hairpin match

The hairpin match is a method often used to match an antenna such as a yagi-uda to a commonly used transmission lines such as 50 ohm coaxial cable. The hairpin match is also known as a beta match. If using a coax, this method requires a balancing transformer (balun) to convert the unbalanced coax to a balanced feed at the terminals of the antenna.

The yagi is an antenna with parasitic elements not physically connected to the feed line. The feedpoint resistance of the driven element is often reduced to around 10-30 ohms (from the typical 70 or so of a dipole), and typically there exists some amount of capacitive reactance jX.

The hairpin or beta match seeks to tune out that reactance by introducing an amount of inductive reactance in parallel with the driven element at the feedpoint. One way to achieve this is by winding a coil to provide the desired value of L and wiring it to the terminals of the antenna. The drawback of this method is that several coils may need to be wound to achieve the desired value of L (unless you have an antenna anaylzer to tell you the exact value you'll need).

Another method makes use of a short-circuit line/bar and transmission line transformer to achieve the desired reactance. This transforms the value of a short circuit through a length of transmission line to provide a nonzero value of inductive reactance (look at your handy Smith Chart to see why this works). In this scheme, two pieces of parallel wire are run some distance from the feedpoint and then tied together at the end. An adjustable rod/sliding bar arrangement is often used instead, where two parallel rods are connected to the driven element with clamps and bar slider connected across the rods. This bar is slid along the length of the rods to adjust the value of reactance produced at the feedpoint. This setup is shown in a general sense below.

|| - driven element
||
||                              _
||B============================| |===
||                             | | 
||--+                          | |
    +--balun-coax              | | shorting bar
||--+                          | |
||                             | | 
||B============================|_|===
||
||
|| - driven element

The two rods form a transmission line with a short circuit as a load. The characteristics of this transmission line are generally unimportant, the user only needs to adjust the position of the bar to achieve a good SWR at the feedpoint.

Other methods of matching a yagi antenna to a coaxial line include the gamma match and the tee match.