LvW
Advanced Member level 6
In many textbooks the double integrator oscillator DIO (quadrature oscillator) is mentioned as a circuit which is able to perform self sustained oscillations at a frequency Fo=1/2*Pi*T (T1=T2=T=RC=Time constants of both stages).
But this circuit has some mystic properties and I ask myself: Why does it oscillate and at which frequency? As far as I know, no textbooks gives a verification/justification of the oscillating frequency!
Here are the details:
1.) AC and TRAN simulations of the shown circuit leads to the following results:
Opamp model: LT1022; R= 1k, C=0.16nF Correction: R=10k
Fo (theory): 99.5 kHz
Fo (tran simulation): Fo1=98.2 kHz (rising amplitudes) and Fo2=97.1 kHz (steady state with minor amplitude clipping).
2.) AC Simulation: of loop gain AL:
At F1=98.26 kHz with AL=0 dB and φL=-1.44 deg.
At F2=1.4 kHz (!!) with φL=0 deg. and AL=73.5 dB.
3.) My questions:
(a) Why does the circuit oscillate at a frequency Fo where the loop phase is not 0 resp. 360 deg.
(b) Why does it not oscillate at F2 where the loop phase is zero and AL>1 (0 dB) ? (Remenber: Each of the classical oscillator circuits exhibit oscillations with rising amplitudes for φL=0 and AL>1)
But this circuit has some mystic properties and I ask myself: Why does it oscillate and at which frequency? As far as I know, no textbooks gives a verification/justification of the oscillating frequency!
Here are the details:
1.) AC and TRAN simulations of the shown circuit leads to the following results:
Opamp model: LT1022; R= 1k, C=0.16nF Correction: R=10k
Fo (theory): 99.5 kHz
Fo (tran simulation): Fo1=98.2 kHz (rising amplitudes) and Fo2=97.1 kHz (steady state with minor amplitude clipping).
2.) AC Simulation: of loop gain AL:
At F1=98.26 kHz with AL=0 dB and φL=-1.44 deg.
At F2=1.4 kHz (!!) with φL=0 deg. and AL=73.5 dB.
3.) My questions:
(a) Why does the circuit oscillate at a frequency Fo where the loop phase is not 0 resp. 360 deg.
(b) Why does it not oscillate at F2 where the loop phase is zero and AL>1 (0 dB) ? (Remenber: Each of the classical oscillator circuits exhibit oscillations with rising amplitudes for φL=0 and AL>1)