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====== Negative buck regulator for Modular Synthesizers ======

Eurorack systems, and other synth systems, use +-12V supply voltages and up to +-10 V signal voltages. My thought is that some power could be saved by working with lower voltage during the signal processing and, if necessary, amplify it back to +-10 V in the end.

OP-amps typically seem to pull a constant current more or less independent from what supply voltage it has, and likewise for the SSI2164. There are of course other parts in a synth, and those also need to be considered.

Since the current is more or less constant, a linear voltage regulator won't do since the input and output current will be the same (disregarding the quiescent current). Thus, a switch mode power supply might be the thing. Why not a buck?

There are plenty of buck regulators available, but only made for positive input and output voltages. I have yet to find any buck regulators for negative supplies, i.e. "a switch-mode replacement for the 79xx linear regulator".

After some searching of information I have a good hope for (miss)using a normal positive buck-regulator in a non-intended configuration as a negative-input-negative-output buck-converter.

But, before I put too much effort into that, I want to do some comparisons and empirical studies to show that it might actually be beneficial to work with a lower voltage.

===== Power consumption for a single op-amp and for 10 quad op-amps =====
The current pulled from the +-12 V is usually what is specified and limits how many modules that can be supplied from the same power supply. But it would be easier to talk about it in power (i.e. wattage) because that is most often what matters and can be compared between different voltage domains.

Buck regulators are usually most efficient over a certain output current. Many buck-regulators brag with a best efficiency just over 90%. There are some regulators that adapt to low loads by switching to PFM-mode, Pulse Frequency Modulation, and can achieve around 80% efficiency down to 1mA and converting 12V down to 3.3V.

The few regulators that I checked the efficiencies for are: MAX17530, MAX17550, TPS629203 and TPS6212x.

I will count with 65% efficiency for 100µA to 1mA, 70% for 1mA - 5mA, 80% for 5mA - 10mA and 85% for >10mA.

For convenience I will decide on the lower choice of supply voltage to be +-3 V.

I will only be looking at quiescent current consumption for now.

The current consumption of OP-amps ranges from a couple of hundred micro-amps up to several milli-amps. For the sake of simplicity I will only look at two models:

^ MPN ^ Current @24V ^ Current @6V ^ Current for 10 quads ^
| TL071 | 1 mA | 1 mA | 40 mA |
| OPA186 | 130 µA | 130 µA | 5.2 mA |

And then for the power consumption at different voltages and number of op amps. The input power to the switch regulator will be ''P = (current @ 3V times 3V) / (regulator efficiency in %)''

^ OP-amp ^ Power @+-12V ^ Input power with +-3V buck ^ Power saved ^
| TL071 | 24 mW | 8.6 mW | 64.3 % |
| OPA186 | 3.12 mW | 1.2 mW | 61.5 % |
| 40 pcs TL071 | 960 mW | 282.4 mW | 70.6 % |
| 40 pcs OPA186 | 124.8 mW | 39 mW | 68.8 % |

And if we do some algebraic juggling we can see that the expression for power saved is ''Saved % = 1 - Vout / (Vin * efficiency)''. That is, we save more if the secondary voltage is lower than the input voltage, and we save more if the buck regulator can work more efficiently.

Based on that, and the knowledge that all variables are always positive, we can solve the inequality ''1 - Vout / (Vin * efficiency) > 0'' to see when we actually benefit from this. I would argue that the most intuitive way of expressing this is ''efficiency > Vout / Vin''. That is, the buck regulator must be more efficient than the ratio of the voltages. For +-12V vs +-3V this is 25% efficiency, which is reaaally low for a buck converter.

===== What do commercial modules consume and how are they built? =====
This, of course, differs. I have assembled this table of modules of which I was able to find the schematics for. However, I do not know the conditions for the stated current consumption.

^ Model ^ Brand ^ +12V mA ^ -12V mA ^ +5V mA ^ Technique ^ Comments ^ Links ^
| Castor and Pollux II | Winterbloom | 100 | 35 | - | LDO 3.3V | Could benefit alot with buck | [[https://winterbloom.com/shop/castor-and-pollux|Info and shop]] [[https://github.com/wntrblm/Castor_and_Pollux/blob/main/hardware/mainboard/mainboard.pdf|Schematics]] |
| Blinds | Mutable Instruments | 70 | 70 | - | 24V fed ICs | Could benefit alot with buck | [[https://pichenettes.github.io/mutable-instruments-documentation/modules/blinds/|Info]] [[https://pichenettes.github.io/mutable-instruments-documentation/modules/blinds/downloads/blinds_v60.pdf|Schematics]] |
| DIY Modulator | Erica Synths | 27 | 22 | - | 24V fed ICs |  | [[https://github.com/erica-synths/diy-eurorack/blob/master/Modulator%20DIY.zip|Schematics]] |
| VCF-4 | Skulls & Circuits | 163 | 91 | - | Mostly 24 fed ICs, some 12V and some LDO 5V fed | Could probably benefit alot from switch mode regulators | [[https://www.skullandcircuits.com/vcf-4/|info]] [[https://www.skullandcircuits.com/wp-content/uploads/2023/04/VCF-4-v5.2.pdf|Schematics]] |
| BURST | Befaco | 56 | 10 | - | LDO 5V and probably some 24V fed ICs |  | [[https://www.befaco.org/burst-2/|Info]] [[https://befaco.org/docs/Burst/Burst_V3_Schematic.pdf|Schematics]] |
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===== Other work on the topic =====


[[https://www.analog.com/en/resources/technical-articles/positive-buck-regulator-makes-negative-boost-dcdc-converter.html|Positive Buck Regulator Makes Negative Boost DC/DC Converter]]

[[https://www.ti.com/lit/an/slyt516/slyt516.pdf?ts=1717195408219&ref_url=https%253A%252F%252Fwww.google.com%252F|Designing a negative boost converter from a standard positive buck converter]]

====== Implementing a negative buck regulator ======
{{:modular_synthesizers:normal_buck.png?300}}

{{:modular_synthesizers:negative_buck.png?300}}

===== The Parallel Universe of Negative Input Voltagess =====
[[https://e2e.ti.com/cfs-file/__key/communityserver-discussions-components-files/196/The-Parallel-Universe-of-Negative-Input-Voltages.pdf|The Parallel Universe of Negative Input Voltages]]

By John Betten and Brian King suggests using a UCC3813 with an external switch mosfet and also provides a circuit to adjust the feedback voltage to make the reference work properly.

{{:modular_synthesizers:parallel_negative_fig3.png?500}}

It is (according to me) a bit easier if we rewrite the circuit and remove some compensation capacitors like this:
{{:modular_synthesizers:parallel_negative_fig3_better.png?500}}
===== Risks and other considerations =====
There are also some risks that needs some investigation before this can be deemed a good way forth.

  * Noise and EMC. A switch-mode regulator could pollute, not only the module it supplies but also the whole system.
  * Higher noise at lower supply levels? Is this a thing? Probably at least worse signal-to-noise ration?
  * Higher impact by offset-voltages
  * Higher price
  * Better to pick a positive-in-dual-rail-out available solution?