Cutoff Frequency of Coil-Loaded Circuits

If the losses are neglected, from equation 70 the circuit will cut off at a frequency of

Figure 10. A coil-loaded cable is equivalent to a low-pass filter.

When L is the final self-inductance in henrys in each loading section (approximately the sum of the inductance added to each wire by the coils), S is the spacing between coils in miles, and C is the capacitance in farads per mile; f_c will be the cutoff frequency in cycles per second.

The various equations derived for low-pass filters also give approximate solutions for loaded cable circuits. Thus, equation 73 becomes

In loading a cable of C farads capacitance per mile, there are two variables: these are the inductance of the coils and the spacing, and these determine the cutoff frequency and final characteristic impedance of the cable.

For the given cutoff frequency and coil inductance, the spacing S in miles, for a cable of C farads per mile, is, from equation 16

and from equation 17 in terms of the characteristic impedance

If equations 18 and 19 are equated,

and if this is placed in equation 18,