Analyzing a Wien-Bridge Oscillator for Stability: Techniques and Tips

[Gokul43201]

I need to analyze a Wien-Bridge Oscillator for stability. Over the last day or so, I've taught myself to understand different op-amp circuits where I have well-defined V(in) and V(out).

For the oscillator circuit though, there really is no such thing as V(in). There's a V(out) which evolves with time, and if the circuit is stable, reaches some steady state value. Is there some standard way to analyze such a circuit? Do I have to set up differential equations, or can I just look for poles in the loop gain (or loop transmission...I'm not too familiar with the terminology)?

A reference will be useful; ideas will be appreciated.

For the Wien-Bridge oscillator, see Horowitz & Hill, Section 4.14 (p 165,166).

 

[berkeman]

I googled wein bridge oscillator tutorial, and this first hit is pretty good:

Tutorials on different oscillator types (Wein Bridge docs at bottom of page):
http://users.pandora.be/educypedia/electronics/analogosciltypes.htm

Wein Bridge Oscillator / Phase Shift Oscillator design:
http://www.ee.sc.edu/classes/Spring02/elct301/Lab_301_2W2001.doc

I'm no expert in oscillator design (although I've certainly made several of them by accident!), but the overall idea is that you want to have unity loop gain with 180 degree phase shift at the frequency of oscillation. BTW, you may already know this, but the 1869 lamp that Horowitz and Hill shows in their Wein Bridge oscillator circuit was the subject of a patent by Hewlett Packard back in the early days. HP used the circuit for their first product, which was an audio oscillator instrument used by Walt Disney Studios in their early productions. The trick of using the variable resistance of the lamp filament as a gain stabilizer was the subject of the patent. Pretty cool trick.

 

[Gokul43201]

I googled wein bridge oscillator tutorial, and this first hit is pretty good:

Tutorials on different oscillator types (Wein Bridge docs at bottom of page):
http://users.pandora.be/educypedia/electronics/analogosciltypes.htm

Wein Bridge Oscillator / Phase Shift Oscillator design:
http://www.ee.sc.edu/classes/Spring02/elct301/Lab_301_2W2001.doc

Thanks berke !

That should give me more to look into, but I think I've got the hang of the thing. What I need to figure out is how (mostly thermal) drifts and mismatches in values of my passive components will affect the gain and the phase. It looks like, if I'm clever and lucky, I can avoid first order effects altogether (and second order terms are smaller than a ppm, which is better than what I need).

I'm no expert in oscillator design (although I've certainly made several of them by accident!), but the overall idea is that you want to have unity loop gain with 180 degree phase shift at the frequency of oscillation. BTW, you may already know this, but the 1869 lamp that Horowitz and Hill shows in their Wein Bridge oscillator circuit was the subject of a patent by Hewlett Packard back in the early days. HP used the circuit for their first product, which was an audio oscillator instrument used by Walt Disney Studios in their early productions. The trick of using the variable resistance of the lamp filament as a gain stabilizer was the subject of the patent. Pretty cool trick.

I heard this bit of trivia from my advisor last week, when he gave me this project. This original HP oscillator is now supposedly a collector's item (though the next version they came out with gets traded on and off on EBay)! Neat, alright.

I won't we using the lamp, though! It'll either be a FET or a modulator chip, like the AD630.

 

[Gokul43201]

Gah, I've run into another problem. I don't know how to arrive at the actual size of the signal.

The values of my passive components affects my gain and stability of oscillation (which I ensure by being close to a zero of my gain denominator, or 1-L(s)). But I see nothing obvious that tells me what the size of the signal will actually be.

My best guess is the following. The gain is set to some value that's a little bigger than 1. In a basic oscillator, this will cause the signal to grow from some miniuscule value till it starts to saturate the op-amp. But this is where the non-linear device kicks in. As the signal gets large the drop across the lamp gets larger (sort of like a viscous damper?). The I-V characteristics of the non-linear device is then what determines the steady state signal (or in my analogy, the terminal velocity).

Am I completely out of the ballpark here?

PS : I'm looking into more of those tutorials as I write this. So far, I haven't found anything that addresses this last problem.

 

[berkeman]

Yeah, as I understand it, the amplitude will stabilize at the point where the gain of the opamp starts to roll off slightly because you aren't in the small-signal region anymore. You might check the opamp datasheet to see f there's a good plot of gain versus output signal size...