The "narrow-band" methods described below cover a very much smaller span of frequencies, by comparison with the broadband methods described above. Antenna matching methods that use transformers tend to cover a wide range of frequencies. A single, typical, commercially available balun can cover frequencies from 3.5–30.0
MHz, or nearly the entire
shortwave radio band. Matching to an antenna using a cut segment of transmission line (described below) is perhaps the most efficient of all matching schemes in terms of electrical power, but typically can only cover a range about 3.5–3.7
MHz wide – a very small range indeed, compared to a broadband balun. Antenna coupling or feedline matching circuits are also narrowband for any single setting, but can be re-tuned more conveniently. However they are perhaps the least efficient in terms of power-loss (aside from having no impedance matching at all!).
Transmission line antenna tuning methods The insertion of a special section of transmission line, whose characteristic impedance differs from that of the main line, can be used to match the main line to the antenna. An inserted line with the proper impedance and connected at the proper location can perform complicated matching effects with very high efficiency, but spans a very limited frequency range. The simplest example this method is the
quarter-wave impedance transformer formed by a spliced section of mismatched transmission line. If a quarter-wavelength of 75 Ohm coaxial cable is linked to a 50 Ohm load, the
SWR in the 75 Ohm quarter wavelength of line can be calculated as 75Ω / 50Ω = 1.5; the quarter-wavelength of line transforms the mismatched impedance to 112.5 Ohms (75 Ohms × 1.5 = 112.5 Ohms). Thus this inserted section matches a 112 Ohm antenna to a 50 Ohm main line. The coaxial transformer is a useful way to match 50 to 75 Ohms using the same general method. A second common method is the use of a
stub: A shorted, or open section of line is connected in parallel with the main line. With coax this is done using a 'T'-connector. The length of the stub and its location can be chosen so as to produce a matched line below the stub, regardless of the complex impedance or
SWR of the antenna itself. The
J-pole antenna is an example of an antenna with a built-in stub match.
Basic lumped circuit matching using the L network The basic circuit required when lumped capacitances and inductors are used is shown below. This circuit is important in that many automatic antenna tuners use it, and also because more complex circuits can be analyzed as groups of L-networks. This is called an L network not because it contains an inductor, (in fact some L-networks consist of two capacitors), but because the two components are at right angles to each other, having the shape of a rotated and sometimes reversed English letter 'L'. The 'T' ("Tee") network and the
π ("Pi") network also have a shape similar to the English and Greek letters they are named after. This basic network is able to act as an
impedance transformer. If the output has an impedance consisting of resistance
Rload and reactance
j Xload, while the input is to be attached to a source which has an impedance of
Rsource resistance and
j Xsource reactance, then :X_\text{L} = \sqrt{\Big(R_\text{source}+jX_\text{source}\Big)\Big((R_\text{source}+jX_\text{source})-(R_\text{load}+jX_\text{load})\Big)} and :X_\text{C} = (R_\text{load}+jX_\text{load})\sqrt{\frac{(R_\text{source}+jX_\text{source})}{(R_\text{load}+jX_\text{load})-(R_\text{source}+jX_\text{source})}}. In this example circuit,
XL and
XC can be swapped. All the ATU circuits below create this network, which exists between systems with different impedances. For instance, if the source has a resistive impedance of 50 Ω and the load has a resistive impedance of 1000 Ω : :X_\text{L} = \sqrt{(50)(50-1000)} = \sqrt{(-47500)}= j\, 217.94\ \text{Ohms} :X_\text{C} = 1000 \sqrt{\frac{50}{(1000-50)}} = 1000\,\times\,0.2294\ \text{Ohms} = 229.4\ \text{Ohms} If the frequency is 28 MHz, As, :X_\text{C} = \frac{1}{2\pi fC} then, 2\pi fX_\text{C} = \frac{1}{C} So, \frac{1}{2\pi fX_\text{C}} = C = 24.78\ p \text{F} While as, X_\text{L} = 2\pi fL\! then, L = \frac{X_\text{L}}{2\pi f} = 1.239\ \mu \text{H}
Theory and practice A parallel network, consisting of a resistive element (1000 Ω) and a reactive element (−
j 229.415 Ω), will have the same impedance and power factor as a series network consisting of resistive (50 Ω) and reactive elements (−
j 217.94 Ω). By adding another element in series (which has a reactive impedance of +
j 217.94 Ω), the impedance is 50 Ω (resistive).
Types of L networks and their use The 'L'-network can have eight different configurations, six of which are shown here. The two missing configurations are the same as the bottom row, but with the parallel element (wires vertical) on the right side of the series element (wires horizontal), instead of on the left, as shown. In discussion of the diagrams that follows the
in connector comes from the transmitter or "source"; the
out connector goes to the antenna or "load". The general rule (with some exceptions, described below) is that the series element of an 'L'-network goes on the side with the lowest impedance. So for example, the three circuits in the left column and the two in the bottom row have the series (horizontal) element on the
out side are generally used for
stepping
up from a low-impedance input (transmitter) to a high-impedance output (antenna), similar to the example analyzed in the section above. The top two circuits in the right column, with the series (horizontal) element on the
in side, are generally useful for
stepping
down from a higher input to a lower output impedance. The general rule only applies to loads that are mainly
resistive, with very little
reactance. In cases where the load is highly
reactive – such as an antenna fed with a signal whose frequency is far away from any resonance – the opposite configuration may be required. If far from resonance, the bottom two
step down (high-in to low-out) circuits would instead be used to connect for a step up (low-in to high-out that is mostly reactance). The low- and high-pass versions of the four circuits shown in the top two rows use only one inductor and one capacitor. Normally, the low-pass would be preferred with a transmitter, in order to attenuate harmonics, but the high-pass configuration may be chosen if the components are more conveniently obtained, or if the radio already contains an internal low-pass filter, or if attenuation of low frequencies is desirable – for example when a local
AM station broadcasting on a
medium frequency may be overloading a
high frequency receiver. The '
Low R
, high C
' circuit is shown feeding a short vertical antenna, such as would be the case for a compact, mobile antenna or otherwise on frequencies below an antenna's lowest natural
resonant frequency. Here the inherent
capacitance of a short, random wire antenna is so high that the 'L'-network is best realized with two
inductors, instead of aggravating the problem by using a capacitor. The '
Low R
, high L
' circuit is shown feeding a small
loop antenna. Below resonance this type of antenna has so much
inductance, that more inductance from adding a coil would make the reactance even worse. Therefore, the 'L'-network is composed of two capacitors. An 'L'-network is the simplest circuit that will achieve the desired transformation; for any one given antenna and frequency, once a circuit is selected from the eight possible configurations (of which six are shown above) only one set of component values will match the
in impedance to the
out impedance. In contrast, the circuits described elsewhere have three or more components, and hence have many more choices for inductance and capacitance that will produce an impedance match – usually at least two, if not a continuum, a few of which may be "bad", i.e. will cause a resonance inside the ATU that results in high loss. Radio operators must experiment and test the available settings, and use informed judgement to choose the best among those possible adjustments that can all match the same impedance. ==Antenna system losses==