Microwave transmission circuits by Ragan George L.

Microwave transmission circuits by Ragan George L.

By Ragan George L.

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Example text

A poti(on of the yz-plane 213. -–l:icld. i,, :LDla,lc wal-c in ILCCspare. of currents and electric fields is more complicated than the assumptions of the conventional theory permit. To st~ldy these so-called “ higher This is modes, ” a more cornprchrnsive approach must be made. afforded by the application of electromagnetic thtwry to the problem. ;Vhereas the conv(’ntional theory chiefly considers cllrr<>ntsand voltages, the electromagnetic theory is primarily concerned with the electric and The conmagnetic fields associatf’d with these currents ancl voltages.

114) If we consider The factor ~ arises, of course, from the averaging process. a width a, in the z dimension of Fig. 16, the power transferred is the product of power per unit area p, and the area ab; P = ~EvHzab. (115) Since the amplitude of the current for unit width of either conducting plane is equal to the amplitude of the magnetic field, 11 = Hz; therefore the total current in width a is I = aH=, (116) and the amplitude of the voltage between planes is V = bEu. (117) Substituting Eqs. (1 16) and (1 17) in Eq.

16, the power transferred is the product of power per unit area p, and the area ab; P = ~EvHzab. (115) Since the amplitude of the current for unit width of either conducting plane is equal to the amplitude of the magnetic field, 11 = Hz; therefore the total current in width a is I = aH=, (116) and the amplitude of the voltage between planes is V = bEu. (117) Substituting Eqs. (1 16) and (1 17) in Eq. (115), \\eobtain P = ~VI, (118) which is in agreement with the result obtained by ordinary lo\v-frequency or conventional transmission-line theory.

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