Adding DC offset to a 0V to 7V sinewave

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If you want to go up to VCC then a TL072-type opamp won't get close. You need an opamp with rail-to-rail output.

I wouldn't recommend the the offset circuit that BoDeadly posted. I'm guessing it comes from this thread:
https://electro-music.com/forum/viewtopic.php?highlight=simple+offset+scaler&t=31528Dave's a nice guy and extremely helpful, but that circuit will bounce on the output on sudden changes in input.

You need a diff amp with a gain of 0.509 and an offset of 8V. Something like this:
https://tinyurl.com/yf6tpqzrDon't use the power rails for voltage refs, better to use a dedicated voltage ref like a TL431, and then scale the 9.6k resistor to match.
 
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True(ish) but, like I said in my post, you don't need 100k resistors or even the second amp necessarily at all. Clearly I scraped this circuit off the net as a rough sketch and so it should be interpreted heavily to suit the users specific need. As alluded to, a lot of synth circuits are hold overs from old designs that used very weak op amps. So with 10K resistors and low gain, I think your "bouncing" would be pushed so high up, it would get shunted at just about any input.

But if someone wanted to limit current with that build-out resistor inside the feedback loop, they could but just make it more like 100R. But at 100R you might as well just put it on the outside which is done precisely to stabilize the output from cable capacitance. But in practice it wouldn't matter anyway because the cable would have to be incredibly long (and no amount of trace capacitance would be enough to be a factor in any of this) to get ringing which is what I think you mean by "bounces" but it also would only occur with a square wave and not a sine wave and barely with a tri and the ringing will be 100+ kHz and, and, and, ...
 
I wrote up why a few years ago over on ModWiggler:
https://modwiggler.com/forum/viewtopic.php?p=1129644#p1129644Without the loop compensation capacitor you've got the "intr" configuration. The reason is that the 1k0 output resistor, together with cable and trace capacitance, puts a damn great pole in the opamp feedback loop, and it bounces rather well (i.e., not what you want).
I am familiar with this concern of opamp stability with capacitive load, but I'm not sure it's really pertinent to synth CV's. The problem you illustrate in the linked page concerns signals with a rise/fall time lesser than 1us. The LTspice simulation seems to show a very small rise time (illegible but certainly less than 300ns). I'm not sure it's very likely to happen in a synth, unless something's broken.
All the same, 1nF is equivalent to ca. 7 meters of patch cable; it's not unseen, but not not very common either.
I made a similar sim with a pulse of 1us rise-time and I can't see any significant overshoot/oscillation.
In addition the unit that will receive the "overshot" signal will filter it due to a low BW.
I agree that stability is a concern, because it could result in a non-functioning circuit, though.
 
Well, that synth circuit as drawn with the 1k0 output resistor is typical of an output driver in a modular synth. To make that work correctly you do need the comp capacitor, this is a well-known circuit and plenty of hardware out there uses it: synths, mixers, effect units, etc.
In this application that we're discussing you don't need the 1k0 resistor, and without it you don't need the capacitor, although it's probably worth having it there to reduce the opamp bandwidth - there's no need to amplify any signal above a few kHz, although if this VCO is going to be used for audio FM then I'd allow a generous dose of kHz bandwidth (but not 10s of kHz).
 
That was my first thought on how to do it. As I understand it the signal gets attenuated by the voltage divider after which the opamp circuit takes care of the DC scaling right?
There are many ways to achieve this. Summing two signals can be done in many ways, but I still think using two inverters is the solution that has the less interactivity, is the most stable, and the less complicated to tune up. It may be a tad noisier, though, if it's a concern.
 
But if someone wanted to limit current with that build-out resistor inside the feedback loop, they could but just make it more like 100R. But at 100R you might as well just put it on the outside which is done precisely to stabilize the output from cable capacitance. But in practice it wouldn't matter anyway because the cable would have to be incredibly long (and no amount of trace capacitance would be enough to be a factor in any of this) to get ringing which is what I think you mean by "bounces" but it also would only occur with a square wave and not a sine wave and barely with a tri and the ringing will be 100+ kHz and, and, and, ...
That may be true for AC outputs, but for CV outputs you really want the stabilisation resistor inside the feedback loop.
A 100R output resistor into a 100k CV input (if you're lucky, many circuits I've seen are neither 100k nor fixed), the pitch error is over one cent per octave. Taking a poor case that output feeding into a passive mult feeding into three VCOs with 50k input resistance the pitch error is huge (maybe 10c/octave).

But that's outside the scope of this question which is simply about shifting and scaling an internal CV on a Buchla card, so there shouldn't be a need for such a resistor. And really, the point of that series resistor is for opamp stability on an output driver, not opamp protection. Another write-up I did a while back:
https://www.njohnson.co.uk/index.php?menu=2&submenu=2&subsubmenu=16
To the OP: try the single opamp circuit with a rail-to-rail opamp and see how it goes. Experimentation beats forum debates ;)

Neil
 
But that's outside the scope of this question which is simply about shifting and scaling an internal CV on a Buchla card, so there shouldn't be a need for such a resistor. And really, the point of that series resistor is for opamp stability on an output driver, not opamp protection.
Actually I'm not sure that's true. A 1K is quite large so again, synth stuff is on it's own plane of consciousness so I'm going to avoid saying it's "definitely" not true in this particular case. If you put a big enough resistor inside the loop, I don't doubt it could cause instability. But putting it on the outside, which is more commonly known as a "build out" resistor, between the feedback point and the cable will definitely stabilize the amp much better than putting the same resistor inside the feedback loop. So the only reason that I can think of for putting a resistor between the amp output and the feedback point would be to limit current from the amp which is to say it's for op amp protection such as because you knew something could be plugged into it like in a patchbay were outputs can be connected to each other or who-knows-what. Usually you don't see it in pro-audio because there's almost always "build out" resistor which works equally well at limiting current and also because vaguely modern op amps can handle shorts. But the build out resistor will incur a an I*R drop so, like you said about CVs, that can equate to an error which is unacceptable. In that case you should put the resistor on the inside of the loop to limit current without voltage error. And don't use a fast op amp. A TL072 et al is good. Note that if the circuit is unity gain, which it frequently is in synth CV type circuits, a feedback cap will do very little to stabilize.
 
Here's how is't done on the 208...inside the feedback loop. Mind you, the 208 is a very old design with some flaws...lots of crosstalk and PSU dirt. (IC2 is an RC4136 and IC1 a LM3900)
 

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Buchla 208 Aux card is done, here some pics...
 

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