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Updated February 2021 to correct an important misstatement (thanks to John C!) One type of balun that is often used in microwave applications is the Marchand balun. First, we will start with reviewing Nathan Marchand's 1944 paper (reference provided at bottom of page). If you don't have a copy, ask us nicely and we'll send it. Then, one of these days we will develop a coaxial Marchand balun design in Microwave Office (they have a microstrip balun in their example library you might want to look at).
The Marchand balun was first reported in December 1944 issue of Electronics, titled "Transmission line CONVERSION TRANSFORMERs" (their caps, not ours), by author Nathan Marchand of Federal Radio and Telephone Laboratories.
Marchand provided an excellent means of converting from coax to a two-conductor transmission line. The article was carried in the trade journal "Electronics", which was first published in 1930. In 1965, Gordon Moore published an article with the title "Cramming more components onto integrated circuits" in Electronics, providing insight into the future of integrated circuits which became known as Moore's Law. McGraw Hill sold Electronics to Dutch company VNU in 1988, and in 1995, "Electronics" ceased publication but its DNA (and user data, breeding ground for all the spam you get at work) live on somewhere... In 2005, an offer from Intel for an original copy of Moore's article caused quite a stir.
Below is a figure of the balun that Marchand presented in 1944. Note that nowhere in the article, was it called a balun, we are not sure of the origin of that name. Maybe a reader can tell us...
Figure 10 from Marchand's paper: the Marchand Balun
Below is Marchand's equivalent circuit model for the device.
Figure 11 from Marchand's paper: balun 3D equivalent circuit
The variation in characteristic impedance was calculated to be just a few ohms across 3:1 bandwidth. Phase variation is negligible across the same frequency range (thanks for the correction, John!)
Figure 13 from Marchand's paper, showing impedance and phase variation across frequency
Today, planar baluns are used in MMICs, especially in mixer circuits. Microstrip will never give you the excellent response of coax. If you need the very best balun performance in a small form-factor, perhaps you should try PolyStrata microcoax.
Reference:
Nathan Marchand, "Transmission Line CONVERSION TRANSFORMERS", Electronics, Vol 17, December 1944, pp. 142-145.