James Long, Ph.D., P.E. Retired Analog and RF Consulting Engineer
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Because electric fields are conservative, the potential difference between three points can be specified by two numbers. The most commonly used pair of numbers used in electrical engineering is the difference between two of the points and the average of the difference between the those two points and the third point. The usual situation in electrical engineering for having three points is when there are two conductors that are used intentionally and a third, parasitic point, such as the earth or the cabinet that surrounds the circuitry. This situation goes back 150 years to the early days of the telegraph and telephone. Back then, the potential between two conductors was called the metallic voltage and the average difference to the earth was called the longitudinal voltage. In the area of instrumentation these are called differential and common mode. Circuits that are designed to have differential potentials and zero common mode potentials can be broken down a line of symmetry and thus are called "balanced."
In electrical circuits it is also common to have a potential between just two points, one of which as a wire and the other is a larger piece of metal that is common to all circuitry. Signals in this situation are called "single ended," or "unbalanced."
In some systems there occurs both types of signal carrying modes. A passive device is commonly used to convert, with high efficiency, signal energy between the two transmission modes. It is not necessary that both portions of the system operate at the same ratio of potential to current (impedance). These devices commonly take the form of magnetically coupled fields (transformers) for wider signal bandwidths or transmission line segments for narrower signal bandwidths. The general term for this device is derived from the concatenation of the initial syllables of the two words BALanced and UNbalanced to form the word balun. It is pronounced just like the first syllables of the two words and not like balloon or bail of hay.
Passive circuits that efficiently convert signals between two systems with different impedances, but the same single ended or balanced transmission form are not baluns. They are impedance transforming networks.
For some reason some people call all passive networks baluns just like some people call all balanced active networks Gilbert.