# How do Sinusoidal output comes out in the Wein-Bridge Oscillator

Isn't this the same circuit that was Hewlett and Packard's first product, a sine wave oscillator? The trick is to have barely enough feedback to oscillate. They accomplished that by using a variable resistance, a tungsten bulb, for R3. If the gain is too high and produces a squarewave, the bulb shines brighter and increases its resistance which in turn reduces the gain.

davenn
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2019 Award
Isn't this the same circuit that was Hewlett and Packard's first product, a sine wave oscillator? The trick is to have barely enough feedback to oscillate. They accomplished that by using a variable resistance, a tungsten bulb, for R3. If the gain is too high and produces a squarewave, the bulb shines brighter and increases its resistance which in turn reduces the gain.
ahhh indeed :)

I went through this a couple of years ago when building a Wein bridge oscillator. Watching the output on a scope was very informative, the smallest of adjustments had it going from a nice sine wave to a square wave

Dave

Note that the reactance of the capacitor is equal to the resistance or 10K. The combination of R1 and C1 in series has an impedance of ~14K ohms. The parallel combination of R2 and C2 has an impedance of ~7K causing 1/2 the output voltage to be fedback to the non-inverting input. To compensate for the 0.5 gain, R3 and R4 have to produce a gain of barely over 2 in order for the circuit to oscillate. The more the overall gain goes over 1, the more of a squarewave will be produced.

jim hardy
Gold Member
2019 Award
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Now you're getting there.

Mother Nature loves sines - they're the only function I know of whose shape does not change when you differentiate or integrate them. So pendulums and other harmonic systems produce them.

So I think of it this way - a sinewave appears for the same reason it does in a spring/mass system - the feedback system is linear(until amplitude grows to point it hits limits as pointed out above) and contains a restoring force that's proportional to rate-of-change of perturbing force.
a quick search took me to this page which shows the principle:(I'll not attempt the derivation right now)
http://www.calpoly.edu/~rbrown/Oscillations.pdf [Broken]

Any help ?

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sophiecentaur
Gold Member
Isn't this the same circuit that was Hewlett and Packard's first product, a sine wave oscillator? The trick is to have barely enough feedback to oscillate. They accomplished that by using a variable resistance, a tungsten bulb, for R3. If the gain is too high and produces a squarewave, the bulb shines brighter and increases its resistance which in turn reduces the gain.
I seem to remember circuits that incorporated a thermistor, to achieve stability in a similar way. Something of the sort is essential is you want to make the oscillator frequency sweepable over a wide range for lab work.

sophiecentaur
Gold Member
Now you're getting there.

Mother Nature loves sines - they're the only function I know of whose shape does not change when you differentiate or integrate them. So pendulums and other harmonic systems produce them.

So I think of it this way - a sinewave appears for the same reason it does in a spring/mass system - the feedback system is linear(until amplitude grows to point it hits limits as pointed out above) and contains a restoring force that's proportional to rate-of-change of perturbing force.
a quick search took me to this page which shows the principle:(I'll not attempt the derivation right now)
http://www.calpoly.edu/~rbrown/Oscillations.pdf [Broken]

Any help ?
Asking what's so 'special' about a sine wave is a bit like asking what's so special about ∏ and e. They just creep out of the analysis. If one is not careful, one could start asking why the mathematical world seems so mimic the physical world so well. You'd soon be into the dimensions of the Great Pyramid and the lost gold of the Incas etc. etc. Move over, Dan Brown.

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I seem to remember circuits that incorporated a thermistor, to achieve stability in a similar way. Something of the sort is essential is you want to make the oscillator frequency sweepable over a wide range for lab work.
When i did this experiment in lab i got all sorts of waveforms until tuning the resistance finally gives a sinusoid.

Now you're getting there.

Mother Nature loves sines - they're the only function I know of whose shape does not change when you differentiate or integrate them. So pendulums and other harmonic systems produce them.

So I think of it this way - a sinewave appears for the same reason it does in a spring/mass system - the feedback system is linear(until amplitude grows to point it hits limits as pointed out above) and contains a restoring force that's proportional to rate-of-change of perturbing force.
a quick search took me to this page which shows the principle:(I'll not attempt the derivation right now)
http://www.calpoly.edu/~rbrown/Oscillations.pdf [Broken]

Any help ?
I am not going to ask for any derivation for mechanical osscillations as i am very much familier with almost all types of mechanical oscillations and i know how to derive those also. The question i would ask is how does these mechanical oscillations relate with Wein-Bridge oscillator?(exept for the fact that the output is sine)

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NascentOxygen
Staff Emeritus
how does these mechanical oscillations relate with Wein-Bridge oscillator?(exept for the fact that the output is sine)
They are characterised by identical second-order differential equations. With each, when given a step or pulse input, their reaction is seen to be a sinusoidal response (superimposed on a decaying characteristic transient).

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NascentOxygen
Staff Emeritus
Isn't this the same circuit that was Hewlett and Packard's first product, a sine wave oscillator? The trick is to have barely enough feedback to oscillate. They accomplished that by using a variable resistance, a tungsten bulb, for R3. If the gain is too high and produces a squarewave, the bulb shines brighter and increases its resistance which in turn reduces the gain.
The Wein Bridge has a reputation for being capable of delivering a high purity sinusoid. But my experiments with a pea bulb revealed, from memory, that its best sensitivity occurred below where it had begun to glow.

sophiecentaur
Gold Member
I am not going to ask for any derivation for mechanical osscillations as i am very much familier with almost all types of mechanical oscillations and i know how to derive those also. The question i would ask is how does these mechanical oscillations relate with Wein-Bridge oscillator?(exept for the fact that the output is sine)
If you are familiar (at a sufficiently high level) with the maths of mechanical oscillators then you only need to replace Masses with Ls and Spring constants with Cs (in principle) etc. etc. to translate your knowledge into electrical oscillators. Oscillators and feedback systems of all types share exactly the same analyses. Could there ever be any surprise that the sinewave appears in both contexts?

davenn
Gold Member
2019 Award
I seem to remember circuits that incorporated a thermistor, to achieve stability in a similar way. Something of the sort is essential is you want to make the oscillator frequency sweepable over a wide range for lab work.
yeah that is an alternative to a bulb.
I used a thermistor in my construction

Dave

Averagesupernova
Gold Member
I don't think a wein bridge oscillators bulbs are EVER supposed to glow.

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If you are familiar (at a sufficiently high level) with the maths of mechanical oscillators then you only need to replace Masses with Ls and Spring constants with Cs (in principle) etc. etc. to translate your knowledge into electrical oscillators. Oscillators and feedback systems of all types share exactly the same analyses. Could there ever be any surprise that the sinewave appears in both contexts?
Glad you put forward this point. I have studied Control Systems, where we replace mechanical systems by a circuit in Force-Voltage or Current-Voltage analogy. Now lets see this problem(the Wein-Bridge Oscillator) in a different way. The question is to draw the equivalent mechanical system for the wein-Bridge oscillator. Can this be done.

I haven't studied the equivalent mechanical thing for an op-amp. Moreover the op-amp is made up of transistors. Do transistors have a mechanical equivalent?

Now you're getting there.

Mother Nature loves sines - they're the only function I know of whose shape does not change when you differentiate or integrate them. So pendulums and other harmonic systems produce them.

So I think of it this way - a sinewave appears for the same reason it does in a spring/mass system - the feedback system is linear(until amplitude grows to point it hits limits as pointed out above) and contains a restoring force that's proportional to rate-of-change of perturbing force.
a quick search took me to this page which shows the principle:(I'll not attempt the derivation right now)
http://www.calpoly.edu/~rbrown/Oscillations.pdf [Broken]

Any help ?
Jim...you see where others see dark !!!! you are spot on....mother nature is simple

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I don't think a wein bridge oscillators bulbs are EVER supposed to glow.
whether they glow or not is irrelevant....they are non-linear

Averagesupernova
Gold Member
But there are parts of that curve that are more linear than others.

But there are parts of that curve that are more linear than others.
The word is non- linear

Glad you put forward this point. I have studied Control Systems, where we replace mechanical systems by a circuit in Force-Voltage or Current-Voltage analogy. Now lets see this problem(the Wein-Bridge Oscillator) in a different way. The question is to draw the equivalent mechanical system for the wein-Bridge oscillator. Can this be done.

I haven't studied the equivalent mechanical thing for an op-amp. Moreover the op-amp is made up of transistors. Do transistors have a mechanical equivalent?
There is no mechanical equivalent for an op amp directly. You need to think in terms of macromodels. So think of it as a device with infinite gain and you go a long, long way to understanding its behavior.

You know, these types of circuits are called analog circuits because they are electrical analogs to mechanical systems, since both mechanical and electrical systems can typically can be described by a set of differential equations.

So yes, the mechanical equiv or the Wein-Bridge oscillator can be drawn. The mathematics are identical.

sophiecentaur
Gold Member
There are plenty of examples of 'mechanical amplifiers' , of course. They can be incorporated into mechanical oscillators to maintain oscillations - such as the escapement system in a clock (essentially a non-linear amplifier), which meters a small amount of energy into the pendulum / hairspring at the right phase, to maintain the oscillation. the Q of the pendulum is very high and acts as a filter to 'smooth' the impulses of energy into the sinusoidal motion of the oscillator. There are fluid and also magnetic amplifiers which are fairly linear and which can give a Wien equivalent oscillator function.

There is no mechanical equivalent for an op amp directly. You need to think in terms of macromodels. So think of it as a device with infinite gain and you go a long, long way to understanding its behavior.

You know, these types of circuits are called analog circuits because they are electrical analogs to mechanical systems, since both mechanical and electrical systems can typically can be described by a set of differential equations.

So yes, the mechanical equiv or the Wein-Bridge oscillator can be drawn. The mathematics are identical.
suppose i want to draw the mechanical equivalent of an op-amp in Force-Voltage or Torque-Voltage analogy. How do i start?

There are plenty of examples of 'mechanical amplifiers' , of course. They can be incorporated into mechanical oscillators to maintain oscillations - such as the escapement system in a clock (essentially a non-linear amplifier), which meters a small amount of energy into the pendulum / hairspring at the right phase, to maintain the oscillation. the Q of the pendulum is very high and acts as a filter to 'smooth' the impulses of energy into the sinusoidal motion of the oscillator. There are fluid and also magnetic amplifiers which are fairly linear and which can give a Wien equivalent oscillator function.
I want to draw the mechanical equivalent of Wein-bridge oscillator with springs, masses etc. Can this be done?

suppose i want to draw the mechanical equivalent of an op-amp in Force-Voltage or Torque-Voltage analogy. How do i start?
The opamp is there to make the circuit more ideal, that is to approximate a mechanical system more closely. You wouldn't need the mechanical equivalent of an opamp in your drawing.

I think this is what you're looking for:

http://lpsa.swarthmore.edu/Analogs/ElectricalMechanicalAnalogs.html

Have fun! :)

The opamp is there to make the circuit more ideal, that is to approximate a mechanical system more closely. You wouldn't need the mechanical equivalent of an opamp in your drawing.

I think this is what you're looking for:

http://lpsa.swarthmore.edu/Analogs/ElectricalMechanicalAnalogs.html

Have fun! :)
I tried this in a Force-current analogy. The mechanical system i got was a first order differential equation for velocity. For velocity stands for voltage, it should have been a second order equation in v for the solution to be sine. Where am i doing wrong?

sophiecentaur