I have a 555 timer producing a 600khz (roughly) 50% on 50% off square wave signal signal. This is fed into a integrator but The output is constantly -11v with smalll variations
I've tried altering the valuses of c1 and r1 with no luck
Maximum frequency of the 555 is 500kHz and you don't need a dual supply, a single +V rail will do. I don't like the componant values used in you differentiator, 100R is a bit too low, and .1 uF looks far too big, the output will be so too small to measure, try 470pf and 1k.
That's not a differentiator, that's an integrator. And you can't run a true integrator "open loop". It will rapidly run off to one rail or the other, depending on input duty cycle and voltage levels. That's what you are seeing. If you want a triangle wave and a square wave, do it in a feedback loop as you said you would do in this thread.
Tell us again why you need a function generator at such a high frequency.
The circuit below (either version) runs at about 45kHz in simulation as drawn. You need to remember to tie unused LM393 inputs to the negative supply voltage (GND or vee, depending on which version you use), and to connect the unused TL072 as a voltage follower, with the noninverting input connected to the vcc/2 divider, or to GND, depending on which version you use. You also need power supply decoupling capacitors.
I congratulate you on coming up with a working circuit.
However, I do think you have used way more parts than you need to get an inferior "triangle" wave. You don't need the push-pull emitter followers. You don't need another 555 just to invert a square wave.
I didn't say you don't need an inverter. I just mean I think a 555 is overkill, and has more propagation delay, than a simple transistor inverter. However, it does use fewer parts!
thanks for the suggestion of a transistor inverter, that's now replaced the second 555 as for the push pull emmitters they are required to get the triangular waves to match, without them the peaks are at different amplitudes