The Balanced-L Network

L. B. Cebik, W4RNL

The demise of the link-coupled antenna tuner has left a hole in the array of available antenna tuners. The link-coupled tuner had been the mainstay among tuners for handling antennas that present a wide range of impedance values to parallel transmission line and required--ideally--a balanced coupler to coincide with the transmission line balance. The multi-band doublet, the horizontal or vertical multi-band loop, and a host of phased arrays come to mind as antennas that achieve the greatest efficiency with a balanced antenna tuner. However, as of this writing (12-2002), despite some initial hope, no maker has come forward with a commercial link coupled tuner to replace the long-gone U.S. Johnson MatchBox or the German Annecke ATU.

The single-ended network--including the PI, T, and L--is inherently unsuited to matching the impedances of such antennas, as presented to the ATU terminals, to the standard 50-Ohm unbalanced outputs of current transmitting and receiving equipment. Placing a 4:1 balun at the output terminals of such tuners has always been a source of concern, since the impedance at the terminals may be highly reactive, a condition unsuited to many balun designs. As well, the terminal impedance may also be low as the line transforms the impedance continuously along each half wavelength, and a 4:1 balun only succeeds in making it lower.

A 1:1 choke balun has been used with some success. As Fig. 1 shows, placing this choke-balun at the shack-entry point can serve two purposes. A. It converts the balanced line input to an unbalanced condition by essentially suppressing currents that would otherwise flow on the outside of the coax braid. B. It permits the installation of a good earth ground at the shack-entry point, which has some advantages for safety and for further isolation of equipment from common-mode currents.

However, the advantages come at a price. The SWR on the coax inside the shack remains in many cases very high. The losses in this line due to SWR increase with both frequency and the length of the line and function as a multiplier on the basic loss per unit length of the coax line selected. The keys to minimal inside line loss are then to use as short as feasible a length of coax from the entry-point to the tuner and to use the lowest-loss coax that one can obtain. Even at QRP power levels, using a large diameter, low-loss length of coax for this run is extremely advisable.

The Balanced L-Network

Recent times have seen the development of balanced network tuners. Fig. 2 shows a comparison between the single-ended L-network and its balanced counterpart, set up here for up conversion and in a low pass configuration. (A down conversion L-network would place the capacitor at the input side of the network. A high- pass configuration would use series capacitors and shunt or a parallel inductor.) The values required for converting a single-ended network to a balanced network are in the aggregate the same as those for the single-ended network. However, the inductors in the lower part of the figure are in series, so each has 1/2 the value of the required single-ended inductor.

The capacitor, as shown, represents the total capacitance required across the network output to effect a match for a given impedance condition. With a single capacitor, we cannot place an earth ground at the line center as an aid to effecting balance between the two legs of the transmission line. In most, but not all, practical applications, this ground is not necessary. However, should we wish to implement such a line-centered ground, we may change the capacitor to a split-stator type and ground its common. Since the two halves of the capacitor must in series yield the required total capacitance for a match under given output terminal conditions, each half of the capacitor must have twice the capacitance of the single unit shown in the figure. This requirement result in large capacitors, especially where high power and high voltage across the plates might be anticipated. The vastly increased space requirements (or cost requirements for one who purchases such a component) generally has led designers to use single-section capacitors.

The 1:1 balun in the balanced L-network appears at the input side of the network, between the balanced L and the line connector for the transceiving equipment. Except for brief periods during initial tune-up, the balun operates under ideal or close to ideal conditions, that is, with 50 Ohms resistive at its output terminals. Hence, most standard trifilar or bead-choke 1:1 balun designs operate at very high efficiency levels.

Fig. 3 shows the balanced L-network--and its single-ended counterpart--set up as a down converter using a low-pass configuration. If we had used a high-pass configuration, with series capacitors and a parallel or shunt inductor, we would achieve a circuit identical to that of the beta or hairpin match. The hairpin match achieves its shunt inductive reactance with a shorted transmission line stub instead of a "lumped" inductor. Otherwise, all of the principles applicable to the up-converting L also apply to the down-converting L, whether single-ended or balanced.

Balanced L-Networks vs. 3-Component Networks

Commercial implementations of the balanced L-network are beginning to appear. In general, they are offered in preference to balanced PI-networks and balanced T-networks. Fig. 4 shows the general outlines of both of these 3-component networks in single-ended configurations. The PI is a low-pass configuration, while the T is a high-pass configuration.

The 3-component network offers a distinct advantage over the L-network. One may effect a match on a given frequency for any "in-range" impedance without switching a component from the output to the input side of the network (or vice versa). As well, one may even effect a match for a 50-Ohm resistive load at the antenna terminals of the tuner. In most cases, the user does not know what the load impedance is, and the ability to tune any load within the overall tuner range is a convenience.

However, we pay a price for the convenience. For virtually any load impedance, the L-network has lower losses than the T or PI. We may define a factor for any of the networks and call it (following Terman) delta. In recent times, we have come to refer to the factor as the network Q or the working Q of the network. For the L-network,

Delta = SQRT ((Ri/Ro)-1)

where Ri is the network input impedance and Ro is the network output impedance.

By itself, delta is simply a number. However, the network losses are directly related to the ratio of delta to the unloaded Q of the network components. In most--but not all-cases, the limiting component Q is that of the inductor. Maintaining a low loss network of any type requires that we uses network components with the highest possible unload values of Q.

The calculations of delta for PI and T tuner networks are more complex. In the series "Antennas From the Ground Up, see the article ATUs, Delta, and Tuner Losses for further information on 3-component network losses, and the following item as well. The general outcome is this: for any matching conditions within the range of both an L-network and a PI or a T network, the L-network sill show lower losses (assuming that the components in all cases have the same unloaded Q values).

However, the L-network, whether single-ended or balanced has a second inconvenience besides the requirement for switching the shunt component when going from up-conversion to down-conversion and back. The component values required to effect a match for impedances within a ratio of about 1.5:1 (or .67:1 for down conversion) relative to the input impedance tend to be impractical in a wide-band antenna tuner. Hence, for matching impedance above 35 Ohms but below about 75 Ohms, one must simply omit the L-network and feed the antenna directly (accounting for the shift from unbalanced coax to a balanced line, of course).

Commercial implementations of the balanced network tuners tend to opt for the L- network because it achieves economy. Anyone who has priced high-voltage variable capacitors of either standard or vacuum design will easily note the saving accrued by eliminating one from the circuit. A patch panel, switch, or relay tends to be far less expensive. While this economy also affects ATU home- builders, the lower losses of the 2-component network may also be appealing, while the inconvenience of switching network ends with the shunt component may be accepted as the appropriate trade-off.

Balanced L-Network Component Values

The next question concerning a balanced L-network concerns the components that we must use to effect a match with various loads. Using calculation methods developed by Brian Egan, ZL1LE, and available on recent version of HAMCALC from VE3ERP, we can survey those values from 160 to 10 meters. Table 1 provides calculated data for some up- and down-conversion loads that are purely resistive.
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 1.  Calculated Values for L-Network matching to various Resistive loads
from 15 to 2500 Ohms.  All inductance values (L) in uH, all capacitance values
(C) in pF.  Loads are in Ohms.

Up-Conversion     Load = 100  Load = 250  Load = 500  Load = 1000 Load = 2500
Freq.             L     C     L     C     L     C     L     C     L     C
1.8               4.4   884   8.8   707   13.3  531   19.3  385   30.9  248
3.75              2.1   424   4.2   340   6.4   255   9.3   185   14.9  119
7.15              1.1   223   2.2   178   3.3   134   4.9   97    7.8   62
10.125            .79   157   1.6   126   2.4   94    3.4   69    5.5   44
14.175            .56   112   1.1   90    1.7   67    2.4   49    3.9   31
18.118            .44   88    .88   70    1.3   53    1.9   38    3.1   25
21.225            .38   75    .75   60    1.1   45    1.6   33    2.6   21
24.94             .32   64    .64   51    .96   38    1.4   28    2.2   18
29.0              .27   55    .55   44    .82   33    1.2   24    1.9   15

Down-Conversion         Load = 35   Load = 25   Load = 15
Freq.                   L     C     L     C     L     C
1.8                     2.0   1158  2.2   1768  2.0   2701
3.75                    .97   556   1.1   849   .97   1296
7.15                    .51   291   .56   445   .51   680
10.125                  .36   206   .39   314   .36   480
14.175                  .36   147   .28   225   .26   343
18.118                  .20   115   .22   176   .20   268
21.225                  .17   98    .19   150   .17   229
24.94                   .15   84    .16   128   .15   195
29.0                    .13   72    .14   110   .13   168
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The table uses amateur-band center frequencies for all but the limiting bands, where we use a low frequency for 160 meters and a high (but not the highest) frequency on 10 meters.

Maximum and Minimum Component Values

For up-conversion, the maximum component values are all feasible, even on 160 meters. However, for down-conversion, the lower the impedance, the greater the chances for requiring a capacitance value that exceeds practical implementation as a standard-construction high-voltage air-variable capacitor. A 3000-pF, 5-kV or higher air-variable is a very large unit, indeed.

The inductor--with respect to maximum required component values--is not a problem. The table lists the total for the 2 series inductors, so each inductor requires only half the total. A pair of inductors, each with a 20 uH maximum value, would easily handle the required load.

The troublesome part of the patterns of required component values concerns minimums. The values given are--in a practical circuit--the sum of the component values and any stray capacitances and inductances within the overall ATU unit. The minimum capacitance available is partly a consequence of capacitor construction. Many capacitors--especially military surplus units found at hamfests--use heavy frames with full size end plates and even bottom plates that cover most of the bottom of the capacitor. Such units may have a minimum capacitance of up to 30 pF for a maximum capacitance of 150-200 pF. In contrast stand the E. F.Johnson (later, Cardwell) high-voltage units that have small trapezoidal end plates and a bar running the length of the unit to connect the end plates and permit mounting. For the same maximum capacitance, the minim is only 12-15 pF. Even better are some current designs that use non-conductive end plates and front-to-rear bracing bars. Their minimum value may be as low as 8-9 pF. Some capacitors also use plate-shaving techniques to further lower the minimum capacitance.

However, minimum capacitance is not solely a function of the capacitor structure. The plates and other components of the network may be at a different potential from each other, from nearby leads, and from the metal ATU case. In all of these instance, we have a level of capacitance that we cannot eliminate with redesign of the circuit and the overall unit. The simplest way to tell if a case is introducing stray capacitance is to remove it and check the ATU settings under very low power and otherwise controlled test conditions.

As the basic table shows, minimum inductance can be a major limitation in down conversion. All is not lost in this regard, even if the minimum inductance that we can obtain is higher than the required component value. Down conversion tends to be very broad-band, and one can obtain usually a match to within less than 1.5:1 50-Ohm SWR, a useful if not perfect value.

Adding to the series combination (additive) of the two inductors in a balanced L-network is the inductance of the leads. The more complicated the switching-- whether we are switching in a fixed capacitor to achieve a high value or switching the capacitor from the output to the input end of the network--the more likely we are to find stray inductance that raises the minimum value that we may obtain. A secondary problem associated with stray inductance within an ATU is the fact that is usually has a low unloaded Q. Hence, the loss level of the circuit rises.

The appropriate countermeasures, of course, include a detailed inspection of the circuit to see if one can redesign component placement to keep leads as short as feasible. With large components designed for high power duty, we can do only so much in this arena. We can also try replacing the case with a non-conductive case. To a large measure, any radiation from an ATU is a function of linear leads that do nothing to confine the fields that surround them. Hence, it is a bit of a gamble to move to a non-conductive case. However, it is worth a try. If the radiation is too high and eludes efforts to reduce it, then one can simply use a larger case within which we try to center the network components, that is, we try to keep the network components well-spaced from the case walls.

Reactive Loads

We have based our initial survey of the conditions under which a balanced L- network must operate on resistive loads. As a general guide, let's look at some sample cases of reactive loads. In Table 2, we shall examine some high- and low- impedance loads, each impedance having a 45-degree phase angle. Hence, we shall match 100 Ohms resistance with +j100 Ohms and with -j100 Ohms. In addition, we shall only look at 160, 80, and 10 meters, the HF frequencies likely to represent the limits of an ATU that we might construct.
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 2.  Calculated Values for L-Network matching to various Resistive +/-
Reactive loads from 100 to 2500 Ohms.  All inductance values (L) in uH, all
capacitance values (C) in pF.  Loads are in Ohms.

Up-Conversion           R = 100     R = 100     R = 2500    R = 2500
                        X = j100    X = -j100   X = j2500   X = -j2500
Freq.                   L     C     L     C     L     C     L     C
1.8                     7.7   1208  7.7   324   44.0  194   44.0  158
3.75                    3.7   580   3.7   155   21.1  93    21.1  76
29.0                    .48   75    .48   20    2.7   12    2.7   10

Down-Conversion         R = 35      R = 35      R = 15      R = 15
                        X = j35     X = -j35    X = j15     X = -j15
Freq.                   L     C     L     C     L     C
1.8                     2.8   2062* 5.1   1158  0.7   2701  3.4   2701
3.75                    1.3   990*  2.5   556   .34   1297  1.6   1297
29.0                    .17   128*  .32   72    .04   168   .21   168
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The starred entries in the down-conversion portion of the table indicate that the required configuration of the balanced L-network is for up-conversion, that is, with a shunt output capacitor. Note the high values of capacitance required for both 160 and 80 meters. such values will likely fall outside the range of what we build into either a 160-10-meter or an 80-10-meter ATU.

At the highest frequency for which I calculated values, down conversion requires the smallest inductance values. 0.2 uH will be difficult enough to attain with the best components; 0.04 uH is outside of practical reality in a multi-band tuner.

For an interesting home-brew balanced-L tuner using tapped coils, see the website of Adam, N4EKV:

Why 160 or 80 Meters Through 10 Meters?

I once designed an SPC single-ended network tuner for 20-10 meters due to the relatively poor performance on my C-L-C single-ended T-network tune on the highest bands (12, 10). No single cause attended the weakness in the 80-10-meter ATU, but the component minimum values and a tight-fitting metal case all contributed to 10-meter problems with a 100' doublet. The SPC unit used Johnson 4.5 kV air variables (a 50 pg single unit and a 50-50 pF split stator), and the rotary inductor had a maximum inductance of 6 uH. The case was no deeper than the original, although the components were considerably shorter. My case was both wider and higher than the commercial case. These measures doubled--at least--the range of matchable impedances, and the component Q was sustained at least through 30 MHz.

Similar thinking is applicable to a balanced L-network. Although we tend to think of an 80-10-meter ATU as some sort of standard, only our demand for convenience has created that standard. Neither commercial nor handbook designs covering those bands tend to address either the range of matchable impedances as it changes with frequency or the loss of component Q with increasing frequency due to strays.

Consequently, it is up to the individual ATU builder to design a unit to meet his or her needs and having the highest component Q available. If attaining a wide tuning range on the upper HF bands requires one to reduce the coverage to 20-10 meters to achieve this goal, then perhaps this is the route to go. In many cases, we shall have to suffer with the shortcomings of a wide-band unit, since it is difficult to carry individual ATUs for each band to a DXpedition on a remote island. Nevertheless, we are not under such restrictions at the home station. As well, it is often easier to find rotary coils with low values at good prices, since they are in far less demand then units with a maximum inductance ranging from 10 to 30 uH.

These notes certainly do not cover every aspect of balanced L-networks. However, they may serve to alert you to both the potentials and the limitations of these substitutes for the link-coupled tuner.

Updated 12-13-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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