Josef,

Is ckt (b)    'real' circuit   or    'ideal' simulated circuit ?

There is no referenced grid for these plots.

I notice that the Hi-Q has a narrow bandpass.

I notice that the Lo-Q has a wider bandpass.

This is expected.  Also the phase of the V(fb) changes.

I think that you question the lower amplitude variation.

The "largeQ" plot shows similar bandpass for blue and red.

The V(out) variation may be due to the variation between

the fixed feedback amplitude  (and phase shift)

vs.

the varying V(in) amplitude.

The balance is varying,   

so   if this is the case,

then  the effects will be different

in  each instant and  should be expected.

In Spice, as I remember from my work-up for Lutz,

I can make this type of Positive-Feedback circuit

change from  BandPass  to  Notch  to  Oscillator ,

by changing the balance between V(in) to V(fb) .

My general thought is :

Ckt (a) is simple, no feedback.

Ckt (b) has feedback,  it is a "moving target" .

*** The simulator will 'slice' a piece of time out for the calculations

which is only true for one moment in time.  

*** The real world circuit (b) is in an  "endless loop" of activity,  

and  It is continually generating an artificial Inductance,

and IF you un-balance he feedback  ,

THEN  it may oscillate, or extinguish.

My personal comment is :

Now, as merely an old student ( retired and independent)  ,

I rely / depend  greatly on the Spice Simulator to handle the math.

I was very happy when Lutz posted the question

about "Simulators Failing"

because it made me re-evaluate the differences between 

"Frequency Domain" bode analysis

vs.

"Time Domain" Transient analysis.

I am familiar with the challenges of different personalities

living in different cultures, having different educations,

and speaking different languages. 

So, I hope we understand each other.

Thank you for writing.

Glen

Glen

it is interesting to investigate voltage U2 - its limitation which is "a function of Q" and of opa supply voltage.

Josef

.

Hi Glen

If we use the actual inductance (with a serial resistance), the problem does not occur.

Josef

Josef - I have to investigate the circuit in detail (simulation). My first answer (preliminary): Something must be wrong - as long as you are within the linear region of the opamp, the transfer ratio must be constant.

OK - got the 'secrets' not given in the original post:

• The 'artificial choke' saturates at higher input amplitudes - exceeding the operating range of OZ2.

Somehow I suspected so much but didn't find the time...

Conclusion: this problem will not show up using 'ideal' OpAmp models resp. any model that does not care about supplies.

From Josef`s diagrams I deduce that he was speaking about the performance in the frequency domain only. Of course, in the time domain, we have to face some other limiting effects like supply rails and slew rate limitations.

However, his diagrams clearly show the transfer function in the frequency domain. Hence, the following answer applies to the small-signal behaviour only:

* Josef, I cannot confirm your results. As expected, the simulated transfer function (active L realization) does not depend on the input signal amplitude.

* However, I have observed a strong dependence of the form of the transfer function (active L simulation) from the non-ideal opamp properties.

Example values:

R1=1k, R2=20 Ohms, Cs=10µF, Rs=10 Ohms L=10mH,.opamp (real model) TL081.

The "notch" is at 500 Hz.

Already at app 3kHz there are severe deviations from the expected theoretical response (passive L).

Josef, 

You wrote 

"...its limitation which is "a function of Q" and of opa supply voltage."

Also the ability of the "Real-World" OPA to respond ( Negative FeedBack ) 

"in proper phase" with the input waveform is a factor.

At higher frequencies, the NFB will be less and less in proper phase.  

This is a "time dependent" factor.  

In my project, I use the "ideal calculating" Spice program, 

but use "Real World" OPA in the circuit 

and always avoid pushing my "Real World" OPA too far. 

In your example,

I assumed that the OPA Vcc-Vee ( Supply Limits ) were not touched. 

@ Lutz

It is somehow difficult to 'model' an amplitude-dependent L in the frequency domain. Though not completely impossible.

Obviously Josef's problem is created in the time domain, the plots being merely a means to 'show' what's happening. (Step or Dirac responses are quite hard to read. And such diagrams might have given him away :) )

OK - so we have to ask Josef if the shown diagrams result from an ac analysis (frequency domain). If not, the result is no surprise because we always have to face non-linearities.

OZ2 must be able work with U2 - see below. It must not limit. From this we can (and a supply voltage) to determine the allowable UImax. See also https://www.researchgate.net/publication/281625533_Maximalni_vstupni_napeti_pro_zadrze_RC

- sorry in Czech only.

Article Maximální vstupní napětí pro zádrže RC

@ Josef

Seems you were low on inductors these times :)

Were these circuits widely used or was this just a niche application? Seeing the 'good old' 741 again after all these years ...

Regards

Josef - please answer my previous question: Is the shown frequency response (notch) the result of an ac analysis (simulation in the frequency domain)?

It is the result of experimental observations.

In the linear region is "solving AC", of course - hence the boundary Uimax.

If it is not valid (see below) the synthetic inductor is "not valid also" - the circuit is non linear - its derivation is not valid. And I would be happy if I could solve the impulse response of this structures with non-ideal amplifiers :-))

Generally, we must examine the level of the signal at each node of the electronic circuit - not just output. In the described circuit it is particularly "tricky" - OZ2 output is not "in the direct path" of signal.

Another mechanism of transfer growth (on fo) is the change of series resistance with frequency - see

https://www.researchgate.net/publication/281495071_Narrow-band-reject_filter_with_a_real_operational_amplifier

Conference Paper Narrow-band-reject filter with a real operational amplifier

Here is example of LTspice calculations for Notch Filter with Gyrator. The model results for Small signal and Large signal are similare  to those at the top of topic.

Are you sure signal levels?

We can use max about 10 V only.

And what about those beautiful real band stop properties?

Hi Josef Punčochář. I hope You know the answer for Your's question.

And what is true answer?

The really cause is increasing of series resistance with frequency. But it will be a lot of work still.

See

https://www.researchgate.net/publication/281495071_Narrow-band-reject_filter_with_a_real_operational_amplifier

Conference Paper Narrow-band-reject filter with a real operational amplifier