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All about Transmission lines

Feed the efficiency (I)

After installed your antenna and found a place for your transceiver, you have still to connect the transmitter to the antenna, usually located at some distance. This link is called the RF transmission line or using a generic term, the feeder. Its role is to carry RF power as efficiently as possible to the antenna and vice versa. However, at radio frequencies the feeder having an appreciable length compared with the working wavelength, it will also radiate power as the antenna. Our objective is thus to minimize the unwanted radiation from the feeder, in order to transfer as much power as possible to the antenna with the less losses as possible.

However, without care the power lost by radiation in the transmission line can be much higher than the resistance of conductors and dielectrics. If we cannot always prevent power loss, we can easily avoid loss by radiation.

Transmission lines radiation

To prevent loss by radiation in the feeder we can use two conductors so arranged that their respective electromagnetic field is in phase opposition from one to the other. Operated this way there will be no radiation. To meet this requirement current of each conductor must flow in opposite directions, the field being shifted of 180. But in placing two conductors very close each another (<0.01λ, or 20 cm on 20 meters band), for each alternance of the current there is a delay for that field of the first conductor reaches the second one and cancel if they are exactly 180 out of phase. As the separation is small but exists, there will be always a delay and it is practically impossible to cancel the two fields perfectly.

Transmissions lines are of two types :

- Two parallel conductors, also called parallel conductor line, open-wire or ladder line that we usually found feeding dipoles antennas

- Coaxial, in which a conductor encloses another conductor in a tube-shaped wire. The current flowing in the inner conductor is balanced by en equal current flowing in the opposite direction on the inside surface of the outer conductor. Due to a skin effect, the current flowing on the inner surface of the tube does not penetrate far enough to appear on the outer surface and therefore using a coaxial line the resulting currents flowing on the conductors inside is always equals to zero because the tube acts as a shield at radio fequencies. Other advantage, the separation or tickness of the insulation between the inner conductor and the outer one does not enter into account in reducing radiation.

Velocity factor and impedance

Whatever the current source, a main or a battery, the current flows from one point to another, from the "+" pole to the "-" one at a speed close the one of the light, so about 300000 km/s or 30 meters in 0.1 μsec. However, the insulation material used in the tube, in other words the dielectric properties of the wire reduce that velocity up to 34% (0.66) in the case of RG-58. The highest velocity factor is usually found is open parallel-conductor lines with values as high as 0.95 or 0.975 depending on the numbers of spacers and dielectric material used. Minus side, their impedance is usually high (over 300 Ω).

All transmission lines are thus associated to a "velocity factor" specific to each type of wire (RG-58, RG-213, etc). For the same reason the electrical wavelength of a physical transmission line is always shorter than the wavelength in free space.

A perfect theoretical line shows no resistance. However we know that all electrical circuits apply the Ohm's Law... That means that at radio frequencies all circuits display some resistance, that mainly depends on the input voltage.

 We can modelize the current flowing in a feeder using a battery connected to a capacitor. Thus a transmission line has capacitance. But it as inductance too.

To illustrate the coupled properties of a transmission line we can represent it as small circuits composed of inductors (coils) and capacitors which L and C values depend on the line design.

Each inductance charges the following capacitor at some rate, what, at the end of the chain,establishes the relationship between current and voltage traveling the line. In other words the transmission line display some resistance, that we conventionally call the characteristic impedance, represented by the symbol Zo. In a perfect line, offering no resistance, Zo = √(L/C). However the inductance decreases as the conductor diameter increases while the capacitance decreases as the spacing between conductors increases. Thus large conductors very closely spaced will show a relativity low impedance while a thin conductor widely spaced will show a high impedance. These properties explain why an open-wire feeder displays characteristic impedance ranging from 200-800 Ω and typical coaxial lines from 40-100 Ω.

Matched and mismatched lines

If we speak in terms of power, along a transmission line the power travels always in one direction, away from the AC source. Several cases have to be considered to understand the principle of matched and mistmatched lines :

- The perfect circuit in which a charge (practically the antenna) is inserted presenting the same electrical characteristics as a LC circuit

- The same circuit in which the load resistance is not equal to Zo

- The short circuit

- The open circuit.

Using a perfect line made of inductors and capacitors, the input power flows from one "LC section" to another without loss; the previous section makes no difference whether the next one has absorbed the power or has forward it to the next section as it had more line in the circuit. Our ultimate objective being to connect our feeder to an antenna, we need to find a way to substitute somewhere in the "LC section" a component of the same electrical characteristics, a pure resistance which value equals Zo. This way this additional resistance will absorb all the power just as will do a infinitely long transmission line in transmitting the power from one LC section to another. In this particular case the line is said to be matched. The current applies the usual Ohm's Law.

Reflection coefficient

where ρ is the reflection coefficient, Er the reflection voltage and Ef the incident or forward voltage. At right, R is the resistance of the load terminating the line. 0 ≤ ρ ≤ = 1. If the load is pure resistive, ρ is positive if R is larger than Zo and vice versa.

If the circuit ends with a resistance not equals to Zo, this additional section does no more looks like more line to the previous LC section. One said that such a line is mismatched. The result is that the resistance absorbs only a fraction of the input power, called the incident or forward power. The remainder is interpreted as reflecting back along the transmission line toward the source. The greater is this reflected power the greater is the mismatch and the larger is the percentage of incident power reflected. In the worst cases, in a short-circuit the resistance is null, and in an open circuit (without terminating resistance to close it) the resistance is infinite. In both examples all the forward power is reflected and dissipated as heat between the transmitter PA and the transmission line. In other words not the single milliwatt will reach your antenna and nobody will hear your signal. But we will see at the end of the next page that operating this way is really risky.

Next chapter

Standing waves and SWR

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