Linear Reactor Chart

In the preceding section, it was assumed that the core air gap is large compared to l_c/μ, where μ is the d-c permeability. In grain-oriented steel cores the air gap may be large compared to l_c/μ_Δ, because of the high incremental permeability of these cores. When this is true, variations in μ do not affect the total effective magnetic path length or the inductance to substantial degree. Reactor properties may then be taken from Fig. 71. In order to keep the reactor linear, it is necessary to limit the flux density. For grain-oriented silicon-steel cores, inductance is usually linear within 10 per cent if the d-c component of flux B_dc is limited to 12,000 gauss and the a-c component B_ac to 3,000 gauss.

Dotted lines in quadrant I are plots of turns vs. core area for a given wire size and for low-voltage coils, where insulation and margins are governed largely by mechanical considerations. Core numbers in Fig. 71 have the same dimensions and weight as in Table VIII.

If the cores increased in each dimension by exactly the same amount, the lines in quadrant I would be straight. In an actual line of cores, several factors cause the lines to be wavy:

(a)   Ratios of core window height to window width and core area deviate from constancy.

(b)   Coil margins increase stepwise.

(c)   Insulation thickness increases stepwise.

A-c flux density in the core may be calculated by equation 36, and B_dc by equation 35. If B_m materially exceeds 15,000 gauss, saturation is reached, and the reactor may become non-linear or noisy.

Instructions for Using Fig. 71.

1.  Estimate core to be used.

2.  Divide required inductance by area (A_c) of estimated core to obtain a value of L/sq in.

3.  In second quadrant, locate intersection of L/sq in. and rated I_dc.

4.  On this intersection, read total gap length (l_g) and number of turns (N). Gap per leg = l_g/2.

5.  Project intersection horizontally into first quadrant to intersect vertical line which corresponds to estimated core. This second intersection gives d-c resistance and wire size.

Example. Required: 15 henrys at I_dc = 50 ma.

Estimate core No. 1.

L/sq in. = 84.3, l_g = 0.015 in., N = 6,000, DCR = 800 ohms.

Wire size = No. 36.

(Example shown starting with dotted circle.)

Fig. 71. Linear reactor design chart.

A similar chart may be drawn for silicon-steel laminations, but to maintain linearity lower values of flux density should be used.