[SOLVED] some problem about the quadrature oscillator configured with Deboo integrator

[HJK2014]

1.The feedback loop offers 0 phase shift regardless of frequency,then how the freq. of oscillation be selected from the others?
Thanks!

 

[FvM]

The oscillation condition is set up by loop gain phase and magnitude. In this oscillator (and other double integrator designs), the loop gain magnitude decides about the frequency.

 

[LvW]

The oscillation condition is set up by loop gain phase and magnitude. In this oscillator (and other double integrator designs), the loop gain magnitude decides about the frequency.

Yers - with other words: There is one frequency only for which the magnitude of the loop gain is 0 dB. If both integrators have the same time constant T, this is the (angular) frequency wo=1/T.
However, it is an interesting exercise to ask: What happens for frequencies slighly BELOW 1/T ? Here, the phase condition still is fulfilled and the loop magnitude is slightly larger than 0 dB.
All other oscillator circuits do oscillate with amplitude clipping - but not the double-integrator oscillator.

 

[HJK2014]

The oscillation condition is set up by loop gain phase and magnitude. In this oscillator (and other double integrator designs), the loop gain magnitude decides about the frequency.

Thanks,and one more question:let's assum that f0 is the freq. which satisfies magnitude condition(ie,the loop gain magnitude equals unity).But,unity gain has no amplify effection,then,how can the oscillation(f0) established from random noise(ie,starts with a tiny magnitude and then bigger and bigger ...)?

 

[LvW]

Thanks,and one more question:let's assum that f0 is the freq. which satisfies magnitude condition(ie,the loop gain magnitude equals unity).But,unity gain has no amplify effection,then,how can the oscillation(f0) established from random noise(ie,starts with a tiny magnitude and then bigger and bigger ...)?

For all other oscillators you must take care that the loop gain is slighly larger than unity (at t=0) and accept amplitude clipping, unless you have incoroprated a soft non-linearity for amplitude control.
However, this is NOT necessary for this oscillator because it is the only one that fulfills the phase condition for a broad range of frequencies (and has a loop gain larger than unity for frequencies below wo)
Hence, self-excitement is always ensured.

 

[FvM]

If you solve the differential equation of the double integrator circuit, you get a slightly different picture.

The solution for the circuit comprised of two ideal integrators is a harmonic oscillation with constant magnitude, neither ascending nor decaying.

The circuit in post #1 differs however from an ideal integrator by R8 = 1.1k and also by the additional poles of OP loop gain. These elements are causing a negative oscillator damping and allow an oscillation to build up from initial transients or (theoretically) from noise.