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Types of L-networks and their uses

The 'L'-network can have eight different configurations which are shown in the diagrams at the right.

All eight possible ‘L’-network circuits

In discussion of the diagrams that follows, the in connector comes from the transmitter or "source" on the left; the out connector goes to the antenna or "load" on the right. Step up means step out up to in, an increase in transformed resistance coming from the antenna to the transmitter; step down means step out down to in, a decrease in transformed resistance coming from the antenna to the transmitter.

Common use

The low- and high-pass versions of the four circuits shown in the top two rows use only one inductor and one capacitor. Normally, low-pass would be preferred with a transmitter, in order to attenuate possible harmonics, but the high-pass configuration may be chosen if the components are more convenient, 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. It is also possible that one or the other of the low-pass or the high-pass networks may have lower enough loss to make it preferred.

In the next-to-bottom row, the Low R, high C circuit on the left 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. In the case of the straight wire, or linear antenna, the inherently capacitive reactance of a short antenna is so high that the L-network is best realized with two inductors, instead of aggravating the problem by using a capacitor.

In the bottom row, the Low R, high L circuit is shown feeding a small loop antenna. Since small loops are by definition far below any self-resonance, this type of antenna always shows inductive reactance, so adding even more inductance by using a coil in the matching circuit would make the reactance even worse. Hence, the L-network composed of two capacitors is preferred. When used for antenna feedpoint matching, this circuit is called an omega match (a variety of gamma match, with both series and parallel capacitors).

The bottom two circuits in the right hand column, High R, high C and High R, high L, are rarely used on their own, but are included in order to show the complete set of all possible L-networks. These two circuits are also used when analyzing more complicated matching networks as combinations of 'L'-networks.

Proper orientation

Without exception, the resistance connected to the horizontal, series element of an L-network must be higher than the reciprocal of the conductance (= resistance, when reactance-free) connected to the vertical, parallel element on the opposite side. Reactance increases conductance, but otherwise the "up" and "down" orientations have nothing to do with changing either the reactance or the total impedance: Only resistance and conductance matter.

Step up: high   ⁠1/ G  ⁠ ┌─ low   R           Step down: low   R ─┐ high   ⁠1/ G  ⁠

where R is resistance and G is conductance (conductance is the reciprocal of resistance only on special occasions).

So for example, the four circuits in the left column that have their series (horizontal) element on the out side are used for stepping up from a low-resistance output (antenna) to a higher-resistance input (transmitter), similar to the example analyzed in the section above. The circuits in the right column, with their series (horizontal) element on the in side, are generally useful for stepping down from a higher output (antenna) resistance to a lower input resistance (transmitter).

The orientation rule only applies to the resistive part of the load, not its total impedance, so orienting the network based on a meter which only indicates total impedance, but not its separate parts, may require matching by elaborate trial-and-error. 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 configuration actually required by the resistances may be opposite the configuration estimated from the total impedance inferred from an SWR meter.

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Types of L-networks and their uses

The 'L'-network can have eight different configurations which are shown in the diagrams at the right.

All eight possible ‘L’-network circuits and there use

Circuit selection

If the load impedance is plotted on a Smith Chart, it will fall into one of the four regions shown. In each region are numbers indicating which circuit can be used to match an impedance in that region. For example, an impedance that falls within the small right circle labled R>50 can be matched using circuits 1 or 3. For a complex impedance falling anywhere in the chart either 2 or 4 different circuits could be used so additional criteria may be used to decide which circuit to choose. This chart was made with 50 ohms at the center. For matching to to other values of R such as 75 ohms, that value should replace 50 everywhere in the Smith Chart.

Additional selection criteria

The low pass circuits shown in the top row (1 and 2) use one inductor and one capacitor. Normally, low-pass would be preferred with a transmitter, in order to attenuate possible harmonics. The high-pass configuration shown in the second row, (3 and 4) may be chosen if the components are more convenient, 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.

In some cases it may be desirable that the circuit either pass or block DC currents. Thus the series (horizontal) component should be either an L or a C. In addition, it may be useful for the phase shift across the network to be either advanced or delayed.

In automatic tuners typically either circuit 1 or 2 is chosen. Many commercial autotuners can switch the C to either the left or right side of the inductor, thus both circuits 1 and 2 are available without additional components. As shown by the green and red sections of the Smith Chart, these two circuits can cover all possible loads, provided the minimum and maximum values of the inductor and capacitor are sufficient.

Loads such as a small transmitting loop may be highly inductive. The impedance will fall well into the L dominant region of the Smith Chart. They can make use of circuit 6 although most designs feed them via an even smaller coupled loop. Short vertical antennas such as used for HF mobile, are C dominant and can be easily matched with circuit 8. However with both of these examples, there are three other circuit options.

Measuring instrument limitations

Older SWR meters do not indicate complex impedance, so they are not very helpful for determining which circuit to use in an L network. Antenna analyzers, however, can separately show the resistive and reactive parts of the antenna impedance, and are suitable for selecting the orientation of an 'L' network. The most convenient of these analyzers are able to plot the complex impedance on a Smith Chart display. When an instrument indicates the complex series impedance, but not the shunt (parallel) equivalent, formulas or a calculator can be used to make the conversion to the parallel values. When complex impedance information is not available, a circuit can be chosen by assuming that a high impedance can be matched using circuit 1 and a low impedance using circuit 2. However where there is a significant reactive component, this simplified rule may fail.

Q and Phase shift

Unlike more complex networks, the L network does not allow independent choice of operating Q and phase shift. High Q leads to more loss and a narrow operating bandwidth. It is made greater when the load impedance differs greatly from the impedance to be matched. Phase shift can be made to either lead or lag by circuit choice, but like the Q, its value is determined by the impedance ratio. Phase shift is only important if two or more loads are to be fed, such as in AM broadcast directional arrays.

references (m,n, and o) can be deleted. Additional sources can be added, suggestions welcome)