In general, transcoding (or "re-encoding") quad recordings will give you a result in which the experience anywhere within the Ambisonic speaker array is at least similar to the experience in the quad "sweet spot", ie the acceptable listening area is significantly enlarged. In addition you may get a better feeling of the acoustic environment if the techniques used on the original recording captured them. In certain cases you may experience better localization and find individual musical components easier to discern.
Additional operating notes are in my two articles, Whatever happened to Ambisonics and An introduction to Ambisonic Mixing, especially the latter.
Here's how to do it.
The Transcoder has very few controls. The main ones are the stage width controls. You can adjust the front stage up to 180 degrees and the rear to 150.
A typical starting point for transcoding discrete quad recordings to UHJ would be route LF and RF to the front stage and LR and RR to the rear stage, with the stage widths set to 90 degrees. However, you may wish to mess with the stage width controls while listening to the decoded UHJ to get the best results. You can sometimes get improved side imaging by opening the width up, especially on the front stage, but check that signals to the North remain reasonably imaged (they are not perfect in the first place, of course, which is why there's a center channel in 5.1). Listen for increased phasiness to the South if you open up the rear stage too wide.
If you are starting from a so-called 4-2-4 recording, you have a bit more of a problem. It is not actually possible to get your original four channels back properly from a matrix recording, so you will be a little at the mercy of the encoding scheme.
You will need to locate a matrix decoder which handles the system with which your source material was encoded. Set up the quad matrix decoder to decode the matrixed 2-channel source material and feed the four line level signals to the Transcoder inputs as described above. You will get better image stability if you use a straight "non-logic" decoder or disable logic decoding if present. However you will get better separation using logic decoding. Which you select will depend on the program material. You may wish to set up the quad decode first and listen to it on speakers to get the feel for what you will be transcoding to UHJ. Then connect the line level decoder outputs to the Transcoder inputs as described. If the quad decoder has logic capability that you can switch in and out, you may wish to experiment with the setting and the stage widths to try to approach (or exceed in some cases) the performance of the original quad decode, however your starting point should be logic decoding off and stage widths at 90 degrees.
If you are using a subcarrier decoder to transfer from vinyl, do ensure that you are using a suitable cartridge and stylus. Ultrasonic HF response and a smaller stylus tip than for stereo are required. Listen to the decoded material before transcoding (that way you will know that the slightly strangled sound is a feature of CD-4 and not UHJ!).
UD-4 recordings work particularly well, by the way, as the locus of a circularly-panned signal is essentially circular (as opposed to CD-4, which is decidedly lumpy).
This technique results in a planar B-Format signal (W, X, Y). You can record this or encode it into UHJ with a regular UHJ encoder.
Listen to the signal through the entire encode/decode chain and adjust for best results. You can try bringing the radius vectors in towards the center (change all four at once to the same settings) but do not go beyond zero (you will transpose the whole soundfield, "come out the other side" and make your brain ache). You may find that you get best results with a less-distant radius vector. Having found comfortable radius vector settings you can mess with the angles, but you may not be able to get better results than your initial settings.
These tips should help you to get
new life out of old quad recordings. In addition, of course, remember that a
UHJ decoder does a very good job of decoding matrixed quad signals, and the
lack of logic decoding dramatically improves image stability on Dolby surround