# Sawtooth wave generator from operational amplifiers

## Homework Equations

See above in the question

## The Attempt at a Solution

I know that I need to be using a summing amp with the sinusoidal terms but I am struggling to calculate the input values that I need, also I think I need a capacitor in place of R6 but I'm not entirely sure. Any help is much appreciated :)

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berkeman
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That series for the sawtooth doesn't look quite right (but I could be wrong). The terms should have alternating signs, no? See the figure below.

It looks like your U2 is upside down. Positive feedback may be useful somewhere in this circuit, but I don't think you want it in the output stage...

https://www.sfu.ca/sonic-studio-webdav/handbook/Graphics/Fourier_Series.gif

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• Fourier_Series.gif
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good spot thanks!

Also, i did think making the alternate sources negative but that does not seem to afftect the output so I think my design may be wrong that's why I was considering a capacitor to store the voltage until it gets to 5 then disperse to form the correct wave form as shown in the question. thanks for the reply

berkeman
Mentor
Also, i did think making the alternate sources negative but that does not seem to afftect the output so I think my design may be wrong that's why I was considering a capacitor to store the voltage until it gets to 5 then disperse to form the correct wave form as shown in the question. thanks for the reply
Yeah, using an integrate-and-dump circuit would be the way I would normally make a sawtooth generator circuit, but it seems they want you to use a summing amplifier on all of the input terms that you are provided. I think the main things you need to get right in your circuit is to scale and offset the output correctly based on the input waveforms.

Yeah that's what I'm struggling with but thanks anyway :)

berkeman
Mentor
Yeah that's what I'm struggling with but thanks anyway :)
So just start with a summing amplifier stage to add up the 4 input waveforms. That will give you an approximation of a sawtooth waveform, but with too large an amplitude and centered at 0V instead of running 0V to 5V as shown in the graph. Then what can you do to offset the output waveform in the positive direction to get closer to the final graph.

Also, keep in mind that you may need to multiply every other term by -1, if the information that I posted is correct. Maybe look around at other sources of information about Fourier series expansions of the sawtooth waveform to see if they alternate terms...

There won't be input waveforms from the DC sources would there? Sorry if I'm way off the mark but this question really has me confused

berkeman
Mentor
There won't be input waveforms from the DC sources would there? Sorry if I'm way off the mark but this question really has me confused
I was confused about the DC sources shown in your schematic. The question looks like it wants you to base the opamp circuit on the "Black Box", which has the 4 sinusoidal input waveforms, and produces something close to the desired sawtooth waveform at its output. Where did the idea of using DC sources in the circuit come from?

definitely me. I had a silly moment, sorry, don't know why I had it in my head that the Sinusoidal (big, massive clue there) was a DC input. I've designed a new circuit so that I'm able to get a square wave, and a capacitance wave, just struggling to get the harmonics right for the sawtooth

berkeman
Mentor
definitely me. I had a silly moment, sorry, don't know why I had it in my head that the Sinusoidal (big, massive clue there) was a DC input. I've designed a new circuit so that I'm able to get a square wave, and a capacitance wave, just struggling to get the harmonics right for the sawtooth
The harmonic amplitudes (relative) are defined by the Fourier expansion equation. You need to adjust the overall gain to get the correct total amplitude, and you need to add in an offset so the waveform has that DC component shown in the graph.