How do they work and how important are they.
Transmission lines are not only relevant to radio but also to power companies. The principles are the same.
Either sort of transmission line (balanced or coax) is considered first as if it has infinite length. If a voltage is applied to the end of the prallel conductors, current will flow because there is an excess (or lack) of charge carriers on the end closest the applied voltage and, initially, neutral on the other. This is the same as saying there is a capacitance that will be charged up.
Because this hypothetical transmission line is infinite in length, the first bit of wire, now having and excess or lack of carriers, will transfer some of this charge to the next bit and so on. So long as there is no end, this process will continue forever.
The current flowing into the end of the wire will be subject to two effects. A transmission line is two pieces of conductor separated by a small distance and so there will be a capacitance between them. Electrical current travels at the speed of light (or close to it). Although light is very fast, its speed is not infinite. It takes time for the current to build up from one piece of wire to the next. There is therefore an apparent inductive effect. (Inductance resists a change in current.) This will be simply by virtue of its length (the time difference between one place and another so to speak).
The inductance resisting a change of current then flowing into a capacitance and the equal and opposite currents, makes a balanced transmission line look like the following:-
Note this is a lossless line where resistive components are insignificant.
The characteristic impedance of the line is the value of a resistor into which the same current would flow.
Suppose now we chop the transmission line short and place a resistor on the end. A typical characteristic impedance for balanced line used in radio work is 300Ω so consider placing a 300Ω resistor on the end of the line. (NOTE: transmission line can have ANY impedance determined by the conductor diameters, separation and dielectric constant of the separating material.)
The 300Ω resistor will behave exactly the same as an infinite length of line. The first part of the line will therefore behave as if there is still an infinite length of transmission line still connected to it.
Coax is different but not a lot. In this case, one conductor is completely surrounded by the other. The electric and magnetic effects of the inner conductor are completely contained by the outer. If coax is used to wind a coil, the inner conductor will have no effect and will not be affected by external magnetic or electric effects. There will be some effect on the inner but only in sympathy with the outer, not of some other conductor.
With coax, there are equal and opposite return currents but these are contained within the outer conductor and on the inner surface of the outer conductor. This is not because of the skin effect. Technically, the skin effect is caused by eddy currents within the conductor.
The currents on the inner surface of the outer conductor must be equal in magnitude and opposite in phase to the currents on the inner conductor. They just simply can't be anything else. Because the inner conductor is completely surrounded, and current in this conductor will produce a magnetic field. This field will induce exactly the same currents (except opposite in phase) in the outer conductor's inner surface. Any imbalance at all must therefore be conducted on the outer surface. The skin effect has nothing to do with it.
Since the return currents are on the inside surface, the outside surface will be a virtual ground along its length (provided the line is properly terminated). Coax therefore looks more like the following:-
Another way to consider unbalanced line is to consider it as half of a balanced line split down the middle thus:-
Either way makes no difference.
Typical coax used in radio is 50Ω although there is no particular reason for this. If radios were made to work into 25Ω then 25Ω transmission line would work as well.
The same situation occurs if 50 ohn line is terminated with a 50Ω resistor or left open circuit or shorted.
BALANCED AND UNBALANCED LINE DIFFERENCES
Because the outer conductor of a piece of coax is a virtual ground along its length, it doesn't matter how long it is provided it is correctly terminated. This usually means an antenna with an impedance the same as the characteristic impedance of the line. The line can be any length.
Balanced feeder doesn't radiate because the magnetic fields of both conductors are cancelled out. Neither side is a virtual ground, each carrying equal and opposing currents.
Provided the transmission line, either coax or balanced feeder, is correctly terminated with a resistance equal to the characteristic impedance, it doesn't matter how long it is. If the termination is not the same as the Z0 of the line, changing the length of the feeder will change the tuning.
CHARACTERISTIC IMPEDANCE AND FREQUENCY
On the surface it appears the characteristic impedance of a transmission line should be frequency dependant. It is to some extent because the inductance per unit length of a straight conductor is frequency dependant. (See the page on transformers.) The capacitance per unit length is also frequency dependant but not so much.
As it turns out, these two factors somewhat balance each other out.
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I think that's pretty fair, don't you?