advice on LFO theory

[jrc4558]

could any of you gentlemen recommend a good tutorial or theoretical reading on LFOs? I know I could exctract a circuit from any modulated pedal, but I want to learn and understand how these LFOs work. I am currently searching for one for my attempted mod to FSH-1 from tonepad. And, after readig the forum and the google search page for about two hours, I found  waaaaaaaaaaaaay too much different circuits. Having failed to choose any one of them for my use, I decided that I need to learn the subject a little better beforehand.
Hence the request.

[chunks717]

I learned alot from building / breadboarding the 4ms LFO

its in most of their pedals, but the trem lune is the bare-est.
It is a pretty standard design.

breadboard one, then start playing with values, and adding their mods, and you will be able to get almost any wave you want.
If you can look at the resulting wave on an osilloscope, even better.

I use my own version of it to modulate many different effects, and in fact have boxes with mainly just that circuit, throbing a LED into ldr, with the resistance between 2 legs of a jack, so that I can add a 'modulate' jack on just about any knob on any effect with a parallel resistance. works out really well almost every time without the hassles of voltage scaleing etc.

ummmm not really sure if that is the sort of thing you were looking for. 
almost any basic op-amp textbook should have a chapter on oscillators....

[gez]

Practical Oscillator Circuits by A Flind (Babani publishing) is a cheap intro to the world of oscillators.  I learnt the basics from magazine articles, but this book sums things up nicely and covers a lot of the circuits that get used in the pedals we build.

Amazon should have copies.

[jrc4558]

ahem, sorry.
thanks for all the advices, but i hoped to find something online...

[R.G.]

There are two kinds of analog oscillators: phase shift oscillators and relaxation oscillators.

The term "LFO" means "low frequency oscillator", and LFOs are distinguished from other oscillators only by their frequency of oscillation. Every oscillator is a low frequency oscillator to some circuit or other.

A phase shift oscillator makes a sine wave or a distorted sine wave.
A relaxation oscillator makes a square or rectangular wave and a triangle or sawtoothed wave, depending on the circuit.

A phase shift oscillator works by having an amplifier with feedback. Both the amplifier and the feedback network have some phase shift which varies with frequency. If there is any frequency where the phase shift through the amplifier and the feedback network add up to 360 degrees or an integer multiple of 360 degrees, and the amplifier gain is equal to or more than the losses through the feedback network, it oscillates. If the gain is *exactly* equal to the feedback losses, the output is a clean sine wave. If it's even marginally less, the output is a ringing that dies out. If the gain is greater than the losses in the feedback network, the amplifier is slightly overdriven and the sine wave amplitude is limited at the point where the amplifier starts clipping. The greater the gain, the greater the clipping in the output sine wave.

For feedback networks with lots of phase shift or complex impedances, involving lots of caps and inductors, crystals, piezo crystals, etc, it is possible to make the amplifier lock on a harmonic of the base frequency if the amp has enough gain.

The trick in making a low distortion phase shift oscillator is having a gain adjusting circuit that adjusts gain softly to some level of sine wave out. This is how HP got started. They used a light bulb to soft limit gain.

A relaxation oscillator is an amplifier and feedback network again, but the feedback is both positive and not DC coupled, or not DC stable.

The classic effect LFO is an integrator which integrates up and down depending on the polarity of its input; this is followed by a Schmitt trigger which has hysteresis - a dead zone in the middle. For inputs below Vlow, the output of an inverting Schmitt trigger is high. You then have to move the input higher than Vhigh to make the output change to low. Once the output is low, you have to get above Vhigh again to make it flip again. It is immune to inputs between Vlow and Vhigh. Schmitts may be inverting or noninverting.

For an inverting integrator, the Schmitt trigger looks at the output voltage and is non-inverting. Assuming the output of the integrator is initially low, then the Schmitt trigger output will go low. That is fed back to the input of the integrator as a low input, and the inverting integrator starts ramping up. It ramps up until the output is higher than the Vhigh level on the Schmitt. The Schmitt trigger output goes high, the input to the integrator goes high, and the integrator starts ramping down. This goes on forever. Once you know the output voltage levels of the Schmitt trigger (which is the integrator input), and the integrator R-C values, you have defined the circuit.

The integrator input current is Vin/Rin. The integrator's feedback capacitor forces the output to rise at a rate which pulls that current through the cap, or I = CdV/dt.
So dv/dt, the ramp rate in volts per second is dV/dt = (Vin/R)/C = Vin/R*C. The time in each polarity is the difference between the Schmitt trigger trip voltages and the ramp rate.

I've left out uController and counter based LFOs, which are much simpler.

[gez]

ahem, sorry.
thanks for all the advices, but i hoped to find something online...

As wonderful as the internet is, it has its limitations (as things stand).  The beauty of books is that you have information readily accessible to you, in one place (not spread over several websites), they have indexes and you can flick through them quickly, plus you can read them anywhere (we won't go into that one).

The thought/time/investment that goes into them also means the info is more likely to be correct.  Each to their own though...

[jrc4558]

Thankyou R.G.!
Gez, I agree, but finances are not allowing for a book at the moment. Things make greater sense to me when read on a subway ride, than off of a computer screen, too.