Encoding SQ at home 

A how to guide in encoding your own matrix quad mixes.

Note: I originally came up with a very complicated way of making an SQ compatible recording using Sound Forge and the Q-tools plug-in.  The following report was sent to me from a fellow quadraphile on AOL (thanks Serge!)  It is kind of old stuff  and I don't have graphics yet, but the process works.  It is much easier than my way (which I never was pleased with anyway).  Read on and be sure to read my final thoughts at the end.

By Kenneth Parsons
( first printed in MCS REVIEW VOL.3, No.1 June 1981 )

I have always been fascinated by the process of matrix encoding and decoding. After studying several articles on the various systems ( in particular SQ ), I soon realized that it shouldn't be too hard to make an encoder. Decoding is simply the inverse of encoding; complex logic circuitry is required only for decoding, not encoding. However, I imagine that interest in quad faded before any manufacturer got the idea to produce a home encoder.

Many readers may have an old style SQ decoder, one with no form of logic assistance, laying around gathering dust. It could be used as an encoder as shown in Figure 2.

Before you get down to the work of soldering and splicing, you may want to verify that the idea does, in fact, work. If so, try this simple experiment. Connect a stereo source to the left (L) and right (r) inputs of the basic (non-logic) decoder in the manner shown in Figure 1 ( R into L, and L into R ). Then connect the right back (Rb) output of the basic decoder to the left input of your logic decoder, and the Lb output to the right input of your logic decoder. From the rear-channel outputs of your logic decoder, you should hear the stereo source with virtually perfect original left to right separation. Front-to-back separation will depend on the logic decoder used, but signal levels on the front channels should be very low. If you are satisfied with the results of this experiment, you may wish to construct the simple encoder diagramed in Figure 2.

( Fig 2 shows a basic SQ decoder with the Rb signal feeding the Lt input, and the Lb signal feeding the Rt input, the Rb output of the decoder is feed via a 10k resistor to the new encoded Lt . The Lb output of the decoder goes to the Rt via a 10k resistor. The Lf input also goes to the new Lt via its own 10k resistor, and the Rf input goes to the new Rt via its own 10k resistor. The Lf input and Rf input bypass the basic encoder. The Lf input and the Rb signal from the decoder are connected after their own 10k resistors, to form the encoded Lt signal. The Rf input and the Lb signal from the decoder are connected after their own 10k resistors, to form the encoded Rt signal. )

An encoder can be constructed with the resistive summing network shown in Figure 2. The easiest method of construction is to buy or make two Y-connecting cables with plugs to match your equipment and to solder 1/4 watt , 10,000 Ohm 5% resistors between the plug and the center conductor of each cable at the top of the "Y".

HOW IT WORKS. In SQ the encoded signals are called Left total (Lt) and Right total (Rt) . Mathematically expressed, this is what they look like:

Lt = Lf + 0.7Rb - j0.7Lb
Rt = Rf - 0.7Lb + j0.7Rb

( "j" signifies that the signal has been shifted in phase 90 degrees, " - " indicates a phase shift of 180 degrees )

Feed this pair of signals to an SQ decoder and out will come four signals approximating the original inputs:

Lf'' = Lf + 0.7Rb - j 0.7 Lb
Rf' = Rf - 0.7Lb + j0.7Rb
Lb' = Lb - 0.7Rf + j0.7Lf
Rb' = Rb + 0.7Lf - j0.7Rf

( Lf refers to the original signal before encoding; Lf' refers to the same signal after decoding. )

When decoded, the front channels ( Lf' & Rf' ) are virtually identical to the Lt and Rt signals. In the decoder they pass through a phase reference network, but retain the same signal components.

But before we can think about decoding, we've got to obtain a pair of encoded signals, and that takes us back to the two formulas for Lt and Rt.

Obtaining the Lf and Rf signal components for these equations is simple, because we already have them. Thus, in Figure 2, Lf an Rf are shown being feed "as is" toward creating the encoded Lt and Rt signals.

Getting the rest of the encoded signals is where using a basic SQ decoder comes in. It happens that if two signals are fed into such a decoder, they appear at the rear output of the decoder in an encoded form. If the signals we feed in are the original Rb signal into the decoder's left input and the original Lb into the right input, we get the following outputs:

Lf' output = Rb
Rf' output = Lb
Lb' output = -0.7Lb + j0.7Rb
Rb' output = 0.7Rb - j0.7Lb

Voila ! Lb' output is exactly the component we need to add to Rf to create an encoded Rt signal:

Rt= Rf-0.7Lb + j0.7Rb

And Rb' output is exactly what we need to add to Lf to create an encoded Lt signal:

Lt = Lf + 0.7Rb - j0.7Lb

Now you're ready to record a fully encoded four-channel program.


The front outputs of an SQ decoder are not exactly in phase with the input signals. The phase reference system causes the phase of the output signals to change with the frequency of the input signal. This means that with our simple encoder the back channels are not in phase with the front channels, and, further, that the phase shift is different for different frequencies. In some applications, such as when mixing down a four-track master tap ( where each track has been recorded independently) the phase problem will not matter. However, in most applications this shortcoming will result in poor imaging when the signal is decoded. We all know that phase coherency is a critical part of good imaging!

One can overcome this shortcoming by using two identical decoders as the encoder. If the front channels are passed through the second decoder before combining them with the rear encoded signals, they will retain the proper phase relationship between front and back. The same Y-connecting cable described previously could be used to combine the output signals. This design is diagramed in Figure 3.

( Fig 3 uses two basic SQ decoders to provide a SQ encoded signal in proper phase relationship. The first decoder is configured as described for the decoder in Figure 2 for the Rb and Lb input, then the second basic SQ decoder is applied to the Lf and Rf signal by taking the Lf input to the decoder and taking the Lf output from the decoder, then through the resistor and then to the new Lt output, while the Rf input is fed to he second decoder and the Rf output is taken through the resistor to the new Rt output . )


One peculiarity of SQ-encoding should be noted: cancellation occurs when the encoder when Lf and Rb signals are the same. This means that, if care is not taken in the mix-down/encode process, important parts of the program could be lost. This is why SQ-encoded records never contain a center vocalists; vocalists are always placed center front. The SQ encoding process involves one 180 degree phase shift ( anti-phase) which causes this problem. Ironically, our simple encoder is free of this problem because the front and back signals are not exactly in or out of phase.

I hope this information will be of use to many readers, whether you build an encoder for serious use or merely to experiment with encoding and decoding in an effort to better understand the concepts involved.

Tab's final thoughts on this process...

The first time I tried this was with my DTS decoder pumping a 4 channel mix into this contraption which was feeding my Tate II in real time.  The results were horrible.  There was so much leakage all around that I thought it didn't work at all.  I tried it again a few days later, but this time I used my quad 8-track player and an old Enoch Light tape (Charge!) and it worked beautifully.  The encode/decode sounded so close to the discrete tape it was hard to tell them apart.  Why?  This question plagued me and the only reason that I could come up with is that SQ has to be mixed down differently than a discrete  recording.  The Enoch Light mix featured different instruments isolated in each channel.  The DTS recording has stereo sound fields in the front and the back.  The problem with that is a stereo mix will almost always produce in-phase and out-of-phase information naturally.  It's like playing a regular stereo mix through an SQ decoder and listening to the rear channels.  You end up hearing quite a lot of the material that is naturally out-of-phase because of mic placement or acoustical effects.  If the rear channels of a quad recording contain any of this phenomena, it's going to come to the front.  I think the trick is to keep the rear channel information isolated (i.e. solos or isolated effects) and keep any information shared between the rear left and right as mono as possible in the mix.  I hope this information helps.  I would love to hear some "new" SQ recordings!