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Mutual Inductance

It is evident from equation 101 that the secondary voltage depends upon the mutual inductance between the coils. Mutual inductance can be calculated by formulas which depend upon the geometric configuration of the coils. If the coils are arranged concentrically, as shown in either (a) or (b) of Fig. 174, the mutual inductance of the coils can be found from

[105]

where N1 = primary turns and N2 = secondary turns.

Fig. 174. Concentric coaxial coupled coils.

All dimensions are in inches. For most purposes, the bracketed portion of this formula is approximately unity, and it has been plotted in Fig. 175 for a single-turn secondary.

Fig. 175. Mutual inductance of coils in Fig. 174.

To find the mutual inductance for any given number of secondary turns, multiply the mutual inductance found from this curve by the number of secondary turns. The range of ordinates and abscissas can be extended indefinitely.

Fig. 176. Coaxial non-concentric coils with rectangular sections.

If the coils are arranged coaxially as in Fig. 176, approximate values of mutual inductance are found as follows:

[106]

In this formula all dimensions are in inches and the mutual inductance is in microhenrys. The factor F can be conveniently found in Fig. 177.

Fig. 177. Factor F in equation 106 as a function of r2/r1 (see Fig. 176).

Self-inductance of single-layer coils is

[107]

where

a = mean coil radius in inches
N = number of turns
l = length of coil in inches
L = inductance in microhenrys
K may be found from Fig. 178.

Equations 105, 106, and 107 are based on equations 192, 187, and 153 in Natl. Bur. Standards Circ. 74.

Fig. 178. Factor K in equation 107.

Receiver intermediate-frequency tuned transformers generally have coaxial coils. If the wire is more than 0.005 in. in diameter, it is commonly subdivided into several strands in the type of cable known as Litzendraht, to reduce losses and increase Q. In transmitters, the size of the coils becomes much larger, and concentric coils are employed. The wire used is Litzendraht at 600 kc or lower frequency, and may contain many strands for carrying heavy currents. At higher frequencies the wire is of solid or tubular section.



Last Update: 2011-01-24