Well, my first "explanation" is as follows:

For constant resistor ratios the inverter gain is smaller than the gain of the non-inv. circuit because in the first case only a fraction of the input signal (factor Hf) arrives at the opamp input terminal. The feedback factor Hr is, of course, the same in both cases.

(To me, this explanation sounds a bit trivial, but I have no other).

A modification of Black`s feedback formula does reflect the situation:

H=Hf*Ao/(1+Ao*Hr)

The difference between them is due to the analysis of the circuit ..........

Nice material... but it does not relieve us of thinking...

Lutz, I like your answer; as though the inverting amplifier has an input attenuator...

Another answer could be:

Why should both circuits have the same gain values?

We have two different circuits, which differ in bandwidth, input resistance, feedback scheme,....

Thus, we cannot blindly expect the same gain values.

Simon, thank you for the hand-drawn picture. I like this way of illustration; here is my working place (2008): http://commons.wikimedia.org/wiki/File:Voltage_compensation_technology.jpg

Actually, you have answered the question, "How do we equalize the gains of an inverting and non-inverting amplifier?", leading to the classic 1-op-amp differential amplifier...

You can also think of this arrangement as of two cascaded voltage dividers - "direct" (R3 and R4) and "inverse" (R1, R2 and the op-amp):

https://www.researchgate.net/post/Can_we_reverse_a_voltage_divider_by_applying_the_input_voltage_to_its_output_and_taking_the_output_voltage_from_its_input

Is this (R4 + R3 = R1 + R2) a sufficient condition?

Regards, Cyril

"Is this (R4 + R3 = R1 + R2) a sufficient condition?"

No - if this condition is fulfilled, the pos gain is R4/R1, but the negative gain of the diff. amplifier is -R2/R1.

Both gains have the same value for R2=R4 only - and, thus, also R1=R3.

Why the gain of the non-inverting amplifier is 1 + R2/R1 while the gain of the inverting amplifier is only R2/R1? Is this a desired difference?

You have to keep one condition in your mind. When an op-amp is in a closed loop configuration, the differential voltage between the inverting input terminal and the non-inverting input terminal is zero OR the voltage at both the input terminals are equal.

Case 1: If I apply 1 V(DC) to the input of the non-inverting amplifier, the output increases until voltage at the inverting input terminal becomes 1 V. Suppose if R1=R2, then output will be 2 V. Since the R1 & R2 act as a potential divider.

Case 2: If I apply 1 V(DC) to the input of the inverting amplifier, the output must go negative, so that the inverting terminal becomes zero. Suppose if R1=R2, the output will be -1 V.

The op-amp has a tendency to keep its input terminals equal. You can measure it practically.

You have two different types of feedback:

shunt-shunt for the inverting; series-shunt for the non-inverting.

So in the first case the Voltage gain is equal to the transresistance closed loop gain divided the input resistance : Av = vo/vs = vo/(is*Ri) = Af / Ri = (-R2) / R1.

The non-inverting instead is a classic case of series-shunt feedback and the closed loop gain is a voltage gain and is equal to the reverse of the voltage divider acting as feedback. Av = vo/vi = Af = 1/k = 1 / [R1/(R1+R2)] = 1 + R2/R1.

I think this a great difference between the two configurations.

An interesting and original explanation... although it sounds a bit formal... Simone, the problem is that, in the beginning of this year, I decided to stop (or, at least, to minimize) my RG contributions (64 questions and 1100 answers during the last year) since I realized that I waste a lot of strength and energy... but get very little in return... Now your interesting insertions make me hesitate:)

Below I have presented, in addition to your explanation, a more intuitive viewpoint at this phenomenon. It is closely related to my unhappy question about NIC (see the attached functional picture below)...

https://www.researchgate.net/post/What_is_the_basic_idea_behind_the_negative_impedance_converter_How_is_it_implemented_How_does_it_operate_What_does_the_op-amp_do_in_this_circuit

... and the related Wikibooks story:

https://en.wikibooks.org/wiki/Circuit_Idea/Negative_Impedance_Converter#Op-amp_bridge_INIC

We can see in both the circuit solutions - inverting and non-inverting, the same arrangement consisting of two cascaded converters - the voltage-to-current converter R1 and the current-to-voltage converter R2. So, the input voltage Vin is applied across the input resistor R1 and then the obtained "output" current Iout = Vin/R1 is passed through the output resistor R2 thus giving an "output" voltage VR2 = Iout.R2 = (Vin/R1).R2.

In the circuit of an inverting amplifier, we use the output voltage VR2 really as an output voltage. Only, for some reasons (the grounded load and the load capacity), we prefer to destroy this "original" output voltage by an equivalent "antivoltage" and use the latter as an actual output voltage. So, in this case, the gain is exactly R2/R1.

In the circuit of a non-inverting amplifier, we can use with the same success the output voltage VR2 as an actual output voltage. But unfortunately, it is "lifted" by the input voltage; it is "floating". So, for the same reasons as above (the grounded load and the load capacity), we are forced to use as an output not only VR2 but the sum Vin + VR2 = Vin + (Vin/R1).R2 = Vin.(1 + R2/R1). That is why, the gain here is greater by one (1 + R2/R1) compared to the inverting arrangement...

I like your explanation.

In a case the input voltage is applied at a terminal of R1 while in the other (non-inverting) to the other terminal.

This implies the change in the sign of gains and the fact that in the second case the input voltage itself is present in the output!

For the unfortunate question on NIC I think that pheraps its length is not so attractive for the audience.

On the other hand I think that in RG you can find simple questions from people that are unaware of the matter, and you can answer for kindness, or simple questions from people who know the matter well that can be revealing challenging.

The most dangerous (from the second type of people) are those that seem naive.

BTW 1100 answers are not few :-)

Very, very original way of thinking... Do you know the remarkable Einstein's thought, "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"?

I have another Einstein quote:

" We should try to explain things as simple as possible - but not simpler"!

To be honest - I do not like to "over-complicate" things.

Therefore - feeling as an engineer - I tend to treat each amplifier with feedback as a control system which fulfills Black`s famous formula for the closed-loop gain:

A,cl=Ao/(1-LG) with Ao=amplifier gain (loop open) and LG=loop gain.

This expression is derived from the classical feedback model where the feedback signal is superimposed directly with the signal input.

* This is true for the noninverting configuration.

* For the inverting configuration with simple resistive feedback the input signal is attenuated by a factor (forward attenuation factor Hf=Rf/[Rf+Rin)] before it is superimposed with the feedback signal. Therefore, Black`s formula is to be multiplied with (-)Hf. The negative sign results because injection into the inverting terminal. This results in the known expression A,cl=-Rf/Rin (Ao infinite).

But there is another chain of Einstein's thoughts: "I am enough of the artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited... "

Lutz, I like your explanation about the input attenuation (although it is quite formal) since I am closely related to it. In the late 80's, I realized that the network of the two resistors (R1 and R2) in the circuit of the inverting amplifier, acts as a voltage summer (subtractor) with weighted inputs. Thus in the circuit of a non-inverting amplifier, we subtract the attenuated output voltage from the whole input voltage, while in the circuit of the inverting amplifier we subtract the attenuated output voltage from the attenuated input voltage...

I visualized this phenomenon many years later by means of the voltage diagram in the Wikibooks story below:

https://en.wikibooks.org/wiki/Circuit_Idea/Walking_along_the_Resistive_Film#Varying_both_V1_and_V2:_a_resistive_summer

But there is another chain of Einstein's thoughts: "I am enough of the artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited... "

Well said!

It becomes obvious that Einstein was a scientist whereas I am only an engineer.

... and I am only a circuit dreamer:)

https://en.wikipedia.org/wiki/User:Circuit_dreamer

Cyril, in the link above (circuit_dreamer) I found the following sentence:

"RC oscillators stay between relaxation and harmonic (LC) oscillators; they possess properties from the both"

I remember well that we recently had two or three different columns here in RG dealing with RC (in particular WIEN type) oscillators. But I am not sure if the above quoted statement was discussed or - at least - relaxed.

To make my position clear: I do not agree. For my opinion, there is no fundamental difference between LC and RC oscillators - and, of course, RC oscillators also belong to the class of harmonic oscillators.

May I ask: What is your position today?

Dear Lutz, your question is so fundamental that I had no courage to answer throughout this week while you were not here. But that evening I was so encouraged by the intriguing Vasile's question about the famous Tesla's inventions...

https://www.researchgate.net/post/Nikolas_Tesla_resonant_circuit_Why_this_circuit_seems_so_complex?

...and especially by his thought "Tesla's resonant circuit was designed to amplify, rather than creating damped oscillations sustained by external power"... so I decided to try to answer your so interesting question...

I suppose you have read my "Comparison between relaxation and LC oscillators" in the Wikipedia talk page about electronic oscillators:

https://en.wikipedia.org/wiki/Talk:Electronic_oscillator#Posing_the_removed_section_for_a_discussion

I continue to assert that my opinion on the similarities and differences between these two types of oscillators. But now I would like to concentrate on the main difference between the two famous arrangements... because I do not share your opinion that "there is no fundamental difference between LC and RC oscillators"...

In my opinion, they are similar only in respect of the final result ... but they are very different in how they achieve it...

Really, they have something in common in their arrangements - they both contain a passive (LC or RC) circuit and an amplifying electronic circuit. But while, in the case of an LC oscillator, the LC circuit (tank) alone produces damped (Vasile) oscillations, and the electronic circuit only sustains ("helps") them... in the case of an RC oscillator, the humble RC circuit cannot produce any oscillations... it can produce only "boring" monotonously changing (increasing or decreasing) signals... it cannot reverse the signal direction... Oscillations can be produced here only by the active "help" of the electronic circuit...

This is the essential difference between them - theoretically (if there are no losses), an LC circuit can produce oscillations without the "help" of the electronic circuit while an RC circuit cannot produce (even theoretically) any oscillations...

So, while in the case of an LC oscillator the electronic circuit plays not so essential role, in the case of an RC oscillator its role is vital... For example, it can sustain the smooth sine oscillations in the LC tank by all means (by periodic signals having any shape, e.g. square pulses, as Vasile has already said about the resonanse, sharp and whatever pulses)... It can do this even without using a positive feedback...

In contrast, the electronic circuit of an RC oscillator must do it very "gently" and "carefully"... just because it "sculpts" the sine waveform... and it does this magic by the help of the positive feedback:

https://www.researchgate.net/post/How_do_sinusoidal_oscillations_arise_in_RC_oscillators

Hi Cyril,

I am back - and I will try to explain my view on the subject „LC vs. RC oscillator“.

I think, there is only one single point of difference between our positions - and that is the following question:

What are the properties of the frequency-selective circuitry WITHOUT the amplifier?

Of course, I agree that there can be a certain difference (as far as the bandwidth or the quality factor is concerned) - however, is this an important argument as far as practical and working oscillator circuits are concerned?

To me, it is not realistic at all to remove the amplifier from our considerations.

On the other hand, you should also take into consideration that there are oscillator circuits which do NOT simply consist of (a) a frequency-dependent network and (b) a fixed-gain amplifier.

Instead, the gain function can also be frequency-dependent and, thus, cannot be isolated from the rest of the circuit (example: One of the various derivates from the WIEN oscillator with crosswise exchange of elements).

Therefore, my conclusion: There is no fundamental difference between the working principle of LC and RC oscillator realizations:

1.) AC domain: No difference in pole positions, phase shift, loop gain response.

2.) Time domain: Both alternatives show the same behaviour during the start phase (no difference in oscillation build-up process resulting from the power switch-on step).

More than that, I can see absolutely no justification for the following statement: (quotataion):

"RC oscillators stay between relaxation and harmonic (LC) oscillators; they possess properties from the both".

I think, relaxation circuits (to me: no "oscillators", but "generators") are first-order circuits - in contrast to harmonic oscillators (RC or LC) with a conjugate-complex pole pair near the imag. axis of the s-plane.

Here is another illustration of my position:

What about overdamped LC tank circuits?

These frequency-selective passice combinations are NOT able to produce as a step response decaying oscillations (like all RC combinations) - nevertheless, together with an amplifier they form a harmonic oscillator.

Where are the differences between LC and RC?

Lutz, after your comments I need to think more on all this...

HI Cyril,

I read the wiki stuff and I was surprised to see people arguing for oscillators. I saw many people arguing about football or politics, now also for oscillator :-)

BTW I go further than Lutz, and think that also the shelf where you want to put the relaxation oscillator is fuzzy. If you take a tunnel diode oscillator it can behave as harmonic or relaxation oscillator only changing the values of its parameters.

The topology is the same, the parameters assume real values so the border beetwen the two categories is necessarily fuzzy.

Also the position of poles in inherently nonlinear circuits is like a "colorless green idea".

It can help you (like in mildly nonlinear circuits) untill it start to "sleep furiously".

Hi Simone,

in my opinion, anything can become a subject of dispute as long as there are people willing to do this:) Will you let me illustrate the two modes (linear and bistable) of the tunnel diode mentioned by you with another Wikibooks story?

The first picture is about the voltage-controlled NDR (e.g., a tunnel diode):

https://en.wikibooks.org/wiki/Circuit_Idea/Negative_Differential_Resistance#Voltage_controlled_N-shaped_NDR

The second picture is about the current-controlled NDR (a tunnel diode acting in a bistable mode):

https://en.wikibooks.org/wiki/Circuit_Idea/Negative_Differential_Resistance#Current_controlled_N-shaped_NDR

Hello Simone,

I cannot comment on your contribution.

The reason: I don`t understand the contents at all - in particular the last two sentences. I am sure this is mostly due to my limited linguistic capabilities.

As far as I could see you were speaking about a very specific oscillator principle only: A circuit which exploits the differential negative resistance of a tunnel diode (differentiial !!). I am not quite sure if this particular circuit can serve as a good example for our discussion dealing with opamp based harmonic oscillators.

Regards

Lutz vW

Hi Lutz,

If you did not understand is because I just did not make myself clear.

Anyway "Colorless green ideas sleep furiously" (Noam Chomsky) is only an example of nonsense.

Regards

Simone, does this mean that you consider the whole discussion as being "nonsense"?

In this case, I strongly disagree.

For my opinion, harmonic oscillators are one of the most interesting group of analog circuits - and the following sentence (quote) can serve as a good example:

"The topology is the same, the parameters assume real values so the border beetwen the two categories is necessarily fuzzy."

I think, this applies also to the well known Schmitt-trigger based relaxation generator. If we continuosly increase the repetition rate of the circuit, the real opamp properties come into the play - and the whole circuit does not act anymore as a first-order system. Without changing the topology, the circuit merges more and more into a sinusoidal oscillator.

Hmmmm... it is too hard for me to imagine how a relaxation oscillator will become harmonic... the behavior of the circuit would be too unpredictable...

Cyril, if you remember that

- the relax oscillator has both a positive as well as a negative feedback path, and

- the opamp behaves as a second-order lowpass,

it is not so hard to imagine that there could be one single set of parts values which is able to fulfill the Barkhausen oscillation condition.

Lutz, I have never thought that there is a negative feedback in a relax oscillator. Maybe you mean that it is implemented by an inverting Schmitt triger (the IC 7414 below) and an RC integrating circuit connected between its output and input. But although this arrangement seems as (and physically is) a negatve feedback, functionally (as an operation) it is not a negative feedback since the Schmitt trigger is saturated until the RC circuit charges/discharges. In my opinion, to say that there is a negative feedback, the active device has to be an amplifier (to operate in a linear mode).

I would like to remember again the main principle of creative thinking - when considering the fundamental circuit ideas, we assume ideal elements and do not see their imperfections. For example, the ideal amplifier can have zero (360 degree) phase shift (in the case of a non-inverting amplifier) or 180 degree phase shift (in the case of an inverting amplifier)... and this phase shift is frequency independent...

Cyril - yes, presumably I have expressed myself not clear enough.

Of course, I was referring to an opamp with pure resistive positive feedback and a R-C series feedback path connected to the inverting opamp terminal. In principle, this is identical to the given figure with an inverting Schmitt trigger.

I think, we are allowed to call this R-C feedback "negative" because it is a path which couples a part of the output back to the inverting input.

However, independent on this question of terminology this path is a "real" negative feedback path in that particular design case I was speaking of:

Namely, when the whole system is designed to work in a linear mode (with frequencies as high as to exploit the frequency dependence of the opamp gain and using the real opamp poles).

Some months ago I have performed a series of investigations (and simulations) to see when and under which design constraints such a circuit works as a harmonic oscillator.

(By the way: Remember the so-called "active-R filters" and "active-R oscillators" which do not require any external capacitors. These circuits exploit only the poles of the used opamps to produce the desired loop gain functions)

Lutz, it is an interesting idea to use the op-amp frequency imperfections for constructing oscillators... and your investigations are very interesting... Can we formulate a conclusion that each amplifier is a potential oscillator?

Talking about relaxation oscillators, I can not refrain from citing the Lancaster's Elegant simplicity:

http://www.tinaja.com/glib/elesimp.pdf

Yes - nice article.

However, it is a bit disappointing that even Don Lancaster (like many other) did not correctly write down the name of the inventor of the passive circuit used in a well-known oscillator circuit:

The Wien oscillator was named after the german physicist Max Wien (NOT Wein). A short look into Wikipedia confirms this (although I do not blindly trust Wikipedia).

Lutz, I have always known (even from my junior high school years) that the name of the inventor is Wien (in association with the Austria's capital)... perhaps because then at Bulgaria the German was more popular than the English...

But yet I have to note that the basic rule when designing op-amp circuits is to make the circuit insensitive to the op-amp characteristics (phase shift, gain...) and sensitive to the external passive elements connected in the negative feedback loop...

....no doubt about this. That is the main purpose of negative feedback.

... where the great paradox is that the contemporary op-amp "serves" the old passive feedback network...