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Twelfth wave TL transformers

The twelfth wave transformer is a narrow band (ie tuned) impedance transformer. It provides a sometimes convenient means of transforming from Z1 to Z2 when transmission lines with Zo=Z1 and Z2 are readily available.

For example, to transform a 75Ω load to 50Ω, it is a series cascade of a section each of 50Ω line and 75Ω line of length nominally 30° (or λ/12) each between the 75Ω load and 50Ω line (and vice-versa). It is a series cascade of a section each of 75Ω line and 50Ω line of length nominally 30° each between the 50Ω load and 75Ω line (and vice-versa).

Telfth wave transformer section lengths

Twelfth wave transformer section lengths

The exact length of the sections depends on the impedance transformation ratio, as shown in the figure above.

Another simple example is to match two 50Ω antennas in parallel to a 50Ω main feedline. In this case, it is a series cascade of a sections of 50Ω line and two parallel 5oΩ lines of length nominally 30° (or λ/12) each between the 25Ω load and 50Ω line. It is a series cascade of a section each of 50Ω line and 25Ω line of length nominally 30° each between the 25Ω load and 50Ω line.


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