FW-Rectifier based “up-Octaver” Designs // jcm(c)2020

JC Maillet, posted Oct22/2020 …

The idea of “frequency doubling”, also known in modern times as “squaring”, comes from the idea of multiplying a sine-wave ‘sin(wo)’ against itself … producing product terms at sin(wo-wo) and sin(wo+wo), or DC and sin(2wo) …

SOME BACKGROUND // IMPORTANT PRACTICAL REFERENCES

Originally created by Roger Mayer, the very first ever instance of a Full-Wave Rectifying “up-Octaver” designed for guitar use (known as “The Wedge” or maybe later re-named “Octavio) used a Helios console amplifier stage to drive a center-tapped transformer feeding a pair of diodes and a volume pot at the output, the same way a Linear “DC” Power Supply circuit works, but without a smoothing capacitor – more on this later.


Another important reference includes the Shin-Ei “Super Fuzz” circuit, also from the 60’s, which is based on a bipolar transistor implemented FW rectifier stage, which is then followed by clipping diodes.

The “Super Fuzz” mainly gets its FUZZ from the subsequently attached clipping diodes. If we remove them we get a much cleaner (clean’ish) Octaving from the circuit … quite comparable to other FW Rectifier style circuits presented here (ie., with or without the smoothing cap included – more on this below)

We are beginning to see a standard FW Rectifier design pattern …

a gainy preamp, in this case affording up to 20db of boost, a unity gain (cathodyne style) phase splitter, and a modified full-wave rectifier


Next, the DanElectro “Green Ringer” circuit from the 70’s on the other hand, is based on diodes implementing the FW rectifier stage – again, similar as they would be in a linear power supply …

This circuit also follows a similar gain structure …

a gainy preamp, in this case providing an automatic 9.5db of boost, a unity gain (cathodyne style) phase splitter, and a lossy full-wave rectifier …a gain-balanced (knob-less) design that produces an appproximate unity gain large-signal transfer

A COMMON FW-RECTIFIER DESIGN STRUCTURE

The up-Octaver type of circuit tends to follow a common approach: some way of amplifying the signal before getting phase-split, and then rectifying somehow.

The following question thus arises: “Why amplify the signal at the front end to begin with …??!”

FW-RECTIFIER THRESHOLD/DEAD-BAND ANALYSIS

Full-Wave Rectifier circuit designs offer an interesting chance to perform some precision large-signal circuit analysis. To study the transfer profile of non-linear gain stages such as the FW-Rectifier we use DC Transfer analysis inside SPICE simulation software. This provides us with a visual representation the dynamic limitations of circuit play outside of its AC response. It also means that reactive elements play no role in this analysis and can temporarily be removed from the circuit – making several versions of a circuit equivalent from a large-scale distortion (wave-bending) point of view.

This means that FW Rectifiers can be analysed for their “threshold” behavior, where some exhibit nearly none, ie., in ideal cases, and some have lots ie., in very non-ideal, or “lossy”, cases.

To this end I took it upon myself to do a roundup of common FW-Rectifier circuits and analyze them in terms of non-linear DC-Transfer profiles – the same way I did it in the first 80 pages of my tube amp book “Inside Fender and Marshall Tube Amps” (ISBN 0-9684849-0-5)

What we find is that some styles of FW Rectifiers have very narrow threshold/dead-bands and some have considerably larger ones. For example, the lowest simulated dead-band corresponds to a class of op-amp based rectifiers known as “ideal” rectifiers while the largest corresponds to the Single-Ended variety running on jFET’s and Triodes (within my small sample set). The input-referred dead-band signal swings range from 170uVpp (ideal op-amp) to 2.20Vpp (12ax7 SE) – a huge variation!

In the case where a guitarist is meant to feed guitar pickup signals to such a circuit, we understand that a varied pick attack (strength) results in weaker or stronger electrical signals ultimately being relayed to the rectifier section. Relative to this threshold, or dead-band, we see that all the FW DC-transfers suggest an absence of “gain” (ie., horizontal-like slope) inside the dead-bands and therefore this will end producing little to no output signal.

It should be mentioned that FW Rectifier circuits, in almost all of their forms, introduce some amount of active noise. With little to no output signal in the dead-band we expect very poor Signal-to-Noise ratios (S/N).

The goal in a good analogue up-Octaver design is to produce a strong FW Rectified wave-form, ie., one with good S/N, which means hitting the DC-transfer functions with signal that routinely exceeds the dead-band.

The amount of pick attack required to produce a strong (dirty) octave translates into things like Sensitivity, and Gating.

As a player it often makes sense to eliminate artifacts (dynamic and spectral) that might distract too much from playing. And I would say, with up-Octaver circuits “gating” is one of the main ones; what we call “fizz” being the other …

It then becomes easy to understand that there’s a Signal-to-Threshold trade-off that inherently gets setup in these designs (again, refer to the “ideal” op-amp case). It then also becomes easy to understand why we may want to hit the rectifier with as large-as-possible signals to increase the perceived sensitivity of the rectification – in essence performing a dynamic pre-emphasis of sorts so that an octave can still be produced when feathering the strings.

From this it becomes clear that as the the dead-band shrinks and the pre-gain goes up we eventually arrive at a perfect ratio where no gating is perceived – such is the response of the Ideal Rectifier. In fact,this is the basic design idea with all known rectifier circuits, even Roger Mayer’s “Octavio” did this, the original FW Rectifier circuit meant for guitar signals.

WHAT ABOUT THE FIZZ …??!

The shape of the DC-Transfer tells use something about what wave-shape to expect at the output. In particular, a DC-Transfer curve with sharp corners inside it (especially near the middle section, around 0v) will have a strong tendency to produce upper harmonics whether we are sending in a Sine-wave or a complex (Gtr) signal …

This is the reason why we find a smoothing/filtering capacitor present in some FW-Rectifier circuits – the “Shin-Ei Super-Fuzz” being the best known example for this

Notice the “Super Fuzz” FW-rectifier has a dead-band of only 50mVpp wide and very well defined (sharp) transitions on the edges … this circuit will produce lots of fizz

Of course, the worse one for fizz is the Super Full-Wave rectifier … it’s an example of what we DON”T want

The tendency would be to try filtering after the fact, which is what the Shin-Ei circuit tries to do with the switch-able filter at the output of the “Super Fuzz” …

But another option would be to nip the production of harmonics at the bud – and that’s where jFET’s and Triodes can come into play



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