A Quadrature Power-Summed Compressor Sidechain For "The Uno Compressor"

[mediatechnology]

A Quadrature Power-Summed Compressor Sidechain

Inspired by Blackmer's figure 4 in his RMS detector patent I'm working on a stereo compressor sidechain that uses a sin/cos Dome filter along with "True" Power Summing.

I call the sidechain topology "Quadrature Power Summation" due to the 90°quadrature relationship between the signals being power-summed.

The "Unocomp" or "Uno Compressor" is named for the Pythagorean identity sin²Φ + cos²Φ = "uno."

Blackmer's original detector RMS detector patent is here: https://proaudiodesignforum.com/images/ ... 681618.pdf

In figure 4 Blackmer describes a method of summing 90 degree phase-shifted inputs to summed detectors. Block 72 in the drawing is an identical detector to the one detailed above it.

Blackmer writes:

In FIG. 4 there is shown an embodiment of the present invention employing two of the structures of FIG. 1 to achieve a substantially ripple-free output related to the logarithm of the instantaneous rms value of an input signal. In the embodiment of FIG. 4 there is included means for providing a constant phase difference such as a 90° phase network...

Preferably, each of circuits 26 and 72 provides an output current which is proportional to the square of its input current in any quasi steady-state interval of the input function. Hence, the outputs of circuits 26 and 72 are connected to junction 40 so that the current from the two circuits can be summed. Because of the 90 phase network formed, inter alia of amplifier 60, these output currents sum to meet the condition that Sin²Φ + cos²Φ = 1 or will thus provide a substantially ripple-free output logarithmically related to E (or to the input current as the case may be).

Note: The Blackmer detector is often called an "RMS" detector. A free-standing Blackmer detector performs about half the computations of RMS conversion. The final computations, taking the square root and exponentiating back into the linear domain, are performed by the VCA control scale and law. The output of the RMS detector is RMS, but it's in the log domain and, at 6 mV/dB scaling, is the square of RMS relative to a 3 mV/dB scaling.

Having built a detector using this technique I can assure the readership that even with the timing capacitor removed the output is essentially ripple-free. Reduced ripple allows super-fast response times with less distortion and audible artifacts.

Details and a schematic for an experimental sidechain will follow...

[JR.]

I looked into this concept for reducing ripple in low distortion sine wave oscillator AGC ( a long time ago). A SVF topology for the sine wave oscillator provides the quadrature sine waves.

I recall trading some notes with Brad (RIP) so this concept has been kicking around for some time. IIRC he shared a schematic using OTAs for sin^2 and cos^2 computing. But it isn't difficult to square terms in the log domain.

I know this has been discussed here or somewhere...

JR

[mediatechnology]

Thanks John.
I forget the oscillator manufacturer that uses sin/cos zero cross to sample the opposite.
E.g. zero cross of sine drives a sample and hold which captures the peak of cosine and vice-versa.

The beauty of this approach is that we already have the squared term in the log domain when the detector multiplies the log(Ein) X2.
All I have to do is hardwire the sin and cos detector outputs so they current-sum.

The logged and squared sin and cos outputs look like this when there is no timing capacitor:


Uno Compressor Sidechain Log-Domain Sin² Top Trace Cos² Bottom Trace 200 mV per Division

When the logged and squared sin and cos outputs are linked to make them current sum it looks like this:


Uno Compressor Sidechain Log-Domain Sin² Top Trace Cos² Bottom Trace Current-Summed 5 mV per Division

The ripple drops over 40 dB so yes, "uno" = sin²Φ + cos²Φ.

[mediatechnology]

It might seem sin² + cos² is overly complex when a stereo detector is required.
By following Blackmer two 90° Dome networks and four log detectors would be needed.

Fortunately that is not the case due to the unique property of the 90° Dome filter to equally weight L+R and L-R inputs.

By splitting the sin and cos all pass inputs and feeding them with Left and Right, both sum and difference are presented to the detectors in quadrature with equal level weighting.
In the log-domain they become power-summed regardless of whether they are the sum, difference or in-between.

The result is a detector which can be faster with lower distortion that power-sums the total signal power and, for either in or out-of-polarity inputs, provides a near 100-fold reduction in ripple.

The Uno Compressor will also have a variable capacitance multiplier that will vary, in lock-step, the attack and release times over a 10:1 range thus maintaining a power response that separate attack and release controls cannot provide.

[mediatechnology]

The sidechain schematic is a work-in-progress. The prototype will use the audio path of a Waveulator and a Quadrature Summing Filter board.



(Schematic updated 4/8/24.)

I'm using an old school dBx 303 type RMS detector with THAT300 arrays. I use the 300 in the Waveulator and really don't want to have to use a 4301/4305 DIP adapter or the SMT RMS detectors of the 4305 or 4316. The DIP adapters are expensive. SMT would certainly simplify the circuit and reduce real estate but it would make DIY in-the-field re-work impossible for some.

The capacitance multiplier has an effective value of 2.2 to 22 µF. When Ct is at 10 µF the log-domain time constant of 35 ms is equal to the original Pico Compressor. Although 2.2 µF may seem a bit too radical with the reduced ripple it may not. I've yet to hear this thing...

The Threshold circuit is almost identical to the THAT app notes and original Pico. I've added a buffer for the "Over Easy" diode. In the original Pico the potentiometer track was part of the voltage divider and, when slugged, the load on the diode varied with ratio. Because it was part of the voltage divider the Ratio pot had to be 5KΩ. Buffering the Over Easy diode eliminates interaction and frees up the value choices for the pot.

There is an additional gain of two for the output to get it to the 120 mV/dB scaling of the Waveulator.

Makeup Gain is on the Waveulator board and is not shown. As I said this is a work-in-progress and prototype schematic.

[JR.]

Interesting but is side chain signal rectification the significant audible concern in side chains? In dynamics processing there are multiple moving parts. Too fast release can cause visible distortion on LF content, too slow attack can allow overshoot, etc. There are multiple strategies to mitigate these weaknesses.

I concede that most of my bench work in this area was to make noise reduction compandors completely transparent. The modern market for compressors is probably expecting some audible sound signatures.

Good luck with that.

JR

PS: I had to bite my lip to not mention digital look ahead...

[mediatechnology]

Detector ripple produces odd-order distortion which is very audible when it's down in the power portion of the waveform.

The Waveulator has shown us you can murder the peaks symmetrically with clipping but not the power portion of the waveform which is far more "delicate."

When I get it connected to a VCA I can easily compare LF distortion but with the 10 µF 7.5 µA 35 ms log-domain tau of the 4301 compressor at 20 Hz there's a significant level of ripple in the envelope.
I measure about 6 mV which at that junction is a dB of signal modulation in the final output from ripple.

The non linear capacitor sought to reduce ripple but it only does so for slow or non-varying envelopes and, as Joe Neil showed, had an altered release signature.

With Quadrature summing I can't measure ripple under those conditions and the ripple reduction it provides doesn't lengthen the attack-release envelopes like a larger Ct would.

I'm willing to venture that ripple is the greatest factor limiting shorter attack-release.
That doesn't mean shorter A/R is always better: It just gives the user more options.
I certainly have the ability to find out.

WRT digital look-ahead I was recently told by an ME that his reason for OTB analog is that he can get to where he wants to be faster even when comparing a plugin-in to the equipment it models.
I'm not going to argue with him or his Grammy's.

[mediatechnology]

Interesting but is side chain signal rectification the significant audible concern in side chains?

https://groupdiy.com/threads/that2180-v ... ter.81970/

https://groupdiy.com/threads/some-ideas ... ost-666719

I thought I recalled Jakob using it:

I used the above Studer circuit for Hilbert transform in my G24 - it works reasonably well (maybe within some 5 degrees off worstcase with decent-precision parts) https://groupdiy.com/threads/did-everyo ... st-1050605

What we did is something old and new: We re-purposed ancient signal processor theory that was aimed at maintaining mono compatibility for stereo signals e.g. when transmitted over AM/Mono – this processor shifts signal phase +90 and -90 degrees in the two (LR), which ensures that when adding the two channels after processing, you get +3dB Side component and +3dB Mid, in stead of loosing all “S” and getting +6dB of “M”. At the same time, this transformation ensures more precise sidechain amplitude demodulation – and thus much less modulation artifacts when compressing audio. A variant of this is known as the “Hilbert transform”, and is gaining popularity in DSP/Plugin compression as well (where it’s MUCH easier to implement )

A tangential use in compressors side-chain exploits the trigonometric property sin²+cos²=1 for providing automatic attack time. I believe the only practical implementation is done by gyraf IIRC. https://groupdiy.com/threads/did-everyo ... st-1050774

[mediatechnology]

Here are some tone burst oscillograms comparing ripple without and with the quadrature channel summed in.

It's a few cycles of 50 Hz with a Ct of 2.2 µF and an It of 7.5 µA for a log-domain tau of 7.6 ms.

Default dBx timing is around 35 ms so this is an example of the fast-response low ripple capabilities.

The repetition rate is pretty low so the camera captured multiple persistent sweeps.


Without Zero Ripple Quadrature Power Summing

With Zero Ripple Quadrature Summation:

With Zero Ripple Quadrature Power Summing

With the tau extended out to 76 ms the ripple is still visible without the quadrature component.

[mediatechnology]

I did a quick video of the variable capacitance multiplier both without and with Quadrature Summation.

Without the quadrature component ripple in the 50 Hz toneburst response can be seen with effective capacitance ranging from 2.2 to 22 uF for a log-domain tau of about 7.6 to 76 ms.

When the quadrature component is summed in at 0:17 seconds the ripple virtually disappears.

Video (33 seconds): https://proaudiodesignforum.com/content ... mation.mp4