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470 Impedance-matching in antenna systems (r 1)2 + X 2 r{N (1/N)2} (r 1)2 X 2 {N (r/R)} B + X r + (XNB) 1 Z1 Zo RL Zo XL Zo
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tan L2 = B = tan L1 = A = where:
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Z= Constraints: Z1 > Zo Z1 < Zo If L1 < 0, then add 180 If B < 0, then Z1 is too close to Zo Z1 not equal to Zo Zo VSWR < Z1 < Zo VSWR Physical length in feet: L1 = L2 = where
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L1 360 L2 360
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984 velocity factor = frequency in megahertz
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The physical length is determined from arctan A and arctan B, divided by 360 and multiplied by the wavelength along the line and the velocity factor Although the sign of B can be selected as either or +, the use of + is preferred because a shorter section is obtained In the event that the sign of A turns out negative, add 180 to the result There are constraints on the design of this transformer For one thing, the impedance of the two sections L1 and L2 cannot be too close together In general, the following relationships must be observed:
Ferrite core inductors 471 Either ZL1 > Zo SWR
or [2436]
ZL1 < Zo SWR
[2437]
Ferrite core inductors
The word ferrite refers to any of several examples of a class of materials that behave similarly to powdered iron compounds, and are used in radio equipment in the form of inductors and transformers Although the original materials were of powdered iron, and indeed the name ferrite still implies iron, many modern materials are composed of other compounds According to the Amidon Associates literature, ferrites with a permeability u of 800 to 5000 are generally of the manganese-zinc type of material, and cores with permeabilities of 20 to 800 are of nickel-zinc The latter are useful in the 05- to 100-MHz range
Toroid cores
A toroid is a doughnut-shaped object, so one can reasonably expect a toroidal core to be an inductor (or transformer) form, made of a ferrite material, in the general shape of a doughnut The type of core must be known for application purposes, and is given by the type number The number will be of the form: FT xx nn, where FT means ferrite toroid and describes the shape, xx indicates the size, and nn indicates the material type The F in FT is sometimes deleted in parts lists, and the core defined as a T-xx-nn A chart is provided by Amidon that gives the dimensions, and a description of the properties of the different types of material, along with a lot of other physical data Some of these data are also available in the annual ARRL publication The ARRL Handbook for the Radio Amateur (the same material has appeared in earlier editions also) Tables are derived in part from both Amidon and ARRL sources From these tables, you can see the sizes and properties of various popular toroids These tables, incidentally, are not exhaustive of either the variety of toroids available, or all of the properties of the toroids mentioned Using the nomenclature mentioned, a T-50-2 core refers to a core that is useful from 1 to 30 MHz, has a permeability of 10, is painted red, and has the following dimensions: OD = 0500 in (127 cm), ID = 0281 in (0714 cm) and a height (ie, thickness) of 0188 in (0448 cm)
Toroidal transformers
A magazine reader once asked a question of this author concerning the winding protocol for toroidal transformers as seen in textbooks and magazine articles My correspondent included a partial circuit (Fig 24-13A) as typical of the dilemma The question was How do you wind it and a couple of alternative methods were proposed At first I thought it was a silly question because the answer was obvious,
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