# Understanding Tee Networks

January 1, 2012

This month we take a more in depth look at the tee network. This impedance matching network, aptly named, has the appearance of a T. The vast majority of AM transmission facilities will have at least one of these networks somewhere in the facility. The substantial versatility of the network is the primary factor in its ubiquity.

The tee network seems almost magical as it has the ability to transform between almost any two complex impedances using only reactive elements. Remember that reactive elements are capacitors and inductors, and have essentially zero resistance. The absence of resistance in the elements comprising the network is critical as it eliminates power dissipation and associated heating. Even though ideally there is zero resistance in the components, the reality is we live in an imperfect world. Thus, some small quantities of resistance are unavoidable. The presence of these miniscule resistances is one of the reasons power is normally measured through the use of current meters at the antenna. In directional antennas, this is accounted for by a fudge factor in the mathematics.

A tee network in action

In addition to transforming two impedances, the tee network also creates controlled phase shifts. The sign and magnitude of any shift in phase across the network is a function of the arrangement and value of components in the various legs. For instance, networks where the shunt leg is capacitive tend to induce a negative, or lagging, phase shift. Conversely, networks in which the shunt is inductive, or has a positive reactance value, tend to result in a leading phase shift.

Use of particular phase shifts, in combination with power division is how directional patterns are created. Although the phase shift across the matching network for a non-directional antenna is irrelevant with regard to the radiation characteristics, it cannot be totally ignored. In cases where the antenna impedance varies wildly from the transmission line impedance, changes briskly from one sideband to the other, or other out of the ordinary cases, judicious selection of the phase shift can improve bandwidth.

## Attention to details

In addition to bandwidth considerations, care should be paid to the current in the shunt leg of the network. Changing the network phase shift will affect the current in the shunt leg for a given set of impedances. For a non-directional station, networks with a phase shift of 90 degrees are fairly common. The reasoning here is the mathematics work out quite nicely. Sometimes, however, the impedances may vary enough on the sidebands that a phase shift in this range results in a shunt leg current high enough to warrant larger components. Swinging the phase shift closer to zero degrees can result in a lower shunt leg current translating into greater savings in the component price.

- continued on page 2

The commonality of the 90-degree tee network is in some part due to the simplicity of its mathematics. The three equations that quantify the reactances in the three legs of the network are as follows:

In these equations, the subscripts 1, 2, and 3 correspond respectively to the input, output, and shunt legs. The Greek letter theta represents the phase shift across the network, and j is the imaginary operator.

In the 90-degree cases the equations collapse as a result of the trigonometric terms. The magnitude of the sine of 90 degrees is 1 and is positive if the phase angle is leading, negative if it is lagging. The cosine of 90 degrees is zero. So after substituting these values back in, we find that the reactance in each leg is nothing more than the square root of the product of the input and output resistance. If there is no reactance on either side of the network, then we are finished as long as we get the signs correct. In the leading case, as previously mentioned, the input and output legs are negative or capacitive, and the shunt is positive or inductive. For the lagging case, the situations are reversed.

We do not, however, live in a perfect world, and have to deal with load reactance. While the reactance on the input side can be eliminated if it is fed by transmission line, we find no such luxury with the load on the far side of the network. As a result, we have to correct for the reactance of the load impedance. This correction is made through the addition of an equal but opposite reactance to the value determined in the third equation above.

## Put into practice

For an example, make the assumption that we have an antenna with an impedance of 72Ω+j50. This antenna will be matched to 50Ω transmission line through the use of a 90-degree tee network. It is desired to derive the most cost effective design for the network and for this example will ignore potential concerns with the shunt leg current.

Thinking about the topology of the network, we realize that the leading phase shift will require at a minimum two capacitors and three inductors if we limit our choices to micas. The lagging phase shift will also require three inductors, but will likely only need one capacitor in the shunt leg. The lagging case looks to be more cost effective.

The magnitude of each of the leg reactances will wind up being the square root of the product of the input and output resistance values. Numerically this is 60Ω. Since we have chosen the lagging network, the shunt leg will be a negative 60Ω, and the input leg will be a positive 60Ω. The output leg is also a positive 60Ω, but we need to subtract off the 50Ω of reactance inherent with the antenna. The result is the output leg has a positive reactance of 10Ω.

Once you have designed the tee network, it may require some adjustment to ensure that it is properly set up. A good technique is to go through and initially setup each of the legs based on the design, then move back to the input to the network, and bridge it when connected to the load. The impedance measured at the input should be very close to the design. If it needs to be trimmed, minor adjustments of the shunt and input legs should do the trick. Adjust the shunt leg to bring the resistance back to the desired value. This will skew the input reactance somewhat, which can then be trimmed out by adjustment of the input leg.

The tee network appears daunting at first, but with a little study is actually fairly simple to master and understand. Its wide versatility combined with ease of design and implementation, has made it a most ubiquitous choice for use in not only AM antennas but a myriad of other applications as well.

Ruck is a senior engineer with D.L. Markley and Associates, Peoria, IL.

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