After all the epic discussions-:) about the Wien bridge oscillator...
https://www.researchgate.net/post/What_is_the_basic_idea_of_Wien_bridge_oscillator_How_does_it_operate
...I have finally arrived at the conclusion that we have to consider the bare Wien network as a key point of understanding the Wien oscillator. For this purpose, we have to reveal the role of each element constituting the whole network. Here are my speculations.
The Wien network consists of four elements - C1, R1, C2 and R2, but they can be grouped into two parts (impedance elements) - the lower part consists of the two connected in parallel C1 and R1; the upper part consists of the two connected in series C2 and R2. Thus, the Wien network can be thought as of a frequency- or time-dependent voltage divider. Let's think freely over and even dream about this ubiquitous arrangement to stir our imagination...
The voltage divider configuration consists of two impedances connected in series. The input voltage is applied across the whole network. The output voltage is taken between the common point and some reference point: the ground, the voltage supply rail or a middle point (virtual ground). In the last case, we obtain a bridge configuration (the Wien bridge in our case).
FREQUENCY DOMAIN. The two elements (resistive, nonlinear, reactive, etc.) of the voltage divider configuration have an opposite influence over the transfer ratio and the output voltage. If only one of them is frequently dependent (a capacitor), it will act as "loosing" or "pulling" element when the frequency increases from zero up to infinity. Thus we obtain the classic integrating (low-pass) and differentiating (high-pass) circuits.
Now assume both the elements are frequency-dependent and we have taken the voltage drop across the lower element as an output (the case of the Wien bridge oscillator). When the frequency increases, the impedance of the lower element decreases up to zero and the ratio (the output voltage) decreases up to zero as well. Contrary, if the frequency decreases, the impedance of the upper element increases up to infinity and the ratio (the output voltage) decreases up to zero again. Only at some ("resonant") frequency the ratio of this frequency-dependent voltage divider reaches its maximum of 1/3 and the circuit behaves as some "mixture" of integrating and differentiating circuits (band-pass). It is interesting to see how such a behavior is achieved... to imagine how Wien was thinking when inventing this clever passive circuits... to put ourselves in his place...
If the two elements had opposite frequency-dependent behavior (a capacitor and an inductor), there was no a problem to create a band-pass voltage divider. The problem here is that we have only one kind of a frequency-dependent element - a capacitor, having a different behavior at different frequencies: it has a low impedance at high frequency and high impedance at low frequency. Then, how do we make it to have the same behavior (not to pass the signal) at both the frequencies - high and low?
If we look closely at the Wien network, we can discern an integrating (low-pass) circuit or a differentiating (high-pass) circuit or both the elementary circuits inside it. First, we can think of it as of an integrating circuit R2-C1 that is "neutralized" at extremely low frequencies by connecting the capacitor C2 in series with the resistor R2 and the resistor R1 in parallel to the capacitor C1. Then, with the same success, we can think of it as of a differentiating circuit C2-R1 that is "neutralized" at extremely high frequencies by connecting the resistor R2 in series with the capacitor C2 and the capacitor C1 in parallel to the resistor R1.
Thus, at the very high frequencies, the behavior of the upper capacitor C2 is reversed and made similar to the behavior of an inductor by connecting in series the resistor R2 (the capacitive reactance has gradually disapeared with the frequency increase and the resistance R2 has gradually dominated). At the very low frequencies, the behavior of the lower capacitor C1 is reversed and made similar to the behavior of an inductor by connecting in parallel the resistor R1 (the capacitive reactance has gradually increased up to infinity with the frequency decrease and the resistance R1 has gradually dominated).
So, this was the great Wien's idea - to transmute a capacitor into an "inductor": at the very high frequencies - by connecting in series a resistor; at the very low frequencies - by connecting in parallel a resistor. Am I right?
TIME DOMAIN. It is even more interesting to investigate the Wien network operation through the time. I would even build a "real-time simulation" arrangement to visualize the operation extremely slowly, in a human friendly manner, like this one:
http://en.wikibooks.org/wiki/Circuit_Idea/Walking_along_the_Resistive_Film#How_to_visualize_the_voltage_diagram_on_the_screen
For this purpose, use high resistances (e.g., 100 kom) and large capacitances (e.g., 100 μF) to obtain an extremely low "resonant" frequency (about 0.01 Hz). Then, drive the network with a varying sine wave voltage source with an extremely low frequency (it is interesting to vary the voltage manually trying to keep a sine wave). Next, connect three Microlab analog inputs (ADCs): the first - to the input voltage; the second - to the voltage of the common point between the upper elements R2 and C2; the third - to the common point between the two network parts (the common point of R1, C1 and R2). Finally, write a program that continuously measures the voltages and draws voltage bars over the respective elements representing the voltages across them like this diagram (in addition, it draws current loops):
http://commons.wikimedia.org/wiki/File:Chung_3_1000.jpg
My next explanations are closely related to the Lutz's considerations about the network operation, e.g. this one: "...However, always: V(P)
Hi Cyril,
I think your ideas as given above (splitting of the circuit`s operation into two different time responses: integrating and differentiating) are confirmed by another 4-element RC circuit hat has exactly the same properties as the WIEN network (and can replace the WIEN network in oscillator circuits without any modification):
It is a simple cascade (without any buffering) of an RC lowpass and a CR highpass (equal R and C values). It is somewhat surprising that this circuit is not mentioned in most of the relevant textbooks or any other publications. Of course, it is an RC bandpass with wo=1/RC and a maximum "gain" of 1/3 (as the WIEN network).
Very interesting straightforward approach where we have two "pure" (2-component) voltage dividers... How simple (and no interesting-:) for explaining and understanding it is...
Yes, you are right if we are interested in circuit implementations. But my pursuit is to deeply penetrate into circuit ideas; that is why I try to imagine what happens inside the network...
Regards, Cyril.
Dear Prof. Cyril,
Every science has its foundations and so the electrical and electronic circuits. If we have a circuit and we want to analyse it to explore its performance we use the circuit laws and the terminal performance of every element in the circuit. It is simply to solve the circuit and examine the results. Circuit synthesis is normally based on experience and there are only few circuit functions that can be formally constructed. An example is the filter circuits. Analog circuit synthesis is based on man experience and analysis.
That is an expert proposes a circuit that he expects to perform the required function and then he solves the circuit see whether it satisfies the requirements or not.
To facilitate the synthesis process he invented the parametric building blocks.An example of the building blocks is the RC, the CR, the LR,.....,the LCR, ...etc.
Wien is an expert and pioneer in electronic circuits and built his circuit to satisfy the requirement:
- The circuit acts a positive feedback circuit in a positive feedback oscillator
-This circuit must have a zero phase shift at certain specific frequency. This is the oscillation frequency
-The magnitude of the feedback ratio must have a peak at this frequency. This means that the frequency response is similar to that of a resonance circuit.
-The circuit must be made of resistors and capacitors only.
Reverting to his experience with the building blocks of RC circuits he proposed his circuit, analysed it and found that it satisfies the requirements above. Then he built the circuit in the laboratory and proved his concept experimentally.
I put my self in place of WIEN to find out how he thought in his circuit.
I think it is the usual way of inventors.It that right? May be!
Thank you for motivating us for more thinking on the foundations of science.
Hi, Zekry! I am happy that still there are people as you, Lutz, Pisupati and maybe others... and that we have met here to join our efforts in this noble undertaking - to reveal the truth behind circuit phenomena and to show it to people. The sorry fact is that the truth about circuits is (intentionally) hidden for a variety of reasons:
http://en.wikibooks.org/wiki/Circuit_Idea/Why_Circuit_Ideas_are_Hidden
http://en.wikibooks.org/wiki/Circuit_Idea/How_to_Hide_Circuit_Ideas
I have never understood why "Electronic devices are based on brilliant circuit ideas that are conceived once in beautiful minds by lots of imagination, intuition and emotions. However, time mercilessly covers up these pearls of human thought and we have to dig for long in the garbage of mediocrity to uncover them"... As you have said, "I put myself in place of WIEN to find out how he thought in his circuit"...
The sorry truth is that the education prefers to show the final perfect circuit solutions than the circuit evoluation, the road to them, where the very truth is hidden; it shows mainly specific circuit implementations than general circuit truths... It is extremely interesting to discuss how to understand, present and invent circuits... Thank you for the encouragement.
Regards, Cyril.
Dear Cyril,
Your words affected me much. I agree with your insight that the today engineer has no sufficient time to grasp the truth behind the many devices and circuits that he has to study during his graduation from the college.
The engineer tasks are to apply basic sciences to build and construct useful products that makes the human beings life easier. They do that by giving shapes to the suitable materials. In doing that they pay attention to the basic laws governing the material behavior. As the human being advances their knowledge accumulates and the education becomes tedious. The engineer is a swimmer as he has to go through knowledge in a comprehensive manner. He has no much time to dig and reach to the truth behind the behavior the objects.
The scientists of the basic sciences have the major task to observe the behavior of the matter and the living creatures and the laws governing them. Therefore they have to dig deep to get the truth and they may not reach it at all.
I think you like diving!
Good evening
Zekry
Dear Zekry,
Thank you for the figurative words explaining the nowadays situation. All you have written is right. I will add only a few thoughts to it.
IMO the main problem is not "that the today engineer has no sufficient time to grasp the truth behind the many devices and circuits"; the problem is that he/she do not have a will to do it. There is no curiosity, enthusiasm, fervour...; there is longing for a professional success and material prosperity... and this is the spirit of the today's times...
Well, I manage, at the cost of many efforts (even citing our RG discussions-:), to bewitch my students during the lectures and laboratory exercises... to make them "dive" deep into circuit phenomena. But I know that this magic will ceases immediately after the class finishes... and they come to the surface again (even feeling some relief) and continue swimming keeping afloat...
Maybe, the main benefit for my students from such a human friendly teaching approach is that they see something different than the conventional formal, dull, callous... up to a merciless way of teaching. They see that it is possible to reveal the truth about circuits by posing the problems, finding the great fundamental ideas and building circuits step-by-step on the whiteboard... then investigating them at the each step in the laboratory... instead to overwhelm them with tons of ready-made slides showing the specific circuit implementations...
I suggest to you and to all the colleagues working in the so noble area of the technical education to start interesting discussions about these problems of the today university and vocational teaching. Actually, I have started this process by asking the first two "philosophical" questions about circuit phenomena:
https://www.researchgate.net/post/What_does_to_understand_a_circuit_mean
https://www.researchgate.net/post/Why_are_circuit_ideas_hidden
Best regards, Cyril.
Dear Cyril, I totally agree with you. thats why the stuff deteriorate fast.
Bohra
The last contribution is already 14 days old - nevertheless, hello again to all R&G members which are interested in engineering tasks connected with the WIEN (and similar analog ) network problems.
I was absent for 6 weeks (journey to exciting Bolivia) and I like to add some thoughts:
Quote A. Zekry: "The engineer is a swimmer as he has to go through knowledge in a comprehensive manner. He has no much time to dig and reach to the truth behind the behavior the objects."
Yes - that´s true as far as engineers working in the industry are concerned. However, I think all lecturers engaged in educating engineers have the duty to explain "the truth behind the behavior of the objects" in detail. I am retired now, but during 30 years of being active as a lecturer at a university I had a lot of discussions with some colleges about the "right" way to teach electronics.
For example, is it allowed and sufficient in this context to treat the the opamp as an ideal device with infinite gain and idealized input/output impedances ?
I think - NO!. Other colleges say: YES.
For my opinion, a good engineer can simplify some calculations of electronic circuits only, if (a) he is able to assess the consequences (errors) of such a simplification and (b) he knows in which situations such a simplification is not allowed.
And, therefore, it is absolutely necessary for an engineer to know about the internal construction and the real properties of these devices.
Quote Cyril: "There is no curiosity, enthusiasm, fervour...; there is longing for a professional success and material prosperity... and this is the spirit of the today's times..."
Yes, unfortunately this seems to be true. But why is it so? And everywhere?
I have made the experience that students, for example, from the "third world" sometimes show another behavior. This could lead to a general question like this: Are there some severe disadvantages connected with the "modern" way of living and earning money in our modern industry nations ("spirit of the today`s times") ?
More critical question: In this context, what is the (indirect) responsibility of electronic engineers which have invented all the "modern" devices for today`s communication? I am afraid, many young people do not find enough time to think about physical principles or to read text books. Instead, they surf through the internet (believing here they could find and learn everything) or they are busy with facebook and similar "social" (really social?) networks.
(Perhaps and hopefully, I am too pessimistic).
Lutz vW
Hi everybody here! I have returned again to the subject of RC oscillators, intending to finally figure out how oscillations arise in these famous circuits. I reviewed carefully everything we have discussed so far, and I began to think back on this phenomenon...
In particular on this issue, I have noted that we have strayed somewhat from the main topic - the passive Wien network. I was not entered here for a long time and now, reading the overview section below the question, I myself was fascinated by what was written by me:-) I notice that I made very original explanations of the circuit ("neutralized" differentiating and integrating RC circuits, capacitors behaving like inductors, etc.), which are not honored by any your attention (excluding the Lutz's question vote). Also, my detailed examination of the operation of the circuit visualized by voltage bars should deserve especially attention...
Before I thought that such a callous attitude towards new ideas and creativity exists only in Wikipedia ... but it is written by ordinary editors and not of designers, inventors and scientists such should be a lot in ResearchGate. I would like to second this chain of bitter thoughts with a quote of Einstein:
"The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift." Albert Einstein
Hi Cyril - I must confess, I am not quite sure what your question really is and what remains to be discussed. Are there open questions regarding the WIEN oscillator?
Probably you remember that recently I have delivered a manuscript on a "rigorous oscillation condition" to RG. In this article, all possible modifications of the WIEN network are reviewed under the aspect of their capability to oscillate.
(By the way: Comments are urgently welcomed).
There is one additional subject that comes into my mind:
* Some people/authors claim that a thorough and deep discussion of analog oscillators is possible only taking non-linear effects into account. This leads to the necessity to use non-linear diff. equations.
* Some other people/authors (like me !) are sure that it is possible and sufficient to use the linear circuit theory only.
What about discussing these two approaches ?
Lutz, I have a sugestion to you and Erik - you may clarify the circumstances surrounding the Wien circuits at the high (abstract) level; I can do it at the low (intuitive) level. Agreed?
So, I will try to answer your questions in an intuitive manner...
Yes - agreed, of course.
I am waiting for your "intuitive" description.
Hello Cyril and Lutz,
The ideal op-amp with infinite gain and virtual shortcut of the input port terminals
carrying zero current is only applicable in connection with analysis of linear
circuits (frequency and time analysis).
Because "oscillators are nonlinear circuits and we need a simple model for the op-amp" I suggest the perfect op-amp model with infinite input impedance, zero output impedance and time-varying transfer relation A, i.e. Vout = A(t)*Vin or maybe Vout = A(Vin(t)).
With Vout = A(t)*Vin you may investigate the nonlinear circuits as time varying linear circuits and study the movements of the poles (eigenvalues) of the instant small signal model in the complex frequency plane as function of time. At each moment the circuit try to oscillate according to the instant natural frequencies. If you can make the imaginary part almost constant in a large part of the period you may minimize the phase noise and the content of harmonics.
In the Wien bridge oscillator we have a linear RC circuit in the positive feedback path from output to the positive input terminal of the op-amp. When Hewlett designed the
Wien bridge oscillator in 1939 he introduced a non-linearity in the negative feedback path from the output to the negative input terminal (a lamp !). In this way he was able to "balance" the non-linearity of the amplifier by "hit-and-try". He obtained almost perfect sinusoidal behavior with very little harmonic distortion.
To Lutz: In spite of your very nice contribution "On a rigorous oscillation condition"
I still believe that we have to deal with "hit-and-try" when we design oscillators.
Erik - please, can you elaborate the term "hit-and-try" (due to my limited knowledge of english language) ? Is it something like "trial and error"?
More than that, WHY do you think we have to "deal with hit-and-try when we design oscillators" ?
Lutz - "Hit-and-try", "trial-and-error" to me means that based on my simulations I try to vary component values so that I obtain a "better performance". It is the approach which we normally tell our students NOT to use ;-)
We have no analytical expressions available (a topology and a set of formulas) for oscillator design ;-)
To enable a discussion I like to respond in a provocative manner:
I HAVE such a set of formulas for designing an oscillator! I have used it several times (Modified Barkhausen).
The only uncertainty is the AMOUNT of non-linearity and the resulting THD of the output signal.
However, don`t we have the same uncertainty for each transistor amplifier?
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