Talk:Wien bridge oscillator

Schematic
Need to add a schematic (or several) -- I'll get to it shortly Madhu 03:23, 21 February 2005 (UTC)

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 = i2R. 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 TALK 17:30, 10 July 2009 (UTC)

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/wiki/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 TALK 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 Wikipedia 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. 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 Wikipedia 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 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)


 * I have never seen so limited mind as you... What a shame! You are disgrace for Wikipedia! The last phrases "the diode limiter at ecircuitcenter.com is not a Wien bridge oscillator" and then "Where is a reliable source that claims the ecircuitcenter.com design is WBO?" are absolute nonsense that completely characterize you. Don't you see the Wien bridge, Wien network, nonlinear voltage divider? If not, browse Google! It will suggest a ready phrase wien bridge oscillator diodes. Click Search button and Google will suggest 134,000 sources considering Wien bridge oscillator with diode nonlinear negative feedback! What more do you want? You are so limited that if I say the Sun rises in the east and the Earth rotates, you will want sources! Circuit dreamer (talk, contribs, email) 15:50, 11 August 2011 (UTC)
 * If you were to edit Sun and add that it rises in the east, I'd revert you and ask you not to add again without a source. Read the article, you won't find the statement, and please don't add it, because it isn't true. If earth didn't state that it rotates, and you wished to add it without a citation, I'd ask for one. But it does list the period of rotation, and it does have a source. Your notion of what is obvious does not match the Wikipedia convention. You are editing Wikipedia. You must learn the convention, or you may find that your ability to edit Wikipedia will come to an end. Soon. --  SPhilbrick  T  20:37, 11 August 2011 (UTC)
 * "Wien bridge oscillator" just means "RC oscillator with Wien bridge connected in the feedback loop". Its voltage divider arm can be linear (resistor-resistor), nonliner (diode-resistor) or inert nonlinear (resistor-lamp) but in all these cases the circuit is, with more or less success, a Wien bridge oscillator! Circuit dreamer (talk, contribs, email) 16:21, 11 August 2011 (UTC)
 * I suppose it comes down to whether or not a Wien brige can have non-linear elements. You can certainly have a bridge with non-linear components.  I'm guessing now that Wien used all linear components and varied the ratio on the negtive side.  Why not call the circuit with diodes a modified Wien bridge oscillator.Constant314 (talk) 23:51, 11 August 2011 (UTC)
 * No, it comes down to what the reliable sources say. We don't get to invent terms. Strauss says it's not a Wien bridge oscillator. The question is then where are reliable sources that say the diode limited circuit is a Wien bridge or a modified Wien bridge. One can find some sources that call the diode version a Wien bridge, but I would challenge the reliability of the sources that I've come across. Given Strauss and Meacham, the WP article could even come out and say the diode limiter version is not a bridge oscillator. Max Wien was certainly using a bridge with linear components. He would, however, have to vary more than just the left ("negative") arms to measure an unknown capacitance. Glrx (talk) 19:11, 12 August 2011 (UTC)
 * Yes, it would be great if a reliable source said that the RC oscillator that would be a Wien bridge oscillator if two diodes were removed had a specific name. But until such a source is found, how should we refer that RC oscillator?Constant314 (talk) 20:02, 12 August 2011 (UTC)


 * A reliable source has been found. Operation Amplifiers by Tobey, Graeme and Huelsman, 1971 on page 385 show the Wien bridge with diode limiters and they call it a "Wien-bridge oscillator".  In light of this reliable source, I can no longer object to discussing the diode limited Wien-bridge oscillator on this article.  However, it is still a marginally interesting RC oscillator and I would rather see it discussed on the RC Oscillater page.Constant314 (talk) 22:18, 14 August 2011 (UTC)


 * I don't have a copy of Tobey et al, its not in the local library, and WorldCat doesn't know where a copy is (shock); a 1986 book by the same authors is 1800 miles away in Mexico City. From the Google books limited preview, the 1971 book discusses a "Precise Wien-bridge oscillator" and a "Low-cost Wien-bridge oscillator". That suggests the book knows the diode limiter version is inferior. The "low-cost" moniker may just be a way to distinguish it from the real Wien bridge oscillator. I doubt the terminology has caught on.
 * Book information shows the three are editors and not authors. The fourth author, Burr-Brown Research Corporation, suggests its a compilation of application notes / material from application engineers. (There's an Analog Devices application note about the diode version that I would attack on reliability.)
 * What sources does the 1971 book cite?
 * none Constant314 (talk) 19:15, 15 August 2011 (UTC)
 * At this time, I still lean toward the balanced bridge is the the Wien bridge oscillator (Meacham, Hewlett, Strauss). Bauer doesn't call the lamp version a Wien bridge -- just Resistance-Capacity Oscillator. From Meacham, the idea is a balanced bridge oscillator. If there's no balance, then it's not a "bridge".
 * Is it Meacham that says "If there's no balance, then it's not a "bridge"." I'd have been willing to accede that a bridge was a bridge even if it was unbalanced.Constant314 (talk) 19:15, 15 August 2011 (UTC)
 * The limiter versions I'd call RC oscillators (compare RC filter, LC oscillator). I'd characterize the diode limiter as a soft limiter.
 * I am not a happy camper. I would, however, give Strauss enormous weight. His book is about waveforms; a big part is the discussion of nonlinear effects on oscillators. The 1971 text is quick coverage about a lot of topics. I need to look for Hamilton, but from its title, it is also more about general topics.
 * I have some thoughts about organization, but that's for another time.
 * Were you thinking along the lines of replacing the analysis section with something shorter that included referneces and a lack of WP:OR? Constant314 (talk) 19:15, 15 August 2011 (UTC)
 * Glrx (talk) 15:12, 15 August 2011 (UTC)
 * Hamilton, from snippets that I can see, uses Wien network, says bridge is better, cites to Williams' app note. Glrx (talk) 17:45, 15 August 2011 (UTC)
 * I have come across several references that show the Wien bridge with a light bulb of FET used to balance the bridge, one that includes the diode limited circuit, a book by Schilling and Belove that has a differential transistor with no amplitude limiting other than the transisters going non-linear and none that say the diode version is not a Wien bridge oscillator. I agree that I would rather see the diode version discussed elsewhere. Constant314 (talk) 19:15, 15 August 2011 (UTC)
 * This section is getting long. If you want to start a new section to discuss what should and should not be included in the article, I'm am in favor of that. Constant314 (talk) 19:15, 15 August 2011 (UTC)
 * Yes, this talk section is too long and covering many topics. With no references, I'd argue that Tobey is not reliable and is not secondary. Meacham wants the bridge balanced; his abstract states the bridge is balance. My sense of the article is the balanced bridge makes it a bridge oscillator, but I'd have to read it again. Meacham wants the amplitude small to avoid limiting; he cites a 1931 paper by Llwellyn claiming that limiting compromises stability. (If you are big on connections, this ties into a nice argument about a clock's balance wheel in phase space.) Hewlett's patent wanted small amplitudes to keep the amplifier running class A; he may have made some more pointed remarks about linearity and harmonics. In the diode limiter version, Strauss would associate the limiter with the amplifier and it would not be a bridge oscillator. That it looks like a bridge is irrelevant to the operation; it just needs gain > 3 compressing to gain < 3. Glrx (talk) 20:01, 15 August 2011 (UTC)

Meacham states, "The 'Bridge Stabilized Oscillator' provides both frequency and amplitude stabilization, and as it operates with no tube overloading, it has the added merit of delivering a very pure sinusoidal output." Meacham p 574. I don't have Hewlett's Master's thesis. Hewlett's patent does not cite Meacham, but it makes claims that Meacham identified. Consequently, Hewlett may have been ignorant of Meacham. Glrx (talk) 20:12, 15 August 2011 (UTC)

Analysis from Shilling and Belove
I'm adding an analysis from Schilling and Belove. It is short, terse, referenced, and has no WP:OR except I added or changed subscripts to the component names to match the figure at the top of the page. I could derive the result, but I think that would be WP:OR. Constant314 (talk) 16:55, 16 August 2011 (UTC)


 * Changing subscripts is not WP:OR. WP:OR and [[WP:SYNTHESIS] are not a set of handcuffs. You are free to offer reasonable explanations as long as those explanations follow what reliable sources say. The discussions above about OR arose because somebody offered his explanations that were not based in reliable sources.
 * BTW, if you look at the Wien bridge balance conditions (adjusting the subscripts), the results fall out from WP:CALC. The bridge balance view also shows that the bridge can still be balanced if the component values are not exactly equal.
 * Glrx (talk) 17:22, 16 August 2011 (UTC)
 * I looked at WP:CALC. It seamed to allow simple arithmatic but not complex algebraic manipulation, solving polynomials and complex numbers. Are you suggesting that do add a derivation for the loop gain formula?Constant314 (talk) 17:27, 16 August 2011 (UTC)
 * I'm not suggesting that you add anything, but I don't want you to think that you cannot make reasonable or even obvious edits to the material. WP:CALC should be viewed in context. In technical articles, more involved calculations would be permissible because technical editors would consent to such calculations. Glrx (talk) 18:24, 16 August 2011 (UTC)
 * OK, thanks, I supposed I have not yet found the middle way with respect to obvious calculations.Constant314 (talk) 19:04, 16 August 2011 (UTC)

Background:High-gain differential amplifier with positive feedback
This is essentially Schilling and Belove's analysis, if I take out the word "non-linear" in the description of the negative feedback. Constant314 (talk) 04:35, 18 August 2011 (UTC)

Is factual accuracy backgroud section still disputed?
It could still use some references, but it looks essentially correct.Constant314 (talk) 13:33, 19 August 2011 (UTC)
 * Yes, it is still disputed. Lead paragraph is wrong (in more ways that 2 != 3). Section omits goals of frequency stability, low distortion, (wide freq range, advantage of RC over LC at audio,) and operation of the lamp. (CD demoted amp control as a minor feature, but it's really the major idea; without the lamp, the oscillator is poor.) Vague info about why circuit oscillates; if you know Barkhausen you get it; if you don't.... Omits the sharp phase transfer. No direct mention of null/notch oscillator (compare twin-T). My intention with the hat note was to delete the whole section. You've been rescuing the diff amp portion. I have trouble with the "two partial feedbacks"; I haven't checked your reference; CD quoted TI for the two feedbacks; it is not a great explanation (if such a view is useful or important, then where's Mason's gain formula with the two loops?); two feedbacks is a disguised version of low gain w/positive feedback explanation. The low gain single ended explanation is the simple RC oscillator and not the WBO. I deleted the negative resistance version. Glrx (talk) 15:50, 19 August 2011 (UTC)
 * It would be fine with me to remove the second explanation. The first description includes the op-amp's gain explicitly where as the second explanation just absorbs the opamp gain into the "low gain amplifier".Constant314 (talk) 18:57, 19 August 2011 (UTC)


 * On second thought, the low gain amplifier approach is useful precisly because it hides the op-amp gain, leaving a second order system that is easy to apply root locus analysis to the poles.Constant314 (talk) 18:01, 21 August 2011 (UTC)


 * Regarding Barkhausen. I believe it is usually correct, but sometimes it indicates that a system is unstable when it is not.  In that case you can apply the Nyquist criteria which is both necessary and sufficient to predict instability.Constant314 (talk) 18:01, 21 August 2011 (UTC)

Oscillator classification
Barkhausen stability criterion has an orphan ref to


 * . URL leads to 56MB conference proceedings download.

Criticizes some textbooks. Article states that steady state oscillators must be nonlinear; linear oscillator is a fiction. Article talks about shifting poles. States an energy balance for the wandering poles. The ref does a classification of oscillators and uses WBO. Make WBO with nonlinear amp a Class I; with nonlinear diode feedback a Class II. Claims that when the ideal diff amp is replaced with a real op amp, the nonlinearities of the real op amp dominate the diode circuit. He cites to Strauss, but does not really address the Meacham/Hewlett bridge design.

I'd criticize the ref on a number of issues. Glrx (talk) 17:37, 25 August 2011 (UTC)

Pronunciation
Is there a standard English pronunciation for this oscillator? Properly, it should be a "Veen" from the German, but I've heard it as "Wine" and "Ween". Glrx (talk) 15:36, 26 August 2011 (UTC)

Schematic
There are some new schematic on commons (see Hungarian version)Wien-hidas oszcillátor --Duhos (talk) 14:21, 24 January 2012 (UTC)
 * There was also a simple schematic in the article. --Netpilots (talk) 01:57, 5 March 2015 (UTC)

Amplitude stabilization: Using an incandescent lamp as a thermistor
“This section includes the sentence “Hewlett used an incandescent bulb as a positive temperature coefficient (PTC) thermistor”. This is incorrect. There seems to be a misconception here that any two-terminal resistor like device with a PTC of resistance is a thermistor. If one simply follows the thermistor link, then one finds the sentence:  "Thermistors differ from resistance temperature detectors (RTD) in that the material used in a thermistor is generally a ceramic or polymer, while RTDs use pure metals.”  Thus, within the introductory paragraphs of thermistor, a device with a PTC of resistance is presented and declared that it differs from a thermistor.  Clearly, there are PTC of resistance devices that are not thermistors.  The filament of a lamp is made from metal.  The lamp is much more like an RTD than a thermistor.Constant314 (talk) 14:30, 3 February 2012 (UTC)


 * I'm sympathetic but also troubled. I believe "thermistor" can generally refer to any temperature sensitive resistance. I don't know what Hewlett called it; I should look at the patent again. I've seen some WBO designs that use actual thermistors (instead of lamps). On the other hand, thermistors are often used to sense temperature (an application where self-heating can be a problem). I'd like a term where the power dissipation aspect is emphasized rather than the temp sensor, but I don't know of one. Bolometer may not be right. Hewlett's WBO used the lamp as a power sensor (and HP had some microwave power sensors using thermistor heads). The Pirani gauge uses a temperature sensitive resistance (essentially a lamp filament) in a power loss sensor.


 * I would not like to say that "Hewlett used an incandescent bulb as ... an RTD"; I'd be happier with him using it as a power sensor or an amplitude control.


 * I need to think and read more. Glrx (talk) 23:41, 7 February 2012 (UTC)


 * The lamp was a brilliant idea. It was a power detector, a low pass filter and a gain controlling device.   I believe that operating at low incandescent temperature helped with the amplitude stability.  The loss is a function of the temperature difference between the filament and the ambient.  With the filament at 1000 or so degrees, a little change in the ambient makes a small fractional change to the temperature difference.  Running a WBO with a thermistor a few tens of degrees above ambient would probably not be very stable.  By the way, if you have a link to a WBO that is stabilized by a thermistor I would like to see it.  With regard to the article, I think maybe it should say Hewlett used a lamp as a power detector, a low pass filter and a gain controlling device without saying it was used as some specific equivalent part.Constant314 (talk) 02:12, 8 February 2012 (UTC)

Questions and comments
1. "Meacham proposed a bridge oscillator to address those problems."

This sentence starts the section and it's disconnected. It should say what it's referring to. I assume it refers to the information contained in the the previous section.

2. "LC versus RC oscillator".

I don't see any inductor anywhere.

3. "The Wien bridge does not require equal values of R or C. At some frequency, the reactance of the series R2–C2 arm will be an exact multiple of the shunt R1–C1 arm. If the two R3 and R4 arms are adjusted to the same ratio, then the bridge is balanced."

It's impractical to expect the reader to follow without a schematic. There should be an image next to the text.

4. "Another analysis, with particular reference to frequency stability and selectivity, will be found in Strauss (1970, p. 671) and Hamilton (2003, p. 449)."

Why "will" and not "is"?

5. "-1.5±(sqrt(5)/2)"

This should be replaced by the actual equation (I'm not sure how to do this).

6. It would be nice to have an introductory sentence to explain what H(s) is.

7. The circuit talks about positive feedback with the R1-C1-R2-C2 components. I seem to understand negative feedback is also introduced with Rb-Rf. What is positive and negative about it? I know feedback has somewhat variable if not vague and standard definitions for positive and negative.

8. Reference "Meacham, L. A. (October 1938), "The Bridge Stabilized Oscillator" (PDF), Bell System Technical Journal 17 (4): 574–591, doi:10.1002/j.1538-7305.1938.tb00799.x. Frequency and amplitude stabilization of an oscillator with no tube overloading. Uses tungsten lamp to balance bridge." is pointing to nowhere.

ICE77 (talk) 19:12, 31 July 2015 (UTC)

Not enough low-level gain
The diode-limited schematic does not have enough low-level gain. At low amplitude, the gain will be about 2 (40k/20k), but the bridge needs at least 3. At high amplitude, the gain falls to about 1.5 (30k/20k). Taking the output at the 10k resistor is also a little odd. Glrx (talk) 16:24, 25 September 2015 (UTC)
 * The output is odd, but that's the way it was in the book. Just to vet it, I did run a SPICE sim and taking the output as shown has a little less distortion than taking it directly from the opamp, so I guess the source knew what he was doing.  The low level gain with the 1K pot all the way to one side is 1 + (30.1 + 10 +1)/19.8 = 3.076, just barely enough.  Constant314 (talk) 21:11, 25 September 2015 (UTC)
 * Ooops. My mistake for NI gain.... Glrx (talk) 22:16, 25 September 2015 (UTC)

Frequency determining network section needs reference
I do not think that there is anything incorrect in this section and indeed I derive the same result. I have no intetion of deleting it. But, there is no reference anywhere in the article for the operation of the Wien bridge oscillator when R1 ≠ R2 or C1 ≠ C2. I thought the preceeding section attributed to Schilling and Belove covered it, but I checked; it turned out that they use the same R1=R2=R and C1=C2=C assumptions as everybody else. I hope someone can find a reference.Constant314 (talk) 21:30, 27 September 2015 (UTC)

Root Locus and phase noise
I hope someone can provide a reference. I am working from memory. I read somewhere that the Wien bridge oscillator has low phase noise and good frequency stability because the root locus plot crosses the imaginary axis at a right angle. That means the frequency of oscillation isn't modulated by small perturbations of the gain. Anybody got a reference? Constant314 (talk) 14:04, 10 October 2015 (UTC)

Hewlett’s patent does not mention Meacham
It is true that Hewlett does not mention Meacham’s work. There is no dispute on that. However, the way it is presented suggests that Hewlett did something unscrupulous. If that is the intent of adding that comment, then let’s discuss that. Otherwise, the comment is unneeded as it is brought out in the article that Meacham’s disclosure of an oscillator using a lamp for stabilization predates Hewlett’s patent and thesis and also establishes that Hewlett was aware of Meacham’s paper.Constant314 (talk) 15:01, 3 November 2015 (UTC)
 * Hewlett did something screwy with Meacham. Meacham published papers in 1938 that used a lamp for amplitude control and frequency stability. Meacham wanted to avoid distortion. Keeping things linear meant better performance.
 * Hewlett's 1939 thesis uses a lamp for amplitude control. In the Acknowledgment, Hewlett thanks Terman for helping him through many impasses. Hewlett also acknowledges the help of Buss, Cahill, and Ginzton on negative feedback matters. (I have Buss' copy of Terman's 1937 Radio Engineering that is signed by Terman; it is reference 1 in the thesis.) The acknowledgment finishes with a vague, "The work of the other various authors which has been drawn upon in collecting material for this thesis is sincerely appreciated." Hewlett does not reference anyone in the body of the thesis. The amplitude control description starts at the bottom of page 6. A lamp's resistance changing with temperature is well-known. The cooling time should be less than half a period. The lamp is better than using a diode. The Experimental Results section starting on page 10 claims good power supply rejection (supply voltage changed ±20% resulted in 0.2% frequency change), distortion of 0.5%, amplitude stability of 1 dB from 20 to 20,000 hertz. Distortion at 8 Hz was less than 1%. If you read the thesis, Hewlett does not reference Meacham for anything in the text of the thesis. However, the thesis' Bibliography reference 5 is "Meacham, L. A., The Bridge Stabilized Oscillator, B.S.T.J. vol. 17, p. 574, Oct. 1938". Hewlett gives us no guidance about what he gleaned from Meacham. *Reference 6 is also intriguing: "Jeffers, L., A New High-Frequency Resistance-Capacity Oscillator, Thesis, Stanford University (Unpublished)".) Reference 2 is "Scott, H. H., A New Type of Selective Circuit and Some Applications, I.R.E. Proc., vol. 26, p 226, Feb. 1938". (I need to pull Scott.)
 * Hewlett then files for a patent on 11 July 1939. The filing makes no mention of Meacham's work, but it does describe using a lamp for amplitude control (patent page 2, col 1, line 20). At line 50 he explains the amplitude stabilization provides frequency stability. Uh, what was Meacham doing? The six numbered claims at the end of the patent all claim amplitude control.
 * Something screwy is going on. Williams tells us Hewlett knew about Meacham. Hewlett references Meacham in the thesis. Hewlett does not reference Meacham in a patent that ostensibly uses a lamp for amplitude and frequency control just like Meacham.
 * Glrx (talk) 20:59, 4 November 2015 (UTC)


 * Thanks for the reply. I think that you are treading into WP:SYN territory.  You have marshaled several pieces of evidence to suggest unethical behavior.  Even if it is true, you need a source that says it is true.  I’ll do my own bit of synthesis and suggest that if Hewlett’s patent was invalid, Bell System lawyers would have been all over it.  HP was selling these things in broad daylight.


 * Looking at the patent, I see that it doesn’t mention any prior art. Maybe it wasn’t standard practice to do that back then.  Maybe Meacham’s work was common knowledge.  But in any case, Hewlett does not claim his patent encompasses all oscillators with light bulb controlled amplitude stabilization.  Rather, each claim describes an oscillator with a combination of attributes that was, apparently, patentable. Constant314 (talk) 13:06, 5 November 2015 (UTC)


 * I've been looking at some more issues and gather more details, but have been distracted. More work is needed. The IRE footnotes do not help. Glrx (talk) 04:35, 12 November 2015 (UTC)


 * Thanks for the update. I'm in no hurry. Constant314 (talk) 12:25, 12 November 2015 (UTC)