How do I predict the output of a wien bride oscillator?

[Dan Moos]

Its in the title. How do I do this?

[dobsonr741]

We need a better worded question.

[Dan Moos]

Not sure what to add. Wien bridge is a well defined circuit. How do I predict its gain? The only variable I can think of is the Vcc. The rest is well defined by the standard wien bridge circuit. If there is something I need to add, I don't know what it is.

[dobsonr741]

I saw your post about the lamp stabilized Wien bridge oscillator. The lamp’s characteristics are hard do define and will change widely by each lamp and the temperature.

To keep the oscillation stable the non-linear element (lamp) changes the gain by the amplitude. Gain need to go below 3 at the desired level of oscillation.

If you want an analytical calculation better to sketch it on up on LTSpice, a diode stabilized one, it can be simulated by LTspice under transient tests.

If your sine output is changing by the Vcc the opamp is probably soft clipping. If you are in the linear range, and your gain control part (the lamp or the diodes) are in the proper operating point then Vcc should not matter.

[Dan Moos]

I solved my problem in the other post by raising Vcc. I think I had the lamp too cold to be useful.

I have a working circuit, but I'm not sure what determines the voltage of the output signal.

[dobsonr741]

It’s how strong you are driving the bulb.

[TimFox]

The Wien bridge oscillator stabilizes when the negative feedback through the resistive legs is 1/3, since the positive feedback through the R-C legs is 1/3 at the frequency with zero phase shift.

[Dan Moos]

Ok, I think you guys are missing my question.

I realize that the positive feedback loop has a gain of 1/3 at the freq of the filter. I realize then that the gain of the amplifier needs to be 3 to get the ~unity gain needed for stable oscillation.

But these are fractions, not absolute values. I want to know how to predict the exact output level for known Vcc (and any other variables I might not know are relevant).

For instance, I currently have a WB on my bench running on a +/- 6V supply. I have a 1 k resistor as my feedback resistor, and I have the bulb in series with my decade box currently set at 447 ohms. This value gets me the purest sinewave. The harmonics are barely above the noise, at least on the low brow FFT my 1054z offers. My filter loop is 470 nF caps, and 10k resistors. I get 35ish Hz, which is pretty close to the math, and even closer with the actual measured values of the parts.

I am getting an 8 volt PtoP signal at the output. (actually, at the output of the opamp buffer I have it going to).

With that info, how might I have predicted specifically the 8 volts? Opamp is a tl072 if its relevant. I do see that 8 is 2 thirds of my supply, which the back of my brain says is a clue. Is it as simple as that?

[TimFox]

The resistive side of the Wien bridge normally contains a temperature-sensitive element (such as the famous light bulb).
The output will be stable when that element warms up to obtain the required 1/3 feedback ratio.
When cold, the light bulb has a low resistance and the negative feedback is < 1/3, so the gain is > 1/3 and the amplitude increases until the bulb heats up (but probably doesn't light up).
The thermal inertia of the light bulb keeps the resistance almost constant over the period of the generated sine wave.
I have seen other R-C oscillators that use a thermistor in the "high" end of the feedback, instead of a bulb in the "low" end for a Wien bridge.
You can take your bulb and do a simple DC measurement where you measure the voltage across it for a discrete set of increasing currents, allowing it to stabilize thermally at each current.

[MasterT]

In short - you can't predict, if WB is based on a light bulb as magnitude stabilizer. Resistance of the filament directly affected by temperature of the environment, so the weather is in power.
 There are others way to control /stabilize magnitude, photo-resistor is the simplest I've seen.  Control loop than include demodulator or AC/DC converter, comparator to pre-set value and regulating element - photo-coupler or may be JFET

[Benta]

@Dan Moos, how about if you post the schematic you're working with?
That would bring much better answers.

The classic gain stabilizer and amplitude regulator was the RA53 NTC thermistor, a self-heating bead thermistor in a glass tube.
Obsolete since 30 years, sorry.
Trying to emulate its function with a lamp is a bit more involved, also because an incandescent bulb is a PTC, not an NTC.

[TimFox]

In short - you can't predict, if WB is based on a light bulb as magnitude stabilizer. Resistance of the filament directly affected by temperature of the environment, so the weather is in power.
 There are others way to control /stabilize magnitude, photo-resistor is the simplest I've seen.  Control loop than include demodulator or AC/DC converter, comparator to pre-set value and regulating element - photo-coupler or may be JFET

-hp- certainly obtained a well-defined design value of the oscillation magnitude, including a suitable adjustable resistance to work with the famous Christmas-tree light bulb.
The other methods work as well.
Krohn-Hite built low-distortion oscillators that directly generated two sine-waves in phase quadrature, triggering a sample-hold on one phase by the zero-crossing on the other phase to obtain a feedback value.

[dobsonr741]

OP: in real life: you don't.  If it would be a commercially produced circuit, you would see a gain adjustment trimpot to set the lamp current at a level that brings the desired output signal amplitude.