor is usually either manufactured from iron powder or a ferrite material. These materials have very different properties. The important parameters of the core material are its relative magnetic permeability, cross-sectional area and diameter and volume
14 APPENDIX A. PRACTICAL INFORMATION ON INDUCTORS
resistivity (which determines the loss). Other considerations for high power applications are the saturation flux density, which determines the largest magnetic field that the core can support, and the temperature rise resulting from power dissipation. For small signal applications these need not be considered. Generally, ferrite cores offer higher magnetic permeability than iron-powder cores which results in fewer turns required to realize a given inductance value. Iron-powder cores generally have lower losses and higher saturation flux densities. A general rule of thumb for high power RF applications is that the power handling capability of a ferrite core is limited by flux saturation, while the limiting factor for iron powder is temperature rise.
An approximate formula for the inductance of a toroidal winding having cross sectional area A and effective length l is
L =
μA l
N 2 (A.2)
= A′ LN 2
where
μ = μr μo (A.3)
A′ L =
μA l
(A.4)
The parameter A′ L has units of (Henries/m)(m^2 )/m = Henries. Sometimes manufacturers will give the units of A′ L as H/turn 2 or μ H/turn 2 (but turn 2 is a “non-unit” - like radians). This is done to remind us to multiply the value of A′ L by N^2 in order to find the inductance.
The cores used in the EE453 lab are manufactured by AMIDON Associates. This manufacturer specifies the parameter AL for their cores. For iron-powder cores AL is related by A′ L by
AL = A′ L(100)^2 (A.5)
and for ferrite cores AL = A′ L(1000)^2 (A.6)
Therefore, the numbers specified on the AMIDON data sheets (AL) give the inductance of a 100- turn winding. For this reason they give the units of AL as “μH/(100 turns)” for iron-powder cores and “mH/(1000 turns)” for ferrite cores, although, strictly speaking, their parameter should have the units of μH or mH. In any case, if we take their definition for AL and assume that the units are in μH for iron powder or mH for ferrite, then the formula for the number of turns, N, can be deduced from Equations A.2 and A.5:
N =
L(μH) AL/(100)^2
iron powder (A.7)
L(μH) AL
16 APPENDIX A. PRACTICAL INFORMATION ON INDUCTORS
Core OD (in) ID (in) Height (in) Cross sect. (cm^2 ) Mean length (cm) Vol. (cm^3 ) FT-23 .230 .120 .060 .021 1.34. FT-37 .375 .187 .125 .076 2.15. FT-50 .500 .281 .188 .133 3.02. FT-50A .500 .312 .250 .152 3.18. FT-50B .500 .312 .500 .303 3.18. FT-82 .825 .520 .250 .246 5.26 1. FT-87A .870 .540 .500 .522 5.42 2. FT-114 1.142 .750 .295 .375 7.42 2. FT-114A 1.142 .750 .545 .690 7.42 5. FT-150 1.500 .750 .250 .581 8.30 4. FT-150A 1.500 .750 .500 1.110 8.30 9. FT-193 1.930 1.250 .750 1.460 12.30 18. FT-240 2.400 1.400 .500 1.570 14.40 22.
Table A.1: Physical dimensions of Amidon ferrite toroidal cores.
Relative permeability 20 40 40 125 850 Saturation Flux (Gauss) 2000 1850 3000 3000 2750 Curie Temperature (C) 500 450 500 350 130 Temperature Coefficient (%/C) .06 .10 .13 .15 1. Tuned circuit frequency range (MHz) 80-180 15-25 10-80 0.2-10 .01- Frequency range for wide-band apps (MHz) 200-1000 25-200 50-500 10-200 1-
Table A.2: Properties of Amidon ferrite materials.
Core Size #68 #63 #67 #61 # FT-23 4.0 7.9 7.9 24.8 188 FT-37 8.8 17.7 17.7 55.3 420 FT-50 11.0 22.0 22.0 68.0 523 FT-50A 12.0 24.0 24.0 75.0 570 FT-50B NA 48.0 48.0 150.0 1140 FT-82 11.7 22.4 22.4 73.3 557 FT-87A NA NA NA NA NA FT-114 12.7 25.4 25.4 79.3 603 FT-114A NA NA NA 146.0 NA FT-150 NA NA NA NA NA FT-150A NA NA NA NA NA FT-193 NA NA NA NA NA FT-240 NA 53.0 NA 173.0 1240
Table A.3: Amidon ferrite toroidal core AL values (mH/1000 turns).
Core OD (in) ID(in) Height (in) Cross sect. (cm^2 ) Mean Length (cm)
Table A.4: Physical dimensions of Amidon iron powder toroidal cores.
30-40 deg
- A.2. TOROIDAL INDUCTORS
- T-400A 4.000 2.250 1.300 7.43 24.
- T-400 4.000 2.250 .650 3.66 24.
- T-300A 3.048 1.925 1.000 3.58 19.
- T-300 3.048 1.925 .500 1.81 19.
- T-225A 2.250 1.405 1.000 2.73 14.
- T-225 2.250 1.405 .550 1.50 14.
- T-200A 2.000 1.250 1.000 2.42 12.
- T-200 2.000 1.250 .550 1.33 12.
- T-184 1.840 .950 .710 2.04 11.
- T-157 1.570 .950 .570 1.14 11.
- T-130 1.300 .780 .437 0.73 8.
- T-106 1.060 .570 .437 0.69 6.
- T-94 .942 .560 .312 .385 6.
- T-80 .795 .495 .250 .242 5.
- T-68 .690 .370 .190 .196 4.
- T-50 .500 .303 .190 .121 3.
- T-44 .440 .229 .159 .107 2.
- T-37 .375 .205 .128 .070 2.
- T-30 .307 .151 .128 .065 1.
- T-25 .255 .120 .096 .042 1.
- T-20 .200 .088 .070 .025 1.
- T-16 .160 .078 .060 .016 0.
- T-12 .125 .062 .050 .010 0.
