Posted on June 2nd, 2013 No comments
Warning: this post contains maths
I can never find on the web or in my text books the general equations for op-amps used as combined multi-input summing and difference amplifiers (ie they have several positive and negative inputs). It makes designing mixers for synthesizers annoyingly awkward as I have to rederive the equations each time. So, to save myself having to work everything out from scratch again, here are my derivations and notes on multi-input Op-Amp circuits. I will also take the opportunity to point out some interesting parts of the results.
So, here’s the setup:
We have an op-amp circuit with “N” negative inputs and “M” positive inputs as shown above. All the positive and negative inputs are identical.
For an ideal op-amp the output is:
Or, in other words the negative gain is:
The positive gain is:
Positive and negative gain
The negative gain is nice and easy and only depends on the input and feedback resistors and not on any other variables, like the number of inputs. Why is this? Well the inverting input of the op-amp is a virtual ground and the voltage isn’t changed by the negative inputs. Therefore the current through each negative input only depends on its input voltage. You can have as many or as few negative inputs as you like and it works the same.
The positive inputs are not in this lucky position! Voltages at the positive inputs change the voltage at both the inverting and non-inverting inputs of the op-amp. The non-inverting input voltage changes because of the voltage drop over Rg. The inverting input voltage changes due to the feedback action of the op-amp keeping the input voltages ideally identical. This means that currents flowing through all the input branches depend on the positive input voltages and hence the complicated positive gain equation.
Limits on positive gain values
Once the negative gain is set, this configuration limits the range of values of the positive gain depending on the number of positive and negative inputs. One particular example:
If the negative gain G- > 1 and number of negative inputs N < M, the number of positive inputs then G+ < G-.
To derive this then consider that the maximum positive gain is when the input resistors R+ = 0 (obvious from the circuit and also by inspection of the equation).
Special cases and derivation
There are several interesting special cases from these equations (including the basic op-amp single input amplifiers) and the derivation is worth reading. So I don’t fill the blog with equations you can read it all in this pdf file.
Posted on August 22nd, 2011 No comments
Dorklake11 was a nice event. Great job by Alex, Greenman and co. to create organization seemingly out of nothing. We had 12 Vibrati Punk Consoles built in two workshops
Mike Challis did a very nice build of the Vibrati Punk Console as a Coffee Can Synth.
Sam Freeman made some great phat sounds by looping the Vibrati Punk Console through a Korg Monotron.
Thanks to all the builders and all the campers that put-up with the massed bleeping!
Posted on June 2nd, 2011 No comments
Retro Electronic Sound
Evening Build Workshop
Tue June 14th, 6:30pm, Nottingham Hackspace
The first batch of kits for the Vibrati Punk Console (aka “Atari Punk Console 2.0″) are in. We are going to have a building session at Nottinghack on June 14th. So if you like electronic music or want to try your hand at soldering then come along.
The Vibrati Punk Console is a beginner-friendly electronic music project that can be finished in one evening. The simple circuit generates an amazing range of retro warbles, screams, glitches, fuzzes and tone ramps.
Workshop Cost: £20 includes teaching and all build materials.
For those that can’t make it to Nottingham the kit should be available to buy on the web soon.
Posted on April 22nd, 2011 No comments
For most of my projects I either need quite dense PCBs that I get professionally made or I use point to point wiring techniques. At the moment though I am working on a new electronics kit under the working title of “Vibrati Punk Console” which is kind-of an “Atari Punk Console 2.0″. To validate the PCB design before sending the first batch for manufacture I decided to make a home made board.
With great timing Matt Little had just done a PCB workshop at Nottingham Hackspace so I had good practical experience. Armed with a UV exposure box from the last DDRC Car Boot Sale and a set of parts from Rapid Electronics I went out to make my PCB.
I basically followed the tips from Mike Harrison’s guide. For etching I used the Seno GS etching system which manages to keep 99.999% of the really nasty stuff in a bag.
I made a second board as a backup, but that was a complete disaster. Once I developed the UV board you could see that the fine lines weren’t sharp and once I started etching they disappeared all together. Still not 100% sure what the problem was there. Possibly over-exposure to the UV or the mask not being completely flush to the board when it was exposed. Anyway one board was enough so as it was getting late I stopped there.
One thing I would note for future builds – the “automatic” pad size in Eagle is too small for home made boards. Use larger pads than the eagle defaults to make your life easier.
Posted on November 1st, 2010 No comments
Last weekend I led the workshop “Electronics for Artists” at South Hill Park in Bracknell. Photos are now on line. Thanks to all the group for your enthusiasm and Martin for organising. Listen out for my wise words on the Digital Media Centre podcast.
Posted on February 8th, 2010 No comments
The crew at MzTEK have just posted this video about their project to help more women get in to technology. Lots of clips from the Electronics for Absolute Beginners workshop plus a cameo appearance from me.
Posted on January 24th, 2010 No comments
My friend Sophie asked me to do a workshop on Electronics for Absolute Beginners for the group MzTEK which ran yesterday. Hard work as a presenter, but I had a really good day. The unflagging enthusiasm and excitement of everybody was great to see and really inspiring. Also lots of fun ideas on different things to do with the circuits in the course. I was also impressed that (almost) everything worked for (almost) everybody. Good building skills all round.
For anybody that wants to see the notes – follow the link above.