Inverting Op-amp signals and Sawtooth waveform generation

[Callum Plunkett]

I’ve been asked to create a sawtooth wave form with four input voltages. After doing this I then added a second op-amp to both change the range of the wave form from -/+5v to -/+2.5 and DC offset of 2.5v to create a wave form that ranges from 0v – 5v as required by the question. For the most part I think I’m close enough with my result apart from the second op-amp seems to of “flipped” the wave form and I can’t quite figure out why and how to solve the issue.

I've included a picture of my circuit, wave form after the first op-amp and after the second op-amp.

Any help would be appreciatedhttps://www.physicsforums.com/attachments/286448https://www.physicsforums.com/attachments/286449https://www.physicsforums.com/attachments/286450

 

[berkeman]

Hi Callum,

I moved your thread to the schoolwork forums from the EE forum, and something about that move messed up your attachments. Could you please re-attach them or add a new reply with them? Also, they were pretty hard to read (when they still existed) -- Is there some way to make the bigger and darker? Thanks.

 

[.Scott]

Could you redo your pictures. I can't read them.
More resolution is required - and the pictures only occupy the top left 10% of the available canvas.

 

[Callum Plunkett]

Could you redo your pictures. I can't read them.
More resolution is required - and the pictures only occupy the top left 10% of the available canvas.

Yeah sorry about that by the i tried to change it but it would not up date. Ae these better?

 

[berkeman]

Whew, much better, thanks!

So you mention synthesizing a "sawtooth" waveform with the 4 voltage sources. You've done a good initial job of doing that, but do they want it to be more like a straight sawtooth instead of stepped? Can you say what you could change/add to the circuit to make it more like a traditional sawtooth?

 

[Callum Plunkett]

Whew, much better, thanks!

So you mention synthesizing a "sawtooth" waveform with the 4 voltage sources. You've done a good initial job of doing that, but do they want it to be more like a straight sawtooth instead of stepped? Can you say what you could change/add to the circuit to make it more like a traditional sawtooth?

View attachment 286459

This is the full question as i was given.

 

[berkeman]

Ah, in that case it looks like you are doing the correct synthesis.

 

[Callum Plunkett]

Yeah i think I am on the right track with it, so I am quite relieved someone else thinks I am some where near.
Cheers.

 

[Jody]

The last op-amp has positive feedback. Isn't that going to be a problem?

 

[berkeman]

The last op-amp has positive feedback. Isn't that going to be a problem?

Good catch! I saw that the simulation output for X2 looked reasonable, so didn't check the schematic in detail. But yeah, with the opamp inputs inverted like that I don't see how the simulation isn't just hitting the rails...

 

[bob012345]

Good catch! I saw the simulation output for X2 looked reasonable, so didn't check the schematic in detail. But yeah, with the opamp inputs inverted like that I don't see how the simulation isn't just hitting the rails...

Op amps invert the signal so you can just use one more with a unity gain to flip it back.

 

[berkeman]

Op amps invert the signal so you can just use one more with a unity gain to flip it back.

I'm pretty sure you're kidding. An opamp with the inputs reversed so that the feedback is positive is a comparator, not a linear amplifier.

 

[bob012345]

I'm pretty sure you're kidding. An opamp with the inputs reversed so that the feedback is positive is a comparator, not a linear amplifier.

A summer gives the negative of the sum. You add another op amp stage to invert that signal.

 

[berkeman]

A comparator slams to the +/- power supply rails when the difference between its inputs is positive or negative. Are you suggesting that a comparator can be used as a linear amplifier like an opamp that uses negative feedback?

 

[bob012345]

A comparator slams to the +/- power supply rails when the difference between its inputs is positive or negative. Are you suggesting that a comparator can be used as a linear amplifier like an opamp with negative feedback?

No. I just thought the issue was the signal was flipped as in multiplied by a minus sign. I was telling how to make it positive.

 

[berkeman]

No. I just thought the issue was the signal was flipped as in multiplied by a minus sign. I was telling how to make it positive.

Okay, that's fair. The quote of mine that you used was agreeing with the catch by @Joshy about the incorrect connection of the 2nd opamp. The question about the inversion or whatever of the signal was in a different post.

 

[bob012345]

Okay, that's fair. The quote of mine that you used was agreeing with the catch by @Joshy about the incorrect connection of the 2nd opamp. The question about the inversion or whatever of the signal was in a different post.

That's fine. Sorry for the misunderstanding.

 

[bob012345]

This is the full question as i was given.

View attachment 286461

Does the output have to be just like fig 2b (going between 0 and 5V) or just similar in shape? Are other DC biases allowed? I take it the input biases all have to be 5V as given. I ran it in LTSpice and got what you got but it's not clear how literal they want it.

 

[Baluncore]

Did you consider simply adding a DC current to the AC harmonic currents at the summing input?
That way it provides the offset without needing a second op-amp.

 

[DaveE]

A summer gives the negative of the sum. You add another op amp stage to invert that signal.

Op-amps have nearly infinite gain, so they will always have a circuit wrapped around them. It is easy to make a summer with positive gain, negative gain or any mixture you like, as in a differential configuration. They can do lots of different things. For example:

This allows you to easily figure out how to do all sorts of summing, subtracting, level shifting, inverting with 1 amp and nearly zero effort. You just need to keep it balanced for the zero algebra option.

edit: also, IF IT'S BALANCED, the ground for the output is the ground at the lower R4, which can be different from the grounds for the inputs (with some common mode limitations, of course). However, "balanced" is relative; variations in the real resistor values will degrade the CMRR, sometimes significantly. There are other configurations which have much better CMRR, like instrumentation amps.

 

[bob012345]

Here is my version of it. I can't get a decent, readable screenshot of the output but it goes between 0 and 5V.

 

[DaveE]

Good work!

A couple of comments: These aren't corrections, more like refinements, like how the pros would do it slightly differently.

1) It is considered bad design practice* to use the power supply voltages for anything except to power devices. Any connection into the signal path like the offset function you needed in this problem is a bad idea. The power supply voltages (usually) aren't intended to be very precise, they are noisy, and can create some really annoying cross coupling between different parts of the system. For example, if this circuit was used in an audio synthesizer, you would probably have lots of hum, pops & clicks, or and other noise at the output (in addition to your triangle wave) that was injected into your signal path through R6. So, in practice you would add a voltage reference of some sort (Zener diode, IC, etc.) to provide a clean and stable reference voltage for your offset.

* In the real world "bad design practice" means a circuit that mostly works but may have problems like low reliability, poor performance, hard to build, expensive, etc. (i.e there are better ways to do it).

2) It's much harder to buy a 3.5KΩ resistor than a 3.48KΩ resistor. Same for many other common values. Resistors are most often supplied with EIA standard values (usually the 1% tolerance for analog designs, in my experience). This really doesn't matter for homework problems or understanding. Theoretically useless, but how the real world works. Similar to choosing nut and bolt sizes. As an aside, I can usually immediately tell if a schematic was drawn by a very experienced engineer by things like this. You really wouldn't learn about these details until you had to choose resistors from a standard list (your stock room, distributors, etc.). For example, go online to your favorite distributor (I like https://www.digikey.com/en/products/filter/chip-resistor-surface-mount/52) and search for a 3.5KΩ 1% 0805 SMT resistor, see how many choices there are. Then do the same for 3.48KΩ.

3) If you adjusted your offset so that the output didn't go below 0V ever, then there would be no need for a negative power supply, you could replace it with a ground connection. You would have to choose an op-amp that can output 0V though, but these are common.

If you have lots of free time and you want a puzzle to solve, try this design using an LM10 op-amp with it's built-in reference and single supply capability. That might be how I would do it.

edit: These are especially not corrections, since this is clearly an unrealistic exercise. No one actually makes triangle waves by starting with 4 synchronized sinewaves. Even if those sinewaves already existed in my design, I wouldn't use them for this.

 

[Baluncore]

Fourier synthesis of the sawtooth waveform is a difficult exercise because there are so many harmonics, and they fall off too slowly. Saw = f1/1 + h2/2 + h3/3 + h4/4 + h5/5 + , , ,

Notice how, each time another harmonic is added to the synthesis, it inverts and attenuates the error function. Since the number of harmonics is sharply limited, I would attenuate the higher given harmonics so as to eliminate the reversals in slope on the rising ramp. That would slightly increase the fall-time, but it would significantly reduce the error function.

That error function minimisation could also be achieved by including a Miller integrator capacitor across the op-amp feedback resistor, but that might be break the rules of the exercise.

 

[Baluncore]

Here I have replaced the coefficients {10k, 20k, 30k, 40k} with {10k, 22k, 40k, 70k} to take the bumps out of the ramp.

 

[bob012345]

3k7=3700?

 

[Baluncore]

3k7=3700?

Yes. The decimal point is replaced by the multiplier in circuit schematics.

 

[bob012345]

If you have lots of free time and you want a puzzle to solve, try this design using an LM10 op-amp with it's built-in reference and single supply capability. That might be how I would do it.

What would be the advantage of using this?

 

[DaveE]

What would be the advantage of using this?

Maybe none, but it's a good exercise.

Operation from a single power supply is often very desirable. For example, suppose your design operates off of a single battery. If you can design your circuits to only use that single power supply voltage you will save lots of complexity, cost, size, etc. If not, you may also be designing a negative output switching power supply as part of your solution. I would wager that nearly every circuit in your average car operates off of a single +12V power supply.

The value of using a dedicated reference for your offset I previously discussed.

Also, buying fewer components with the features you need integrated within them saves lots of space, cost, and can increase reliability.

 

[Callum Plunkett]

Sorry for the late reply I've been busy with work the past few days and have not had a chance to get back to anyone.

 

[Callum Plunkett]

There is a lot of information here and its a massive help. Electronics isn't something I do that much of at home or at work so it does not come that natural to me.

Thank you guys.