Transformer, Impedance

a device for transforming the impedance of a microwave transmission line (a hollow or dielectric wave guide, a long coaxial line, or a strip line) in order to match it with a load or to obtain a specified mismatch. Impedance transformers are used in microwave engineering; they also include devices for transforming types of waves in radio wave guides.

In most impedance transformers the matching or mismatching effect is based on the use of the transformation properties of sections of a transmission line that have discontinuities. The discontinuities produce reflections (perturbations) of the waves, resulting in a change of the equivalent resistance and/or reactance of the corresponding section of the line. The discontinuities are created by pins, diaphragms, short-circuited stubs, dielectric bushings, wave-guide joints of unlike cross sections, and so on.

In the general case a transformer can be treated as a passive, linear two-terminal-pair network with distributed parameters and negligible losses; a microwave source is connected to its input, and a load to its output. The input impedance Z_in of such a network is a function of the characteristic impedance ρ of the section of wave guide or line, its length l, the effective wavelength λ in the wave guide, and the load impedance Z_L. The desired impedance transformation can be obtained by varying these quantities. For example, if l = λ/4, then Z_in = ρ²/Z_L; if the load is a pure resistance, Z_in = R_in = ρ²/R_L is also a pure resistance. Such a transformer, called a quarter-wave transformer (Figure 1, a and b), is used to match two lines having different values of ρ.

If the value of the load being matched varies over a wide range, a short-circuited stub is used (Z_L = 0, Z_in = jρ tan 2πl/λ), in which the length is adjusted, for example, by a plunger. Transformers may have one, two, or three stubs (Figure l,c). Reactive pins, dielectric bushings (Figure l,d), and diaphragms are frequently used instead of stubs. Transformers using a double tee junction with short-circuited E- and H-arms (Figure l,e) are common.

The degree of matching produced by an impedance transformer is described by the value of the standing-wave ratio (SWR). As a rule, the match is considered satisfactory if the SWR is ~ 1.2–1.3 (when making accurate measurements it is 1.05–1.1). Impedance transformers may have fixed or adjustable parameters. A transformer is usually tuned to maximize the power delivered to the load (accurate adjustments are made by using a measuring line or a panoramic SWR meter). A distinction is made between narrow-band transformers, in which the SWR when adjusted remains below a given level in a frequency band not larger than 1 percent of the average frequency, and broadband transformers, in which the band width is 5–10 percent and more.

Impedance transformers for transforming wave types are made in the form of matched (SWR ≤ 1.2) coaxial-wave-guide junctions, strip-line-wave-guide junctions, and wave-guide-waveguide junctions. The main elements of such transformers are exciters of specific types of waves (metal pins, slots, and gratings of various shapes) and devices for suppressing undesirable types of waves (smooth, extended junctions, absorbers, filters, and so on).