More specifically: For proper function the circuit needs a certain parameter that was not considered during the design process.

Well - let us investigate one of the classical opamp-based linear oscillator circuits:

A closed loop containing two Miller intergators and one inverter. It is a well-proven approach to design the circuit assuming ideal integrators (opamps modelled as large gain VCVS blocks). Each hardware realisation will produce a continuous oscillatory signal in the close vicinty  of the envisaged frequency (as long as the design frequency corresponds to the small-signal and large-signal frequency limits of the used opamps).

However, a circuit simulation based on ideal large-gain VCVS blocks will not result in continous oscillation. Instead we must use real opamp models. Why?

Answer: The loop gain for the ideal chain will fulfill the oscillation condition (phase) for infinite frequencies only. We need at least one real opamp model (with frequency-dependent gain) in order to allow a loop gain phase shift of 0 deg. at a fixed and finite frequency only.

Each electrical system must have the final frequency bandwidth. This is a physical necessity. Otherwise, noise would "consume" endless energy. See too https://www.researchgate.net/publication/281495081_POVINNY_POL_ZESILOVACE_PRI_ANALYZE_STABILITY

(only in Czech). But abstract:

In this paper we argue against some parts of papers [1] and [2] which are engaged in determining of stability by means of " classical " procedures. It is always possible to determine the stability in this way. But we must respect the obligatory pole of an amplifier that always exists and describes a fact that a noise-bandwidth of any electrical devices must be limited. It must be always limited because the attainable power is always limited, too.

Conference Paper " POVINNÝ " PÓL ZESILOVAČE PŘI ANALÝZE STABILITY

Dear Lutz,

The classical opamp-based linear oscillator circuits are not real world circuits.

We have discussed that before. A steady-state oscillator is a nonlinear circuit.

The bias point of the circuit varies with time. The opamp do not have a dc bias point.

All the best

ERIK

Hello Erik - thank you for your comment.

However, may I ask you to read again my original question? I did not speak about "real world" circuits! I am aware that real circuits contain real components only!

But - you certainly will agree that (at least in the lower frequency range) it is common practice to design opamp-based circuits assuming IDEALIZED gain blocks, OK?

Examples: Active filters and simple gain stages. We all know that each REAL circuit will slightly deviate from the such a simplified design approach.  But this is not my point! I did not mention non-linearity or real-world circuit properties or bias points.  

Instead, the core of my problem is the following:

For circuit simulation of these active devices (active filters, gain stages) we CAN use simplified opamp models (fixed-gain VCVS), which were the basis of the design process (instead of real models) - and the result will be as expected!. 

But there is ONE SINGLE EXCEPTION (as far as I know): The double-integrator oscillator, which REQUIRES real opamp models for simulations - in spite of the fact that the design equations were based on IDEAL components.

And, for my opinion, such an exception from our common practice deserves some attention  - unless there are other exceptions (which was a part of my original questiuon).

Do you now understand what I mean?

Thank you

Lutz

Dear Lutz,

Thank you for your response. I am sorry. I was too fast in my response to your question.

(1) concerning:

However, a circuit simulation based on ideal large-gain VCVS blocks will not result in continuous oscillation. Instead, we must use real opamp models. Why?

Answer: The loop gain for the ideal chain will fulfil the oscillation condition (phase) for infinite frequencies only. We need at least one real opamp model (with frequency-dependent gain) in order to allow a loop gain phase shift of 0 deg. at a fixed and finite frequency only.

My Answer: Ideal large-gain VCVS blocks are linear and imply a fixed and time-independent dc bias point. The circuit is unstable and we end up in one of the rails with no oscillations.

(2) concerning:

But - you certainly will agree that (at least in the lower frequency range) it is common practice to design opamp-based circuits assuming IDEALIZED gain blocks, OK?

My comment: Of course. I agree with you 100 pct.

(3) concerning:

But there is ONE SINGLE EXCEPTION (as far as I know): The double-integrator oscillator, which REQUIRES real opamp models for simulations - in spite of the fact that the design equations were based on IDEAL components.

My comment: An oscillator is a circuit which searching for a dc bias point. The double-integrator oscillator with two active RC integrators is a very interesting circuit. We have only two energy storage components i.e. either steady-state limit cycle behaviour or no oscillations. Apparently, both opamp models must be real nonlinear models in order to create the mechanism with a time-varying small signal model giving rise to steady state oscillations based on energy balance. We should study how energy is moving around in the circuit. The energy delivered from the battery corresponds to the losses.

All the best

ERIK

Dear Erik - please find below my comments to your contribution.

Quote: "My Answer: Ideal large-gain VCVS blocks are linear and imply a fixed and time-independent dc bias point. The circuit is unstable and we end up in one of the rails with no oscillations."

No - this is against my observations (and against theoretical aspects). The double-integrator oscillator circuit - if realized with IDEALIZED large-gain VCVS blocks - shows decaying but no continuous oscillations. This is in accordance with theory for large-Q circuits (a pole pair in the left half, but very close to the imag. axis)..

Quote: We have only two energy storage components i.e. either steady-state limit cycle behaviour or no oscillations. Apparently, both opamp models must be real nonlinear models in order to create the mechanism with a time-varying small signal model giving rise to steady state oscillations.

Again - this is against corresponding observations. As mentioned above, we can observe (slowly) decaying oscillations in case of idealized gain blocks, but the circuit works well (steady-state oscillations) if at least one of the integrators contains a frequency-dependent gain block (with corresponding phase shift). A "real and nonlinear model" is not necessary  for producing steady-state oscillations in the simulation environment (and only THIS was my question; I did not refer to real and practical circuits, which always contain a certain amount of nonlinearity).

Lutz