Artificial Lines

Sometimes a certain amount of time delay must be interposed between one circuit and another. Or, if the length of a transmission line is not an exact multiple of 90°, some means must be found to increase its length to the next higher multiple of 90°. For either of these purposes, artificial lines are used. They may operate at a single frequency or over a range of frequencies. They may be tapped for adjustment to suit any frequency in a given range, so that impedance and line length are correct. The configuration may be either T or π, high- or low-pass.

Fig. 138. Artificial line relations.

Figure 138 shows these four combinations for any electrical length θ of line section in degrees. It is assumed in this figure that the line operates at a single frequency and is terminated in a pure resistance equal in value to the line characteristic impedance Z₀. Figure 139 is the vector diagram for a leading phase shift pi-section line of 90° electrical length. Proportions of L and C are somewhat different in these line sections than in wave filters.

Fig. 139. Vector diagram for 90-degree line length.

To obtain approximately constant time delay over a range of frequencies, several constant-K low-pass filter sections may be used, each having a cut-off frequency high enough so that the phase shift is proportional to frequency. The time delay per section is then θ/2πf at any frequency in the range, and θ = 2πf√(LC), where 8 is the phase shift in radians, L is the inductance per section, and C is the capacitance per section. In Fig. 139, E_R = E_s. If the section were terminated in impedance higher than Z₀, E_R > E_s. The line section is then a kind of transformer, although the ratio E_R/E_S varies with frequency. Ninety-degree line sections are often used at high frequencies to obtain transformation of voltage.