Misplaced Pages

Revision as of 01:30, 11 August 2011

Need to add a schematic (or several) -- I'll get to it shortly Madhu

link broken

the link to the other schematic, supposedly in spanish, is broken. —Preceding unsigned comment added by 172.213.91.54 (talk) 20:16, 14 April 2008 (UTC)

An oscillation circuit in which a balanced bridge is used as a feedback network is the Wien bridge oscillator shows in fig. —Preceding unsigned comment added by 117.98.64.51 (talk) 18:18, 11 May 2009 (UTC)

Is explanation of operation of light bulb gain control correct?

I think the explanation of the cause of the nonlinear resistance of the light bulb is misleading. The actual cause of the nonlinearity is that the power dissipation in the filament is proportional to the square of the current P = iR. I would think that the large nonlinear increase in power radiated away from the filament with temperature due to the Stefan-Boltzman law would tend to reduce the temperature rise of the filament, thus reducing the nonlinearity. --Chetvorno 17:30, 10 July 2009 (UTC)

How do RC oscillators produce sine wave?

Some intuitive explanations

(copied from Electronic oscillator talk page)

... I will add to this discussion all RC oscillators (e.g., Wien bridge) that are a big challenge for human imagination. Why? Just because it is too hard for a mere mortal:) to imagine how the humble RC circuit can produce sine wave, how it can act as a "resonator" at all. Three years ago I managed to reveal how the more sophisticated LC circuit does this magic. Then I began thinking about how the humbler RC circuit could do it... and this was a big challenge for my imagination. Here are my intuitive achievements about the most general (philosophical:) idea behind RC oscillators. I have used, as usual, a figurative and colorful language to picture the circuit operation.

RC oscillators stay between relaxation and harmonic (LC) oscillators; they possess properties from the both. Like relaxation oscillators, they have only one storing element (capacitor) that continuously charges and discharges; it stores only one kind of energy (electric) that is wasted. Like LC oscillators, the storing element is connected in a positive feedback loop to sustain the oscillations; they produce "rounded", "smooth", sine waves... Let's see why and how.

Simply speaking, both the relaxation and RC oscillator consist of a voltage source (an amplifier) driving a capacitor through a resistor. To make the voltage across the capacitor wiggle, this source has somehow to change its polarity at the peaks of the halfwaves.

• In a relaxation oscillator, the amplifier output voltage stays constant (maximum or minimum, at one of the supply rails) until the capacitor charges/discharges. When voltage drop across the capacitor reaches the peak, the amplifier switches sharply (helped by the accelerating positive feedback) this voltage from the current to the other rail. As a result of this voltage jump, the shape of the relaxation oscillation is peaked, angular, not sine...

• In an RC oscillator (Wien bridge oscillator is a good example), the storing element (the grounded capacitor in the figure on the right) is connected in the positive feedback loop. (IMO) the loop gain has to be close to but yet a little more than unity. At these conditions, the amplifier output voltage is constantly a little higher than the voltage drop across the capacitor and the latter continuously charges. The capacitor voltage tries to reach the amplifier voltage that continuously shuns up because of the positive feedback. Figuratively speaking, the capacitor is "self-charging"; it "pulls up" itself (with the help of the supplied amplifier) like Baron Münchhausen escaping from a swamp by pulling himself up by his own hair:) If the loop gain was exactly unity, the amplifier output voltage would be equal to the voltage drop across the capacitor... no current, no voltage change, no wave... Another impressive analogy is a cage equipped with "antiweight". Imagine you are in the cage but some "joker" has increased slightly the antiweight and, of course, loosed the brakes:) As a result, to your great surprise, you will begin lift up just like the voltage across the capacitor... If the antiweight was equal to the cage weight, you will stay immovable.

When the capacitor voltage approaches the positive supply rail, the amplifier begins saturating; the loop gain begins decreasing and the voltage change looses its nerve. Finally, at the top of the halfwave, the amplifier does not amplify at all and the voltage stops changing; thus the upper sine peak. Now the grounded capacitor begins discharging through the parallel connected resistor (note there is no charging current from the amplifier output since the upper capacitor impedes it). The positive feedback helps this process as above (now the joker has decreased slightly the antiweight and you travel down:) Its voltage begins decreasing trying to reach the amplifier voltage that continuously shuns down. When the capacitor voltage approaches the negative rail, the amplifier begins saturating; the loop gain begins decreasing and the voltage slows its change. At the bottom of the halfwave, the amplifier does not amplify and the voltage stops changing; thus the bottom sine peak.

As a final conclusion, RC oscillations arise because of the slight positive feedback with dynamic loop gain (between peaks it is bigger than one; at the peaks it is exactly one). The shape of an RC oscillation is smooth (sinusoidal) since at the peaks of the halfwaves the amplifier output is saturated and does not change its voltage (just like an LC oscillator).

These were only my insights. I would be glad if you share and enrich them... Circuit dreamer (talk, contribs, email) 20:22, 28 July 2011 (UTC)

All you need to make a sine wave are an LC and an excitation source. If you solved a few differential equations you would discover sinusoids are very common. Tape an LED to a bicycle wheel and watch it's locus as the wheel rolls - another sinusoid! Zen-in (talk) 05:31, 29 July 2011 (UTC)

Well, LC oscillator is clear but RC one is the problem. The big question is (was:), "How does a sine wave conceive in the humble RC circuit?" Differential equations will show sinusoids in detail but will not answer this question. The LED example is very attractive; I will carry out it to explain to my grandson what a sinusoide is:) Circuit dreamer (talk, contribs, email) 06:16, 29 July 2011 (UTC)

In actual fact the led on a bicycle wheel will trace out a curate cycloid not a sinusoidal curve. Dmcq (talk) 16:49, 5 August 2011 (UTC)

A sine wave is the time-wise representation of a single frequency. If you just have one RC you can only have one frequency. Another question though is: If you haven't been able to grasp this basic concept then why are you editing this page? Zen-in (talk) 16:38, 30 July 2011 (UTC)

I have begun editing this page to find out the answer to this basic question:) And as you can see, I have managed to find it... The next question is, "Why does the circuit oscillate exactly at the Wien network resonant frequency? Is this really true?" If you (and Grlx) can, help me to find the answer. Circuit dreamer (talk, contribs, email) 21:21, 30 July 2011 (UTC)

Adding your WP:OR damages the article. Editing an article is not an opportunity to find answers; editing an articles requires consulting actual sources -- not one's own thoughts about the material or some blogger's ramblings. I don't have the time to fix this. Glrx (talk) 23:19, 30 July 2011 (UTC)

Oh, but this was only a joke! Can you joke at all? Otherwise the topic is extremely serious and difficult for understanding. Circuit dreamer (talk, contribs, email) 04:19, 31 July 2011 (UTC)

Just revert C-F's edits. There's no point in trying to edit what he has written. We aren't his secretaries. Zen-in (talk) 05:09, 31 July 2011 (UTC)

The sorry fact that you cannot understand the simple truth about this clever circuit does not mean that it should be removed. Circuit dreamer (talk, contribs, email) 06:42, 31 July 2011 (UTC)

Interesting TI material

I have extracted the "philosophical" text below from a TI material. There are valuable thoughts there that can be useful for this page. See for example the third alternative: "(iii) The system stays linear and reverses direction, heading for the opposite power rail. This produces a sine-wave oscillator." Please, discuss why "the system reverses direction". Circuit dreamer (talk, contribs, email) 11:01, 31 July 2011 (UTC)

"...As the phase shift approaches 180° and |Aβ| → 1, the output voltage of the now-unstable system tends to infinity but, of course, is limited to finite values by an energy-limited power supply. When the output voltage approaches either power rail, the active devices in the amplifiers change gain. This causes the value of A to change and forces Aβ away from the singularity; thus the trajectory towards an infinite voltage slows and eventually halts. At this stage, one of three things can occur: (i) Nonlinearity in saturation or cutoff causes the system to become stable and lock up at the current power rail. (ii) The initial change causes the system to saturate (or cutoff) and stay that way for a long time before it becomes linear and heads for the opposite power rail. (iii) The system stays linear and reverses direction, heading for the opposite power rail. The second alternative produces highly distorted oscillations (usually quasi-square waves), the resulting oscillators being called relaxation oscillators. The third produces a sine-wave oscillator..."

I am glad to see that these considerations second my explanations. Circuit dreamer (talk, contribs, email) 17:45, 31 July 2011 (UTC)

Revert of new material

Note discussion at http://en.wikipedia.org/Wikipedia:No_original_research/Noticeboard#Wien_bridge_oscillator

The new material was largely unsourced. It had factual errors. An editor above was for a complete revert or material that is apparent WP:OR. What sources do you have for the material? As stated in the edit summary, the material has problems. Reducing to a gain of one does not cut it; Strauss will contradict. Glrx (talk) 20:55, 2 August 2011 (UTC)

The Xicor application note has problems. Its primary goal is showing off a variable resistor. The AGC circuit has very fast attack. At large positive excursions, output of U3A drives input of U3B through diode; there should be a series resistor. Glrx (talk) 21:04, 2 August 2011 (UTC)

Am I responsible for the Xicor application? And if it has some problems, don't you think you should remove the link, not all the Background and Operation sections? Circuit dreamer (talk, contribs, email) 21:11, 2 August 2011 (UTC)

Yes, if you continually reinsert it. How would the material in the app note improve the article? Glrx (talk) 22:12, 2 August 2011 (UTC)

Please, explain below what these factual errors are and I will immediately remove them from the text. Circuit dreamer (talk, contribs, email) 21:08, 2 August 2011 (UTC)

The discussion sections above were about your original research not belonging in WP articles. Both the Background and Operation sections that you added to the article are your original research.

I have added extremely simple and obvious intuitive explanations based only on the fundamental electricity concepts. There are references for most of them but it would be comic to cite them. Circuit dreamer (talk, contribs, email) 06:30, 3 August 2011 (UTC)

The Background section does not have a single reference in it. The statement "positive feedback amplifier with high open-loop gain" is factually wrong. Such a circuit would be a multivibrator or stuck at a rail. To make an oscillator, the ideal loop gain must be one. The loop gain must include the attenuation in the bridge. You've quoted Barkhausen before; why do you contradict him now? The paragraph is also seriously confused about how the nonlinear feedback system works. There are two nonlinear feedback systems. Neither one "turns on". The unity gain at the peak statement is false; if that were true, the fundamental would still be increasing. The section does not appreciate harmonic balance.

• Looking at the circuit from the first viewpoint, it is exactly a feedback amplifier with high open-loop gain. It consists of two components: an operational amplifier having a very high open-loop gain, differential input and single-ended output, and a feedback network (Wien bridge) connected between the op-amp output and (differential!) input. I have written it but will say it here again. This bridge circuit is a quite odd feedback network since it can have a positive, extremely low (up to zero) or negative transfer ratio (this is a basic property of any bridge circuit). But the overall loop gain is ever close to one. So, it is not a multivibrator because of this low gain and the grounded capacitor that does not allow guick change ("avalanche").
• "...To make an oscillator, the ideal loop gain must be one..." This Barkhausen assertion can be right in the case of an LC oscillator where an LC tank produces the oscillations and the feedback system only sustains them. But it cannot be right in the case of RC oscillator where the humble RC circuit cannot produce any oscillations without an external control. Do you realize the simple truth that Barkhausen is not always true? In this case, unity gain is unsufficient; it has to be more than one! How can you expect that the voltage across the capacitor will increase if you "copy" this voltage (voltage follower, gain of one, bootstrapping...) and then apply the same voltage across the capacitor? What is this mystic force that will make the voltage across the capacitor change as no current flows through it? I have described it clearly in the article and in this discussion by means of funny analogies...only and only to convince you in this simple truth!
• How the nonlinear feedback system works... I have described it thoroughly. You may considered the system as comprised by two feedbacks - negative and positive. The first (the voltage divider with a nonlinear grounded resistor) is amplitude nonlinear; the second (the Wien network) is frequency sensitive (and, if you want, nonlinear with respect to frequency). Saying "turns on" I mean "begins changing its transfer ratio" or "enters the nonlinear part of the curve" or "begins loosing its nerve":)

The unity gain at the peak statement is false; if that were true, the fundamental would still be increasing.

I have already discussed this above: the gain begins decreasing and when it become equal to one the voltage stops changing. The voltage would increase if the gain is more than one. Circuit dreamer (talk, contribs, email) 13:35, 3 August 2011 (UTC)

The second bold paragraph is wrong for the same reason: a faulty notion of power balance. The loop gain should not be "small", it should be "unity".

I have said "small" since it is not constant; it varies with the voltage magnitude. During the sine "excursions", it is bigger than three and the loop gain is more than one; at the peaks, it becomes exactly three and the loop gain is exactly one. Circuit dreamer (talk, contribs, email) 13:35, 3 August 2011 (UTC)

The third paragraph is full of your connecting different ideas together.

Where are the WP:RSs?

The Operation section is unsourced except for a citation in the generalization section.

Generally, the section confuses oscillator start up (initial noise) with the steady state operation of a linear oscillator. The comments about avalanche are inappropriate. Positive feedback can create exponential growth, but it is not an avalanche process. Avalanche does not involve feedback.

I have frequently used the word "avalanche" with meaning of "regenerative", self-reinforcing, self-accelerating, continuously increasing, etc. I do not understand what you mean when saying "avalanche". Circuit dreamer (talk, contribs, email) 13:42, 3 August 2011 (UTC)

The section does not distinguish between the two nonlinear processes. It confuses them.

What are these two processes? Describe them.

The comments about stability and the decrease to unity gain are unstudied and wrong. A changing derivative does not imply instability. The anthropomorphic motives are confusing. The upper cap prevents the output from charging the lower cap? Where is the reliable source for that statement? The output voltage is "constant" at the bottom is a careless mistatement. The voltage on a sinewave is constantly changing. That the derivative is zero at the extrema is a tautology.

Well, let's consider thoroughly this part. Here I have tried to explain how the peak of the sine halfwave concieves. The reference has said, "the system stays linear and reverses direction, heading for the opposite power rail" but my goal is even more ambitious - to reveal how and why it reverses direction. It is very simple and obvious for everyone. The nonlinear feedback (nonlinear voltage divider) begins decreasing the gain; the voltage begins slowing its rate of change and the curve begins "loosing its nerve". Finally (at the peak), the loop gain becomes one and there is no more regeneration (see the explanations above). The output voltage stops increasing; for a while, at the top of the sine wavw, it stays constant positive and equal to the input one; no charging current flows and the voltage across the capacitor stops changing. But note this state is not stable. Why? This is the main question. At this moment, the Wien network is supplied by the constant output voltage. If there was a galvanic connection between the output and the grounded capacitor, the voltage across the latter will stay constant as well. But the upper capacitor disconnects the output from the grounded capacitor and the latter begins discharging through the resistor connected in parallel. The voltage across it begins decreasing, the nonlinear fedback begins increasing the gain and the regeneration begins operating. Circuit dreamer (talk, contribs, email) 14:17, 3 August 2011 (UTC)

The sections that you added are wrong.

I do not understand this assertion. Circuit dreamer (talk, contribs, email) 14:17, 3 August 2011 (UTC)

Glrx (talk) 22:12, 2 August 2011 (UTC)

Circuit dreamer, please take note of WP:3RR. Do not reinsert your material until you have a consensus for it. Glrx (talk) 22:17, 2 August 2011 (UTC)

Well, now it is fine... For clarity and unambiguousness, I will insert my comments between yours. Circuit dreamer (talk, contribs, email) 06:30, 3 August 2011 (UTC)

I agree with Glrx. This is an encyclopedia, Circuit dreamer. The analysis of circuits has to stick to established sources. From the WP:OR page:

"Material for which no reliable source can be found is considered original research."

"...synthesis of published material to advance a new position...is original research..."

"Do not add unsourced material from your personal experience."

"Do not analyze, synthesize, interpret, or evaluate material found in a primary source yourself..."

Your additions are WP:OR and will have to be removed, and if you keep adding them you will be blocked from editing WP. There are lots of places on the web where you can present your original analyses of circuits; this just isn't one of them. Cheers --Chetvorno 21:54, 3 August 2011 (UTC)

Please clarify "voltage peak", "voltage changing"

It is not clear to me what these two terms are intended to convey. Is it the instantaneous voltage such as would be seen with an oscilloscope, or is the time averaged envelope such as would be measured with a voltmeter? Constant314 (talk) 01:04, 6 August 2011 (UTC)

To trace out the circuit operation through time, the quantities are represented by their instantaneous values. Circuit dreamer (talk, contribs, email) 01:47, 6 August 2011 (UTC)

And so you are suggesting the the temperature of the light bulb follows the instantaneous voltage, which it would, if only minisculy. But there would be some lag; the peak of temperature would lag the peak of the instantaneous voltage.Constant314 (talk) 14:25, 6 August 2011 (UTC)

Congratulations! It is so wonderful to see that still there are thinking wikipedians that want not only to "copy and paste" circuit explanations from sources but to deeply understand them as well; I had already given up all hope to see them! My answer is very simple: my explanations are implicitly based on using a non-inertial nonlinear network in the negative feedback (e.g., a resistor-diode network or a non-inertial light bulb) or a very low oscillating frequency. I have not yet begun thinking about the role of the time constant of the non-linear network; we can do it together. Circuit dreamer (talk, contribs, email) 18:37, 7 August 2011 (UTC)

And by non-inertial you mean the light bulb temperature and resistance instantaneously follows the instantaneous voltage?Constant314 (talk) 18:48, 7 August 2011 (UTC)

Yes, maybe noninert is the right word. As I can see, the problem is considered briefly in Amplitude stabilization section (Wien bridge oscillators that use thermistors also exhibit "amplitude bounce" when the oscillator frequency is changed is interesting assertion). BTW sorry for the delay, I was absent during the weekend. Circuit dreamer (talk, contribs, email) 19:49, 7 August 2011 (UTC)

Well now I can sort of understand your posting. But Wein bridge oscillators are mainly designed to be operated where the period of oscilation is very much smaller than the thermal time constant of the light bulb (or time constant of some other stabilizing components). I would expect to see that any signal related variation of the light bulb temperature would be much smaller than random disturbances. Constant314 (talk) 00:30, 8 August 2011 (UTC)

Exactly... thank you for the patience. It seems I have revealed the circuit operation only for the special case with zero time constant while you, Grlx and the most people assume the case with nonzero constant. The circuit in the figure has also inert negative feedback. So, I think, there are two alternatives - to leave the current explanation with the reservation that it is "instantaneous" or to replace it with an "inert" explanation as more common. I have not still reasonable explanation of the latter; maybe Grlx will suggest some as he has began discussing this case. I admit your speculation about the bulb temperature reaction to signal and random variations. Now we have only to ascertain what the "inert" loop gain is - exactly one, more than one or varying. I cannot imagine how the circuit will oscillate if it is exactly one... Circuit dreamer (talk, contribs, email) 04:14, 8 August 2011 (UTC)

My understanding is that the gain will vary from a little less than 1 to a little more than 1 in response to disturbances which could be the application of a sudden load or wind currents or temperature shift or shaking the circuit or turning on the power. The variation is small and the longer time you look at it, the closer the average is to unity. There is another way still of looking at this circuit: that it is a servo that has as its functon to control the resistance of the lamp to be one half of Rf (see the new diagram). It does this by heating the lamp with an AC signal. And you can do a root locus analysis of the oscillator. What you will see is that the dominent poles will stay very close to the imaginary axis, but not exactly. You will see that the poles meander back and forth across the imaginary axis, spending some time in the right half plane and some time in the left half plane.Constant314 (talk) 04:42, 8 August 2011 (UTC)

Wonderful, especially the "servo viewpoint"! Is it your insight? I use a similar way of looking at a relaxation oscillator - as a bistable regulator whose function is to control the voltage across the capacitor. All sorts of bistable regulators (e.g., the humble iron having a thermostat) can be considered either as a regulator or oscillator depending on the current usage. Your explanations stay close to Grlx's ones; I have copied them from NOR noticeboard:

__________ Yes, it is my insight. Sorry, I do not have a reference.Constant314 (talk) 15:30, 8 August 2011 (UTC)

"In the linear model, the loop gain is exactly 1 throughout the cycle; the complex poles are exactly on the imaginary axis, so the amplitude neither increases nor decreases. In the almost linear model, the loop gain is slightly higher than one at low amplitudes, and slightly smaller than one at high amplitudes. The result is an average gain of 1 throughout the cycle. Oliver suggests that a reasonable gain variation in the almost linear model is about 0.001 (third harmonic 60dB down)."

Circuit dreamer (talk, contribs, email) 05:03, 8 August 2011 (UTC)

__________ Make that "In the ideal linear model, the loop gain is exactly 1 throughout the cycle"Constant314 (talk) 15:30, 8 August 2011 (UTC)

Well, I begin realizing the situation... It seems my "instantaneous" explanations are true and they only need filling out. Let's begin speculating on circuit operation.

Obviously, a simple form of AGC is realized by the lamp; its role is to maintain a basic amp gain about three. For this purpose, the lamp resistance varies slow to compensate slow disturbances; its resistance follows slow these variations. But its resistance varies quickly as well under the sine variations; these AC variations are superimposed over the base resistance.

__________Yes, there will be a small change in instantaneous resistance that follows the instantaneous voltage. It causes harmonic distortion. But the Wien bridge oscillator's harmonic distortion is very low which means that the instantaneous variation compared to the time average variation is very small; it is on the order of 0.1%. Also, although there is a component of the resistance that follows instantaneous voltage, it has a large lag compared to the signal period.Constant314 (talk) 15:30, 8 August 2011 (UTC)

Now about the loop gain... At small voltages, it is bigger than one (to make the current flow and the capacitor charge). At high voltages, the loop gain begins decreasing and (IMO) it becomes equal to one. It stops decreasing immediately as soon as the voltage across the capacitor stops increasing and this is the moment where the gain is exactly one (I cannot imagine what can make it continue decreasing below one). So, the lamp resistance is a sum of two ingredients - the base slow changing DC resistance and additional quickly changing AC resistance. Thus the lamp resistance is modulated with the oscillating frequency; its light pulsates slightly. All this is valid for the gain as well - it wiggles with the oscillating frequency with respect to the base value. Circuit dreamer (talk, contribs, email) 09:48, 8 August 2011 (UTC)

__________ The loop gain could go below 1 because of several causes. Some of the causes are: overshoot in the AGC system, load changes, air currents, change in air temperature, mechanical shock, noise in the opamp. Regardless of how the loop gain dropped below unity, the output starts ramping down and the lamp cools off enough to restore a loop gain of unity.Constant314 (talk) 15:30, 8 August 2011 (UTC)

Are you familiar with root-locus analysis. If you are, consider what happens to the dominent pole pair as you change the lamp resistance. The lamp starts out as a cool low resistance, the loop gain is greater than one, and the dominent pole pair are in the right half plane. You increase the resistance of the lamp and the poles move toward the imaginary axis, then touch the axis and then move past the axis into the negative half plain. Now here is the payoff. Look at the trajectory of the dominent pole pair; it crosses the imaginary axis at exactly 90 degrees. This means that the frequency of oscillation does not vary with loop gain, act least for loop gain close to unity. Most oscilators show the dominent pole pair crossing the axis at an angle so that as the AGC control meanders around a loop gain of unity the frequency also varies. But not the Wien bridge oscillator.Constant314 (talk) 15:30, 8 August 2011 (UTC)

I congratulate you again for the powerful "servo" idea! Many years ago, I also noted that it is extremely useful for understanding and presenting to think of electronic circuits with negative feedback (emitter follower, op-amp amplifiers, etc.) as of a kind of servo systems that react slowly to various disturbances including the input signal (that is a sort of a "disturbance" as well - another my insight; you will understand me). I have emphasized "slowly" since exactly this is the trick - to think of something noninert, proportional (the usual notion of the op-amp) as of a something slow, sluggish... only and only to understand how does it do what it does in all these circuits....

As I can see, you are good at both the intuitive and formal level. I reveal the secrets behind circuits staying only at the lowest but the most reliable intuitive level of understanding. My mission in Misplaced Pages is to reveal circuit ideas in the introductory article parts and this "qualitative " activity needs "qualitative" means; formal methods do not help at this stage. I trace out circuit operation through time in my imagination by varying some quantity as an input and observing some other quantity as an output (exactly as you have said, "...consider what happens...as you change the lamp resistance..." In this mental "movie", electrical quantities are only instantaneous. I visualize them by voltage bars/current loops with according instantaneous height/thickness superimposed over the circuit diagram. These colorful pictures represent separate typical "shots" of circuit operation. That is why, I present AC input sources as varying "batteries" with concrete instantaneous voltage magnitudes and polarities.

Now about the varying loop gain... The questions are, "Why does it vary?" and "Should it vary?" IMO you have not realized my idea. I think, the gain (lamp resistance) varies not only as a response to various undesired disturbances (as you have said, load changes, air currents, change in air temperature, mechanical shock, noise in the opamp, etc.); it must vary (quickly) as well in a response to voltage variations for a more principal reason - just to obtain sine oscillations.

_____________but it cannot. The thermal inertia is too high.Constant314 (talk) 21:36, 8 August 2011 (UTC)

In an LC oscillator, the very LC circuit produces sine oscillations and the amplifier only sustains them by adding additional energy; in an RC oscillator (Wien bridge here), the RC circuit cannot produce sine oscillations since it cannot reverse the direction of the voltage "movement" at the peaks. So, there is a need of some "mechanism" to "pull up" the voltage -> stop -> "pull down" -> stop... to make it wiggle... For this purpose, the loop gain has to be bigger than one to change the voltage and exactly one to stop the change (at the peaks); it must be dynamic. The gain cannot be constant since if it is bigger than ohe, the voltage will increase continuously up to the rail; if it is exactly one, the voltage will stay constant. Assertions like "the loop gain is exactly 1 throughout the cycle" are misleading and impede understanding at intuitive level. The clarification "the average gain is one throughout the cycle" hides the mechanism of creating sine oscillations. Regards, Cyril. Circuit dreamer (talk, contribs, email) 20:21, 8 August 2011 (UTC)

The circuit starts to oscillate because initially the lamp is cold and the gain is high. I tried to take some scope photoes today, but my hands were to shaky. But I'll describe what I saw. Initially, the oscillator started banging from rail to rail and produced almost square waves. About a second later, it was still banging rail to rail, but there was some slope along the sides. And about a second after that it settled down to a nice sinewave.Constant314 (talk) 21:36, 8 August 2011 (UTC)

IMO all these observations second the explanations above. As you have noted, in the beginning the amp gain is quite bigger than three. The charging current is big, the voltage across the capacitor changes vigorously and the amplifier exits slow from saturation; thus the almost square waves. Actually, the circuit can oscillate even without nonlinear but constant negative feedback setting a constant amp gain bigger than three (loop gain bigger than one). Circuit dreamer (talk, contribs, email) 22:10, 8 August 2011 (UTC)

Yes it would oscillate under those conditions, but the distortion would be higher.Constant314 (talk) 02:19, 9 August 2011 (UTC)

I have a favour to ask of you - can you look at Negative resistance that was removed yesterday without any comments about the contents and replaced with this older one? Can you compare the two versions? Your opinion is very important for me. You may write it in an email if you have some fears. Thank you in advance. Circuit dreamer (talk, contribs, email) 21:05, 8 August 2011 (UTC)

There way too much material there to be looked at for me to make any statement.Constant314 (talk) 02:19, 9 August 2011 (UTC)

Constant314, you are very close to understanding what is going on. Circuit dreamer is still confused about a number of issues (such as the ideal linear oscillator steady state solution).

In the usual case, you may consider the lamp resistance constant over a single cycle. If the amplitude is wrong, the lamp resistance will gradually correct it by twiddling the real part of the complex poles. Both Meacham and Hewlett viewed the lamp as bringing the bridge almost into balance. A little bridge imbalance is required for operation; the imbalance times the amplifier gain produced the unity loop gain for oscillation. For example, an imbalance of 1/300 and an amplifier gain of 300 gives unity loop gain. The higher the amplifier gain, the better the bridge balance.

Meacham and Hewlett probably believed the ideal linear oscillator model came into play then. Oliver showed that view is wrong. For AGC stability, a small nonlinearity is needed in the instaneous transfer function. Oliver's article has some fabulous photographs of that AGC instability. It is the ordinary oscillator amplitude limiting via gain compression, but since the bridge is so well balanced, a much smaller gain compression works. Instead of an ideal linear oscillator, there is a limit-cycle in the non-linear phase space. Consequently, there are two nonlinear processes in operation.

I've added some relevant references to the article. Meacham and Oliver are available online. Strauss covers a lot, and I recommend it. In particular, Strauss does a root locus of the non-bridge version of the WBO. Poles split at gain 1, cross imaginary axis at 3, and rejoin the real axis at gain = 5.

FWIW, Jim Williams told me about Oliver's article. Jim had this fabulous story about Barney Oliver finding out that about 1 percent of the production HP oscillators failed to settle quickly, so Oliver studied the problem, and he figured it all out. Oliver then stormed into Bill Hewlett's office and shouted, "This company is founded upon a lie!" Jim also cribbed one of his Wien bridge oscillator designs from an HP distortion analyzer.

Glrx (talk) 07:19, 9 August 2011 (UTC)

Until Constant314 prepares his answer to you, I will place below two extracts from the talk and article pages to compare them. It is very interesting and indicative that you reject the first viewpoint presented by me in Background but here you say exactly the same. It seems you have only reproduced Meacham and Hewlett's text without understanding it...

Glrx: "...Both Meacham and Hewlett viewed the lamp as bringing the bridge almost into balance. A little bridge imbalance is required for operation; the imbalance times the amplifier gain produced the unity loop gain for oscillation. For example, an imbalance of 1/300 and an amplifier gain of 300 gives unity loop gain. The higher the amplifier gain, the better the bridge balance..."

CD: "...Wien bridge oscillator can be considered as a combination of an op-amp and a Wien bridge connected in the positive feedback loop between the op-amp output and the differential input. At the oscillating frequency, the bridge is balanced and has very small transfer ratio. The overall loop gain is a product of the very high op-amp gain and the very low bridge ratio. As the resistive bridge arm is made nonlinear, the loop gain is dynamic..."

Some notes... The bare lamp cannot "bring the bridge into balance"; the op-amp does it controlling the lamp. Also, it is too strange and misleading to give an example of amplifier with open-loop gain of 300 while it is more than 100000 for the humblest op-amps. Circuit dreamer (talk, contribs, email) 17:25, 9 August 2011 (UTC)

__________100,000 would be dc gain. At the oscilator frequency the gain of an op-amp might be 300.Constant314 (talk) 18:32, 9 August 2011 (UTC)

It is unlikely the op-amp gain to decrease so vastly at the oscillating frequency. IMO the text is written in 50's when 300 was a great achievement:) Circuit dreamer (talk, contribs, email) 19:02, 9 August 2011 (UTC)

More notes... It is also very interesting that you have removed the negative resistance viewpoint from Electronic oscillator but here the analysis of the Wien bridge oscillator (a kind of electronic oscillator) is performed exactly by looking at the circuit from this viewpoint. Then don't you think you should remove completely this section since the negative resistance viewpoint is not reliable? Circuit dreamer (talk, contribs, email) 18:24, 9 August 2011 (UTC)

__________In my opinion, the negative resistance explanation is the least useful.Constant314 (talk) 18:32, 9 August 2011 (UTC)

More correctly, it is a negative impedance than resistance. Really, it is more abstract but it is still another viewpoint at this circuit. IMO the phrase "the input admittance can be thought as of a negative resistance in parallel with an inductance" is the least useful in this explanation.

BTW we can use another not so useful but impressive memristor viewpoint since the lamp, especially if it is inert, is a memristor:) This application is described by Prof. Chua in his materials. Circuit dreamer (talk, contribs, email) 19:21, 9 August 2011 (UTC)

CD, your text is confused -- as an editor has noted at WP:NORN#Wien bridge oscillator. In addition, you have selectively quoted yourself. The entire paragraph is:

Positive feedback amplifier with high open-loop gain. Wien bridge oscillator can be considered as a combination of an op-amp and a Wien bridge connected in the positive feedback loop between the op-amp output and the differential input. At the oscillating frequency, the bridge is balanced and has very small transfer ratio. The overall loop gain is a product of the very high op-amp gain and the very low bridge ratio. As the resistive bridge arm is made nonlinear, the loop gain is dynamic - it is bigger than unity when the sine wave changes and equal to unity at the sine peaks where the nonlinear element turns on. The overall feedback can be also considered as composed of two partial feedbacks - a nonlinear negative feedback (the voltage divider connected to the inverting op-amp input) and a frequency-dependent positive feedback (the Wien network connected to the non-inverting input). Thus the feedback voltage applied to the op-amp differential input is a difference between the two partial voltages. In the parts where the sine wave changes, the positive feedback dominates over the negative one; at the sine peaks they become equivalent.

It is a confused mixture of falsehoods and truths. I clearly state the open-loop gain is unity. You talk about a "high open-loop gain" and an "overall loop gain". How many loops are there? Sources do not have the loop gain changing during a cycle unless the output frequency is very low. Your explanation still has a confused belief about the gain going to one at the peaks; we've talked about that before; you've noted that Constant314 agrees with me and that you don't see how it works. I've already criticized "at the sine peaks where the nonlinear element turns on"; it is a gentle nonlinearity. The paragraph does not demonstrate an understanding of what is going on in an ordinary oscillator -- let alone a low distortion oscillator.

Constant314 is right about the op amp gain/GBP issue, but I used 300 because, IIRC, Hewlett said his amplifier gain was about 300.

The negative resistance description of the WBO is unsourced. In fact, the description points to other sources that take a different approach. I haven't crawled back in the edit history to find out who presented it, but the negative resistance explanation is on my hit list.

Glrx (talk) 19:58, 9 August 2011 (UTC)

Glrx, let's finally clarify things; I have the feeling that I have finally realized the problem. Saying "open-loop gain" in this context, I mean "open-loop gain of the op-amp" (the gain obtained form the op-amp when no feedback is used in the circuit, typically > 100000).

_________ yes, open loop gain with no feedback is typically one million at DC and begins a one pole (20 dB per decade) roll-off at typically 1 Hz. So the gain at 1 KHz is 1000 and the gain at 10 khz is 100 etc. Opamps are generally characterized as having a certain gain bandwidth product ( gain x bandwidth = 10^6). If you want more bandwidth then you accept less gain.Constant314 (talk) 22:41, 9 August 2011 (UTC)

Also, when I said in Background, "Positive feedback amplifier with high open-loop gain" I have meant "An op-amp amplifier with high open-loop gain (> 1000000) that is comprised by a positive feedback". As I can see, you probably mean the overall gain of the broken loop, i.e. loop gain. IMO it is incorrect to say "I clearly state the open-loop gain is unity"; it is correct to say "I clearly state the loop gain is unity". Circuit dreamer (talk, contribs, email) 20:29, 9 August 2011 (UTC)

"high open-loop gain" = "high gain of the op-amp without feedback"

"overall loop gain" = "loop gain"

Now about "at the sine peaks where the nonlinear element turns on". It is obvious that I have said shortly "turns on" since below, in Operation section, I has noted that the process is smooth: "Before the output voltage approaches the positive rail, the nonlinear feedback begins decreasing the gain; the voltage begins slowing its rate of change and the curve begins rounding."

And about the negative resistance... It is funny to see how you and your likes remove with great eagerness everything connected with negative resistance including the very article about negative resistance. The sorry fact that you (a few people inhabiting this space) are unable to understand this great idea does not mean that you should deprive the chance of other people to do it. It will be better for you and for all the people visiting electronics Misplaced Pages if you finally understand what negative resistance is and how useful it can be. Circuit dreamer (talk, contribs, email) 21:28, 9 August 2011 (UTC)

Finally, about the relation between the gain and voltage magnitude. You have said, "Sources do not have the loop gain changing during a cycle unless the output frequency is very low." In the diode version, it changes. How does it work then? Circuit dreamer (talk, contribs, email) 21:58, 9 August 2011 (UTC)

I don't remember everything that you have written, but yes, the diode version works much as you say, but it is not low distortion. The light bulb version does not work as you have described and achieve's much lower distortion.Constant314 (talk) 22:41, 9 August 2011 (UTC)

So, it seems we have been talking about two different circuits. Glrx and I (Constant314) are talking about the oscillator described in the leading paragraph and in the first figure. It is non-linear in its amplitude control process, but essentially linear at signal frequencies. In particular, its Wien bridge is constructed out of components that are essentially linear at signal frequencies. Its amplitude control function is slow with respect to its period of oscillation and it is capable of very low distortion. Circuit dreamer is referring to a circuit that has a bridge constructed of components that are non-linear at signal frequency that act essentially instantaneously to limit amplitude. It has no slow acting gain control and produces moderate distortion. So, what are we to do about it? To those of us in the trade, The Wien bridge oscillator is the thing that HP produced and uses a lamp to stabilize the amplitude. It is what the first paragraph says. It is simple and elegant and pure. It is worthy of study. The thing with diodes is just another marginally interesting diode clipped RC oscillator. In my opinion, it has to go. The page RC oscillator might be a good place.Constant314 (talk) 03:42, 10 August 2011 (UTC)

How beautiful you have said it - wisely, calmly and appeasably... And what is more important, these are your own genuine, not else's, words... You have processed, extracted and generalized the simple truth about these circuits and then exposed it in this compact form where every word is meaningful... You are the ideal wikipedian for me...

All that you have written is true but... I need time to classify and make into a system my notion about this circuit. I have just entered the talk to express my admiration of you. Thank you again for the mental pleasure. Circuit dreamer (talk, contribs, email) 05:54, 10 August 2011 (UTC)

Lots of things.

First, CD, you got me. I misquoted myself: I wrote "I clearly state the open-loop gain is unity" when what I stated earlier was "... produced the unity loop gain for oscillation" (and you quoted me as just unity loop gain). I screwed up; I did not want to say "open-loop gain"; I wanted to use the clearer gain and loop gain.

Strauss page 664 describes a feedback system for making an oscillator. He explicitly uses the terms "forward transmission" and "closed loop gain". He then uses the term "open loop transmission" to refer to the loop gain. Strauss even has a nice little switch in his feedback diagram that he can "open" the loop.

The ecircuitcenter.com website that CD refers to breaks the loop and looks at an open loop system. That open loop system is the same as the loop gain.

My control theory reference uses "open-loop" to mean a controller with no feedback. It does not have "open-loop gain" in the index.

There are some who equate "open-loop gain" with "forward gain". That makes an easy comparison to closed loop gain -- except that oscillators don't have external inputs and the closed loop gain has a singularity.

I knew where you were coming from with your comments about large open-loop gain and small open-loop gain. But you are inconsistent. For your small open-loop gain, you still have the same op amp with its high open-loop gain; the negative feedback turns it into an amplifier with low closed-loop gain. The resulting low gain amplifier is still part of another, larger, loop.

My criticism is not that I don't understand what you (CD) write. It's not even that my fundamental complaint is the precision of your terminology. (I'm biting my tongue about "inert".) My criticism is that what you write is wrong. Even if the gain and feedback terminology is fixed, you still are not explaining how oscillators work.

CD, I'm sure you think you understand some parts, but how can you be sure that your understanding is correct? Constant314 has pointed out some problems with your views. You ignored the lamp time constant. You ignored the frequency dependence of op amp gain (and Constant314 didn't mention the phase shift or slew limiting aspects).

You state that "At the peak, the loop gain becomes equal to unity and there is no more regeneration." Unity gain allows a steady-state solution. Unity gain does not mean you must be at the peak. Constant314 and I claim the instaneous loop gain in the nonlinear model is less than one at the peak. Strauss pages 666-667 agrees with us. You still don't think that it should be less than one. Why do you think you are right? What sources support you? Constant314 may not be quoting sources, but he's coming from solid theory; he has, for example, described the root locus interpretation accurately. I suspect he believes in Barkhausen. You, however, are relying on your intuition, and you are willing to violate Barkhausen.

My comments do not mean that I do not understand your argument about why the gain is exactly one at the top. Your view is something like this. Imagine the instantaneous output is at 1 volt and the loop gain is exactly 1. At that point, you believe that the output cannot increase any further (regeneration has ceased), so the output must be at the peak. That is not, however, the requirement for a steady state solution. Consider that the output is at 1 volt and that the output is increasing at 1 volt per microsecond and that the loop gain is exactly 1. We are not at your peak. Your intuitive methods fail. In fact, a large enough positive derivative allows the output to increase even when the loop gain drops below 1. BTW, linear oscillators are second order systems; I've left out the second derivative.

But even that your faulty reasoning is not the main point. Whether your description is right or wrong, it does not cite reliable sources. WP does not want your WP:OR original research or your personal take on what's happening or your personal insights. WP wants reliable sources that it can verify.

FYI, Meacham and Hewitt were doing bridge oscillators in the 1930s - not the 1950s. The references have dates; one need not read the sources to learn the time frame.

My sense is that even when CD has good sources available online, he does not use them. Meacham, Hewlett, Oliver, and Williams are online. Meacham is certainly a serious effort. Both Strauss and Williams cite to Meacham. Strauss is a reliable secondary reference.

When CD uses sources, they are poor: consider your http://www.ecircuitcenter.com/circuits/opwien/opwien.htm "reference" (which is now doubled in the external links sections). Why do you believe that is a reliable source? It's some random SPICE blog that doesn't cite to any sources that it uses. Nothing on the webpage is traceable to a reliable source.

Strauss page 666 gives a similar circuit diagram to the one at ecircuitcenter.com, but Strauss does not refer to it as a Wien bridge or even a Wien network or even a bridge. Strauss calls the two resistors and two capacitors a "frequency-determining network". He then goes through the root locus plot with the interesting points at gains 1, 3, and 5. (I mentioned these points above. I note that CD has never responded whether he understands root locus plots.) A few pages earlier in his book, Strauss discussed nonlinear limiters and Barkhausen. On page 664, Strauss discusses "gross nonlinear operation" of a limiter oscillator.

On page 671, Strauss discusses the Wien bridge. Strauss explicitly criticizes the poor performance of the oscillator on page 666 as having "extemely poor selectivity"; in addition, Strauss states, "Any second-harmonic components introduced not only are not reduced but are actually increased in amplitude." Strauss then goes into a balanced bridge description as a solution to those problems. Strauss goes on to explain lamp balancing.

Both Meacham and Hewlett were looking for high performance. Both used balanced bridges. Running a balanced bridge oscillator has significant advantages. Meacham understood that in 1938.

The bridges are balanced with slowly varying elements - the lamps. The time constant is significant. If you look at Williams application note, his WBO uses a balanced bridge. Sometimes the lamp is replaced with a FET, but the reaction time of the FET is slowed down. (BTW, Williams' app note is all about "Bridge Circuits".) Williams is not using fast acting (e.g., diode) limiters. (Oliver is not using explicit fast acting limiters, but he points out the need for a very subtle fast acting limiter for the lamp balancing.)

The fast diode limiter of ecircuitcenter.com should never be mistaken for a slow balancing of the bridge. That circuit should never be mistaken for a delicately balanced bridge. That bridge is out of balance by 10 percent. HP operated their bridges at 0.33 percent.

As Constant314 has essentially recognized, the diode limiter at ecircuitcenter.com is not a Wien bridge oscillator. It is just an RC oscillator. Constant314's observation about the WBO being the circuit that HP built can be focused this way: where is a reliable source that claims the ecircuitcenter.com design is WBO?

Circuit dreamer does not understand the subject matter of this article. He should not edit this article.

Glrx (talk) 01:30, 11 August 2011 (UTC)