Matching 50Ω to 75Ω

A simple two-resistor minimum-loss pad will do this. Use very short lead lengths to minimize stray inductance and pickup of local broadcast signals. The loss is 5.58 dB. For calibrated voltage output, set the signal generator to 1.55 times the desired output level in microvolts.

You can eliminate nearly all loss by using an L-network. This circuit isn't broadband like the minimum-loss pad, but it easily covers 88-108 MHz.

This shows the L-network in a small metal box. The inductor is made of #14 wire and the capacitor is a small mica trimmer. I adjusted the turns spacing and the trimmer for best return loss over the FM band. Response must be checked with the box cover in place.

This shows the return loss of the L-network with a coaxial 75Ω load from 88 to 108 MHz. I used an HP 141T/8553B/8552B spectrum analyzer, 8443A tracking generator, and Anzac THV-50 power splitter. The return loss of the power splitter with a 50Ω load was a constant 30 dB across the FM band. This is the limit of the test setup. Results beyond this figure indicate cancellation of the residual return loss.

The simplest way to losslessly match 50Ω to 75Ω is with a twelfth-wave matching transformer, a special case of a series-section transformer.

The transformer consists of a 75Ω coax section in series with a 50Ω section, each about 1/12-wavelength long. I installed a BNC connector on the 75Ω cable, an F-connector on the 50Ω cable, cut the cables a bit long, and then trimmed them for maximum return loss over the FM band.

The return loss is nearly identical to that of the L-network at the band edges. Anything beyond 30 dB indicates cancellation of the residual return loss of the test setup.

Install the connectors and then cut each cable 6-1/8" from the far end of its connector. Cut the jackets back 1/4", strip the dielectric 1/8", overlap the center conductors, and solder them. Place a 1/8" piece of slit dielectric over the joint, put a dab of superglue in the slit, overlap the shields, and solder them. Finally, cover the splice with heat-shrink tubing. The final end-to-end cable length should be 12-1/8". All lengths are for cables with a velocity factor of 0.66. Use branded cables with a product number and verify the velocity factor. While you're at it, verify the nominal impedance. It may not be exactly 50Ω for some RG-58 cables.

I actually cut each cable 6-1/4" long for the transformer I made, whose response is shown above. But when I rechecked the return loss several days after building the cable assembly, the dip had shifted down a couple MHz. I found that its frequency varied somewhat with cable tension. I recommend that you use 6-1/8" to better center the dip.

The twelfth-wave transformer and L-network losses measured 0.05 dB each. For calibrated voltage output, set the generator to 0.83 times the desired output level in microvolts.

Matching 50Ω to 300Ω

The loss is 13.27 dB. For calibrated voltage output, set the generator to 1.88 times the desired output level in microvolts.

More is here.

Updated May 11, 2008