generating sine wave

It isn't a mistake - if the OP asked the question, he isn't in state to make any sense of your kind of answer. And he still won''t get more than the 160mV out=put swing set by the 0.5V/usec slew rate as worked out by TuT - I haven't checked that calculation, but it looks to ba about right.

My guess is that it would still oscillate at the same frequency, because you'd still have a 180 degree phase shift bewteeen the voltage drop across L and C, not to mention the 180 degrees across the two op amps.

No it won't. The frequency would be lower. This "oscillator" is less obvious than it first appears. A quick analysis should have revealed that the drawn one shouldn't oscillate, but...

For the case of perfect 1MHz GBW opamps:

1) phase shift isn't 180 degrees. The opamp has a 1MHz GBW, giving -45° phase shift for the follower at 1MHz. The inverter has a 500kHz loop GBW product, giving 180-atan(1M/500K) = 116° phase shift, and a total 71° shift for both amplifiers going asymptotically down to 0. 2) the filters are 2nd order HPF and LPF and phase shift isn't 180°, but respectively +90° and -90° at, not resonance, but corner frequency.

So for the LPF case, total phase shift is 71-90=-19 at the 1MHz corner frequency. The LPF phase shift ranging from 0 to -180°, there's clearly a solution slightly before 1MHz. Now loop gain would be: -3db (follower) -7 db (inverter) + 20 db(Q=10) =

+10dB. So it'll oscillate sligthly before 1MHz.

For the drawn HPF case, the filter phase shift ranges from +180 downto 0. For the amplifiers, phase shift ranges from 180 down to 0, and there's no solution to the total phase=0 condition. It won't oscillate at all.

This for perfect 1MHz GBW opamps.

Now, we use real opamps. The opamps are not perfect at all and have extra poles and excess phase shift too. Using a good LM324 model, at 1MHz the follower shows -90° and the inverter

+69° for a -22° total (and still -10dB gain). Above, phase continues droping at a fast rate.

Looping this through the HPF, which didn't oscillate with the perfect 1MHz GBW opamps, there's now a solution which has to be _above_ the HPF corner frequency. A quick AC sim indicates 1.06MHz.

Looping this through the LPF, which phase shift is always negative, the frequency has to drop _below_ the LPF corner frequency to satisfy the Barkhausen criteria.

Hence exchanging L and C will lower the frequency. A quick AC sim shows about 770kHz.

When the amplitude rises from 0 at startup, it'll set where the slew rate limiting will make the average gain unity. The slew rate limiting introduces additional phase shift which will lower the oscillation frequency, down to about 650kHz and 1.03MHz.

One funny side effect is that if you substitute the LM324 for a better opamp, or if the LM324 hasn't enough excess phase shift, the "oscillator" as drawn won't oscillate.

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Thanks,
Fred.
Reply to
Fred Bartoli
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Why are you doing the student's homework assignment? Do you really want that kind of twit to graduate?

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 JosephKK
 Gegen dummheit kampfen die Gotter Selbst, vergebens.  
  --Schiller
Reply to
joseph2k

by

(unless

Did you really look at the answer?

I doubt bulk copying such an answer does any good to his graduation. Now, if he's clever enough to understand it, explain it and argue about the pros and cons, he's probably well above the required level of this homework (which he isn't since he posted the dumb question here).

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Thanks,
Fred.
Reply to
Fred Bartoli

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