Design Ideas July 20, 1995

Program matches filter-network impedances

David Kirkby,
University College, London, UK

In RF circuits, it's often necessary to match one impedance to another. The program in the Listing 1 can design a network to match any resistive impedance R₁ to another R₂ (where R₁ is less than R₂) at a specified frequency and specified Q. The program employs a lossless (in theory) network that uses just capacitors and inductors. Five matching networks are possible, including two L types, one T type, and two Pi types. Although electrically equivalent at the design frequency, the networks have different responses at other frequencies. The networks require different component values, often making one more practical than another. All the equations come from Introduction to Radio Frequency Design by WH Haywood. The following is a typical output from the program, requested to match a 10 Ohm source to a 50 Ohm load at 82 MHz, using a Q of 100.

You can transpose the inductor (48 nH) and capacitor (97 pF) in the L-type network, thereby yielding five networks in total. Although the program matches only real impedances, it can also match complex impedances, if you do a little work on a calculator. If, for example, you need to match (10+j5) Ohm to 50 Ohm at 82 MHz, you must calculate the value of a capacitor having a reactance of j5 Ohm, which at 82 MHz is 388 pF. You place this capacitor in series with the source, so it becomes a pure resistance of 10 Ohm. You can then use any of the above networks. The L-type would be particularly convenient because you could combine the 388- and 97-pF capacitors into one capacitor of 77.6 pF.

The C program in Listing 1 compiles for a PC using Quick-C. However, because the program uses no PC-specific code, it should run on any machine for which a C compiler is available. In the compressed ZIP file attached to /DI_SIG#1736 on the EDN Readers' BBS, you can find the Listing, as well as an executable program. (DI #1736)