Low Frequency Oscillators (LFOs) and why they are hard to design

[R.G.]

Actually, that's a mis-title. They are not hard to design. But they are hard to adapt well to the circuits they drive. And even then, it's not because the LFO is hard to adapt.

The underlying issue is not the LFO at all. It's whatever they are driving. Each thing a LFO drives has its own different needs for whether it needs a voltage or a current drive, what the minimum and maximum levels for these voltages or currents are, and what amount of variation you get per change in the LFO quantity.

Examples:
- JFETs used as variable resistors need an on-to-off voltage of between their Vgsoff and Vgs = 0. For that range, the JFET drain acts like a variable resistance, between the values of essentially an open circuit and the rdson for the JFET, generally under 1K and maybe under 10 ohms. Note that each JFET, even of the same type number, may have a different Vgsoff and rdson. That's what makes matching important if you use more than one with the same LFO
- bipolars have a variable resistance from collector to emitter. This varies with base current much more linearly than with base voltage, although the voltage changes a little too.
- LDRs change with the amount of light. This is usually done with an LED or incandescent bulb. Both LED and incandescent bulbs have a different response to voltage and current. LEDs are almost linear with current through them. incandescent bulbs are essentially not linear with anything, as they glow based on temperature, and that varies with the emissivity of the lamp and the power into it. So the resulting amount of resistance change per volt/amp/whatever can be quite different depending on the device
that makes the light as well
- OTAs are (usually) linear in transconductance (i.e. change in current out per change in voltage in) with the current into the bias pin. They are exponential with respect to the voltage on the bias pin, and that can only vary from zero to about 0.7V for simple OTAs or 0 to 1.4V for the 13700/3280/5517 types

And that's what makes LFOs tricky - they drive tricky things and get blamed for the oddities of the thing they're driving.

[Mark Hammer]

So I guess the take home message is that just because the LFO can be measured on a scope as being flawlessly triangular or sinusoidal doesn't mean that the net effect of the LFO, once it starts interacting with the control element (FET, LDR, OTA, etc.) will reflect that triangular perfection: what you hear is not the same as what you measure on the output pin of the LFO.

[R.G.]

So I guess the take home message is that just because the LFO can be measured on a scope as being flawlessly triangular or sinusoidal doesn't mean that the net effect of the LFO, once it starts interacting with the control element (FET, LDR, OTA, etc.) will reflect that triangular perfection: what you hear is not the same as what you measure on the output pin of the LFO.

Oh, sure, say it the simple, easy, obvious way that's easy to understand!



Right again on the take-home message! LFOs are only one piece of getting a smooth - or properly un-smooth - sweep. And they are the easy part.

[Hides-His-Eyes]

Of course, with vactrols and PWM, you can do pretty well...

[Mark Hammer]

So I guess the take home message is that just because the LFO can be measured on a scope as being flawlessly triangular or sinusoidal doesn't mean that the net effect of the LFO, once it starts interacting with the control element (FET, LDR, OTA, etc.) will reflect that triangular perfection: what you hear is not the same as what you measure on the output pin of the LFO.

Oh, sure, say it the simple, easy, obvious way that's easy to understand!



Right again on the take-home message! LFOs are only one piece of getting a smooth - or properly un-smooth - sweep. And they are the easy part.

Sorry.  A thousand pardons.  Honestly, sometimes I just plain forget I'm a civil servant, and the clarity just kinda sorta leaks out without intending to.   It's a bad habit I have to break one of these days.  I'll go back to needless obfuscation now.  My paycheck and performance review are depending on it! 
To my credit, though, I did use four different abbreviations (LFO, FET, LDR, OTA) within the same sentence, so I haven't completely lost it. 

[boogietone]

Just wait until we have to work with subminiature fluorescent lights (SMFLs) as part of the driver circuit.  I can only imagine the debates about true vintage vs NOS on those.

[earthtonesaudio]

Of course, with vactrols and PWM, you can do pretty well...

Sure, but that's cheating. 

[R.G.]

Sorry.  A thousand pardons.  Honestly, sometimes I just plain forget I'm a civil servant, and the clarity just kinda sorta leaks out without intending to.   It's a bad habit I have to break one of these days.  I'll go back to needless obfuscation now.  My paycheck and performance review are depending on it! 
To my credit, though, I did use four different abbreviations (LFO, FET, LDR, OTA) within the same sentence, so I haven't completely lost it. 

Remember, a sufficient number of TLAs* can cover a multitude of shortcomings in any official document.

Do try to keep in mind the Primary Maxim of Bureaucratic Endeavor: If there are more than two signatures on the document, the blame will never be placed.








* Three Letter Acronym 

[soggybag]

Speaking of PWM, I built the MXR Envelope and in the process gained some understanding of it's operation. It uses a PWM as it's VC. I would not have thought this would have worked as well as it does in the MXR filter. The MXR filter works very well. I think there is a Phaseshifter that also uses PWM as a control system.

[DDD]

There's an easy way to create sinusoidal LFO without any problems.
Adding a simpliest filter can smooth the output signal.
The aricle is in the middle section of the page:
http://forum.gtlab.net/cgi-bin/yabb2/YaBB.pl?num=1194184104/280
(Name of the article is "Simple Sine-Wave Generator Has No Low- Or High-Pass Filter")

[Thomeeque]

There's an easy way to create sinusoidal LFO without any problems.
Adding a simpliest filter can smooth the output signal.
The aricle is in the middle section of the page:
http://forum.gtlab.net/cgi-bin/yabb2/YaBB.pl?num=1194184104/280
(Name of the article is "Simple Sine-Wave Generator Has No Low- Or High-Pass Filter")

Nice, very smart (he's from Czech Republic, that's why ), but you cannot use this as modulation FX sweep LFO, 5-bit resolution sinus has way too big steps, you need very fluent curve for sweeping.. T.

[DDD]

Sorry,
but there's no 5 (five)-step approximation at all.  
The generator produces  32-step approximation  of each sine-wave period, so the simple filtering can do the job more than decently.

[Perrow]

I'll submit the effort of linking to the article in question: http://www.audioscientific.com/28_Simple_Sine_wave_generator_has_no_filters_.jpg

[Gurner]

Sorry,
but there's no 5 (five)-step approximation at all.  
The generator produces  32-step approximation  of each sine-wave period, so the simple filtering can do the job more than decently.

Exactly, 5 bits (which is what Thomeeque said) = 32 steps ....& 32 steps - even with smoothing -  isn't much at all (16 steps per 'swing')

[merlinb]

Exactly, 5 bits (which is what Thomeeque said) = 32 steps ....& 32 steps - even with smoothing -  isn't much at all (16 steps per 'swing')

It's not bad though- in the CMOS Cookbook it notes that a 16 step sinewave approximation (I think) results in the lowest harmonic present being the 9th, so its not too hard to filter.

[Thomeeque]

Sorry,
but there's no 5 (five)-step approximation at all.  
The generator produces  32-step approximation  of each sine-wave period, so the simple filtering can do the job more than decently.

It is actually 4bits (16 levels) in both time and voltage domains for full swing (modulation going from one end to another end), 5th bit "just" switches direction (EDIT: as Gurner already noted ). Flangers do have period even tens of seconds (e.g. Electric Mistress longest sweep period is around 30 seconds IIRC, it would be almost one step per second).



simple_sine_brno.asc

Filtering would not be simple.

It's not bad though- in the CMOS Cookbook it notes that a 16 step sinewave approximation (I think) results in the lowest harmonic present being the 9th, so its not too hard to filter.

Really? Tell me how, I'll try it

T.

[R.G.]

I'm a big fan of the stepped sine approximation. See: "Digital Generation of LFOs for Modulating Effects" (2000) 
http://www.geofex.com/article_folders/lfos/psuedorandom.htm

However, the simplest way is with a microcontroller. The programming is simple enough that it makes a good test of your programmer setup, and you can go to as many bits internally as you want. The limitation is really the number of output pins to make the D-A outputs. Or most newer uCs have PWM outputs for 10 to 12 bit accuracy - that's a *very* accurate sine wave for an LFO.

[DDD]

Anyway, analogue circuitry intended to process frequencies below 1 Hz is too complicated and too sensitive to leaks, humidity etc.
At the same time it's almost impossible to use usual scopes to check such an ultra-low frequency waves and its disortion while digital scopes do it easily.

[soggybag]

Of course all the talk of sine oscillators and micro controllers loses the point of the original article. But, while we're on the digression, I used a micro controller to create random voltage source for a sample and hold effect. This type of control voltage is difficult and problematic to create in the analog realm. With the MCU it was reduced to a programming problem and became a single 8 pin DIP.

That said, the real problem then became interfacing PWM output as a CV for an analog circuit, which was not easy as it looked on the surface. And we're back to the point of the original article.

[PRR]

> The underlying issue is not the LFO at all. It's whatever they are driving. Each thing a LFO drives has its own different needs

Maybe pictures would help.

Since LFOs aren't much to look at, let's take a heavy-metal analogy.

I got a car-lift cheap because the control valve is %$#@!ed-up. In a 9-foot (9V?) garage the lift runs down to 1 foot and up to 8 feet several times a second.



This is no-good as a car-lift.

But there's other stuff which can use this kind of "LFO" up-down action.

Rolling paint on a wall is one idea.



But note that we must cover the whole 8' wall with the 7' stroke of the lift. We need a 7:8 lever. We also need to offset down with a high pivot or a bent arm. And real walls are never 8'0", we need some trim of lever and offset.

Tooth-brushing requires even more lever-down. Lever ratio is fairly critical: too little misses the gumline, too much rips a cheek. Stroke changes as baby-teeth are shed for adult teeth. And the offset tends to change as the child ages.



Wet basement. Run a piston pump.



Note that the lift is above the floor, the pump is below the floor. Big offset. Unlike the roller and brush jobs, the exact stroke of a piston-pump may not be critical.