Phase Shift Oscillator not Oscillating

Question

May I please ask why my phase shift oscillator as shown is not oscillating? My R1=R2=R3, and C1=C2=C3. I am trying to get around 1kHz of oscillation, so using the simple equation of fr=1/(2*piRC*sqrt(6)), I get all the values as shown in the pictures.

But why is it not oscillating? I tried at both Multisim and LTSpice, but it just doesn't simulate. I am using ideal opamp at both simulators (gain is very high, 200x let say). I put Rf(feedback resistor of opamp) to be 220k to have Rf>29*R, which will make the loop gain >1 (to fulfill the Berkhausen criteria), but it is still not oscillating. I thought the circuit fulfills both of the criterion for oscillating to happen?

I tried changing Rf to even higher value, and even play with the RC values. I also tried to use LM741 op amp and rise the supply voltage slowly, but I never get oscillation. May someone please give me enlightenment on what is wrong/lacking? Thank you very much.

Answer 1

For some oscillators, it helps to "kick-start" to get them going in a simulation that doesn't model the noise that gets a real oscillator going. In this case, the kick-start is done by initializing node n005 to 0.01V (anything other than zero volts). Node 5 is at the right-hand end of C3:

This oscillator uses a virtual op-amp with open-loop gain of 100K. Since it has no power supply and is perfectly linear, oscillations grow exponentially...forever.

XU1 N001 0 N002 opamp Aol=100K GBW=10Meg
R1 N002 N001 180k
R2 0 N003 560
R3 0 N004 560
R4 0 N005 560
C1 N003 N002 .1µ
C2 N004 N003 .1µ
C3 N005 N004 .1µ
R5 N001 N005 5.6k
.IC V(n005)=.01
.tran 0 .1 0 .00001
.lib opamp.sub
.backanno
.end

Your oscillator also hasn't quite enough phase shift.

Answer 2

I have simulated your circuit using Intusoft IsSpice as you can see below. The feedback resistance is calculated to compensate the attenuation where the phase lag is 180°. I derived the oscillation frequency here for the two phase-shifted oscillators (\$RC\$ and \$CR\$) here Deriving the formula of oscillation frequency for the Phase Shift Oscillator. In a circuit like this, with perfect elements, there is no noise as correctly pointed out by glen_geek. You can crank the circuit with an external source but the easiest way is by using a .IC statement as I did on \$C_3\$:

When you run the simulation, it nicely oscillates as shown below at a frequency of 1.16 kHz. Please note that my feedback resistance (your \$R_4\$) is 162 k\$\Omega\$ and not 220 k\$\Omega\$ as in your circuit. Oscillations are nicely maintained without clipping so perfect compensation of the attenuation. Please make sure to check the UIC box (use initial conditions) before starting the simulation.

Please note that \$R_f\$ must exactly compensate the attenuation where the phase lag is 180°. The condition for oscillation is a 360° total phase lag (-180° of the \$CR\$ network plus -180° of the inverting op amp) and a gain of 1. If the gain is less than one then the poles have a real part and oscillations will cease quickly. If the gain is greater than 1, the the poles jump into the right-half plane and oscillations diverge until a real op amp rails up or down. So \$R_f\$ must be 29 times 5600 in your example to match this criteria: 162 k\$\Omega\$ not more, not less. See the two examples below with more than 162 k\$\Omega\$ and less than 162 k\$\Omega\$:

Answer 3

Change Vin(+) to Vcc/2 with 2 R's like 470K. You are violating Vin CM range.

Then increase gain to make stable oscillation, let R4= 1M if you have enough GBW at fo.

Overall is a poor design at best, and worse when you dont consider GBW and attenuation and CM in range.