Oscillator with op amps

[MrAl]

MrAl,

Why are you talking about "saturation"? If a nice sine wave is desired, saturation is the last thing I desire. I would want the feedback nonlinearity to gradually limit the amplitude to just below the rail voltage. Like the light bulb does in a Wien-bridge oscillator.

There are lots of ways to arrange the amplifiers and phase-shift network to give the highest frequency, lowest distorion, greatest amplification, etc. They all involve compromises.

Ratch

Hi again,

I am talking saturation because that's currently the only way to stabilize the gain with this thing. With the second stage op amp going into saturation for even a tiny amount we've achieved gain stabilization. There's no light bulb in this circuit. But even if there was, it would not work very well with a gain of 1 buffer at the output...i said your equations looked like that, not that the circuit should be like that

But back to the main point, the circuit will not work well with a gain of 1 buffer at the output because the output amplitude will be too small. Yes there are other ways to arrange the amps and set the gains, but with a buffer with gain of 1 at the output is not one of them.
Calculate the max output voltage that YOU can get with that thing, and you'll see at least part of what this is all about.

 

[Ratchit]

MrAl,

Hi again,

I am talking saturation because that's currently the only way to stabilize the gain with this thing. With the second stage op amp going into saturation for even a tiny amount we've achieved gain stabilization. There's no light bulb in this circuit. But even if there was, it would not work very well with a gain of 1 buffer at the output...i said your equations looked like that, not that the circuit should be like that

No, I don't believe that. Negative feedback can be increased dynamically to keep the op amp output from exceeding its voltage limits. That is what the light bulb does. It won't keep any distortion from happening, but it won't be saturation distortion. I would put the light bulb in the highest gain amplifier.

But back to the main point, the circuit will not work well with a gain of 1 buffer at the output because the output amplitude will be too small.

The gain at the other op amp will be enough to make the circuit work.

Yes there are other ways to arrange the amps and set the gains, but with a buffer with gain of 1 at the output is not one of them.

Why not? 1 multiplied by 29 is still 29.

Calculate the max output voltage that YOU can get with that thing, and you'll see at least part of what this is all about.

It doesn't have the highest voltage that can be attained, but it has very low harmonic distortion. All things are compromises.

Ratch

 

[MrAl]

Hi Ratch,

Part1:
MrAL said: Yes there are other ways to arrange the amps and set the gains, but with a buffer with gain of 1 at the output is not one of them.
Ratch said: Why not? 1 multiplied by 29 is still 29.
MrAL now replies: Because the output voltage level is then too low, and the upper frequency limit is too low.

Part2:
MrAL said: Calculate the max output voltage that YOU can get with that thing, and you'll see at least part of what this is all about.
Ratch said: It doesn't have the highest voltage that can be attained, but it has very low harmonic distortion. All things are compromises.
MrAL now replies: We only have to compromise when there is a reason to compromise. There is no reason to compromise here. All we have to do is adjust the gains to be better distributed between the two op amps and we get everything we want: clean output and higher much more usable output voltage amplitude.

Part3, The solution:
MrAL says: Adjust the gains of the two op amp sections to about 5.4 each and see how much more useful the output amplitude is and how the upper frequency limit increases about 5 times.

Part4: The qualifying tests:
MrAL says: With a plus and minus 15 volt supply test the circuit with gain of 1 buffer at output for output amplitude and THD. Test the circuit with two gains of 5.4 (approximate) for output amplitude and THD. Compare the output amplitude and THD of both circuits and try to draw a conclusion. (Also compare for upper frequency limit).

Part5: The results of the tests:
MrAL says: The circuit with a buffer of 1 at the output has very very low output amplitude and decent THD and is limited in useful frequency. The circuit with two 5.4 gains has a much higher output voltage amplitude and THD equal to the circuit with the gain of 1 buffer at the output and has higher useful output frequency.

Part6: The conclusion:
MrAL says: The circuit with two gains of 5.4 has higher much more useful output amplitude and THD equal to the other circuit, and this also has the benefit of increasing the useful upper frequency limit, so this circuit is the better choice.

 

[Ratchit]

Hi Ratch,

Part1:
MrAL said: Yes there are other ways to arrange the amps and set the gains, but with a buffer with gain of 1 at the output is not one of them.
Ratch said: Why not? 1 multiplied by 29 is still 29.
MrAL now replies: Because the output voltage level is then too low, and the upper frequency limit is too low.

Why? The output voltage and the high frequency may be lower than othen other configurations, but the harmonic distortion is the lowest. It depends on the application as to whether a particular configuration is best.

Part2:
MrAL said: Calculate the max output voltage that YOU can get with that thing, and you'll see at least part of what this is all about.
Ratch said: It doesn't have the highest voltage that can be attained, but it has very low harmonic distortion. All things are compromises.
MrAL now replies: We only have to compromise when there is a reason to compromise. There is no reason to compromise here. All we have to do is adjust the gains to be better distributed between the two op amps and we get everything we want: clean output and higher much more usable output voltage amplitude.

No, the least distortion occurs when the amplifier with the most dynamic feedback is before the filter. If both amps have equal gain, then the amp with the dynamic feedback will have to change the gain more radically because its change is multiplied by 5.4 due to the other amplifier. That causes more distortion than a more moderate gain change of an amplifier with a gain of 29. So we get a wider bandwidth with more distortion.

Part3, The solution:
MrAL says: Adjust the gains of the two op amp sections to about 5.4 each and see how much more useful the output amplitude is and how the upper frequency limit increases about 5 times.

Yes, higher bandwidth with more distortion. Designer's choice.

Part4: The qualifying tests:
MrAL says: With a plus and minus 15 volt supply test the circuit with gain of 1 buffer at output for output amplitude and THD. Test the circuit with two gains of 5.4 (approximate) for output amplitude and THD. Compare the output amplitude and THD of both circuits and try to draw a conclusion. (Also compare for upper frequency limit).

Good idea.

Part5: The results of the tests:
MrAL says: The circuit with a buffer of 1 at the output has very very low output amplitude and decent THD and is limited in useful frequency. The circuit with two 5.4 gains has a much higher output voltage amplitude and THD equal to the circuit with the gain of 1 buffer at the output and has higher useful output frequency.

The circuit with the unity gain buffer at the output has the lowest distortion, lowest output, and lowest bandwidth. Whether it is useful or not depends on the application.

Part6: The conclusion:
MrAL says: The circuit with two gains of 5.4 has higher much more useful output amplitude and THD equal to the other circuit, and this also has the benefit of increasing the useful upper frequency limit, so this circuit is the better choice.

No, it does not have the same low distortion of the configuration with the unity gain output. The choice depends on the application

Ratch

 

[MrAl]

Why? The output voltage and the high frequency may be lower than othen other configurations, but the harmonic distortion is the lowest. It depends on the application as to whether a particular configuration is best.



No, the least distortion occurs when the amplifier with the most dynamic feedback is before the filter. If both amps have equal gain, then the amp with the dynamic feedback will have to change the gain more radically because its change is multiplied by 5.4 due to the other amplifier. That causes more distortion than a more moderate gain change of an amplifier with a gain of 29. So we get a wider bandwidth with more distortion.



Yes, higher bandwidth with more distortion. Designer's choice.



Good idea.



The circuit with the unity gain buffer at the output has the lowest distortion, lowest output, and lowest bandwidth. Whether it is useful or not depends on the application.



No, it does not have the same low distortion of the configuration with the unity gain output. The choice depends on the application

Ratch

Hello again,

What you are arguing here is that two amplifiers one with a gain of 29 followed by another with a gain of 1 is BETTER than two amplifiers one with a gain of 5.4 followed by another with gain of 5.4. So we have a gain of 29 and gain of 1 versus a dual gain of 5.4.

With plus and minus 15v supplies we find the following:

The 29,1 combination has a 0.3 vrms output maximum.
The 5.4 pair has a 1.6 vrms output maximum, and 5 times higher usable frequency range.

That alone is enough to seriously think about rejecting the 29,1 combination.


But then there's the THD...
An amplifier with a gain of 1 has the highest bandwidth, higher than a gain of 5.4, and therefore the frequency rolloff is not as extreme for the gain of 1 amplifier and that means it passes higher harmonics without attenuation than the gain of 5.4 amplifier. That makes the 29,1 combination output actually have more THD than the dual gain of 5.4 combination.

But even if the THD was higher for the dual 5.4 combination, how much more higher could it really be?

Look at the computation for THD. THD is computed by adding the squares of all the harmonic components and then taking the square root, then dividing by the fundamental:
THD%=100*sqrt(E2^2+E3^2+E4^2+...+En^2)/E1

Now if an amplifier that has a gain of 1 will pass the En^th component with attenuation of 1/m then an amplifier of the same make set with a gain of approximately 5 will attenuate that same harmonic by 1/(5*m) meaning that harmonic actually gets reduced by a factor of 5 for the gain of 5.4 amplifiier. This will no doubt lower the THD for that output. So in terms of voltage, that means for a gain of 1 if the Nth harmonic is reduced to 1/2 then that same harmonic in the gain of 5 amp will be reduced to about 1/10, which is much better for the overall THD. How much better will depend on what the base frequency is.

So the conclusion must be that the gain of 29,1 pair must have higher THD at the outpout than the dual 5.4 pair.

The 29,1 pair has lower output level and higher distortion, so the clear winner is the dual 5.4 gain pair.

Yes, many things depend on the application. If 0.3 vrms is good enough for your application the THD may not matter as much so you're good to go. For my purposes i would always prefer the 1.6v rms output however and get the benefit of the lower THD and higher frequency range.

Just curious, how did you determine that a gain of 1 amplifier has less THD than a gain of say 5 amplifier?

 

[Ratchit]

Hello again,

What you are arguing here is that two amplifiers one with a gain of 29 followed by another with a gain of 1 is BETTER than two amplifiers one with a gain of 5.4 followed by another with gain of 5.4. So we have a gain of 29 and gain of 1 versus a dual gain of 5.4.

I aver that the 29:1 amp will have a lowest distortion. If that is your definition of "better", then I agree.

With plus and minus 15v supplies we find the following:
The 29,1 combination has a 0.3 vrms output maximum.
The 5.4 pair has a 1.6 vrms output maximum, and 5 times higher usable frequency range.

For the 29:1 configuration, we have (15/29)*1, which is approx 0.5 v-p. For the 5.4:5.4 configuration, we have (15/29)*5.4, which is approx 2.7 v-p.

That alone is enough to seriously think about rejecting the 29,1 combination.

It all depends on whether you want higher gain or lower distortion.

But then there's the THD...
An amplifier with a gain of 1 has the highest bandwidth, higher than a gain of 5.4, and therefore the frequency rolloff is not as extreme for the gain of 1 amplifier and that means it passes higher harmonics without attenuation than the gain of 5.4 amplifier. That makes the 29,1 combination output actually have more THD than the dual gain of 5.4 combination.

Faulty reasoning. The amplifier with the highest automatic gain control (AGC) will have the highest harmonic distortion. The unity gain amp has no AGC, and and distortion it does have only gets multiplied by one.

But even if the THD was higher for the dual 5.4 combination, how much more higher could it really be?

Look at the computation for THD. THD is computed by adding the squares of all the harmonic components and then taking the square root, then dividing by the fundamental:
THD%=100*sqrt(E2^2+E3^2+E4^2+...+En^2)/E1

Now if an amplifier that has a gain of 1 will pass the En^th component with attenuation of 1/m then an amplifier of the same make set with a gain of approximately 5 will attenuate that same harmonic by 1/(5*m) meaning that harmonic actually gets reduced by a factor of 5 for the gain of 5.4 amplifiier. This will no doubt lower the THD for that output. So in terms of voltage, that means for a gain of 1 if the Nth harmonic is reduced to 1/2 then that same harmonic in the gain of 5 amp will be reduced to about 1/10, which is much better for the overall THD. How much better will depend on what the base frequency is.

If the harmonics are within the bandwidth, then that reasoning does not apply, does it? And if that is not the amp with the AGC, then there is not that much distortion to start with.

So the conclusion must be that the gain of 29,1 pair must have higher THD at the outpout than the dual 5.4 pair.

The 29,1 pair has lower output level and higher distortion, so the clear winner is the dual 5.4 gain pair.

No the 29:1 has lower distortion for the following reasons. The first op amp has the distortion producing AGC and high amplification. But its lower bandwidth helps to filter out the higher frequencies as you explained above. Then the signal goes into a phase-shift network filter which is positioned at exactly the right place to be the most effective at filtering out the harmonics regardless of their frequencies. I aver that if the gain were 5.4, then it would produce more harmonic distortion because the AGC would have to work harder to compensate for the other 5.4 amplifier following it, thereby producing more distortion than the 29 gain amp would.

Yes, many things depend on the application. If 0.3 vrms is good enough for your application the THD may not matter as much so you're good to go. For my purposes i would always prefer the 1.6v rms output however and get the benefit of the lower THD and higher frequency range.

That is a benefit you do not have. You have compromise choices.

Just curious, how did you determine that a gain of 1 amplifier has less THD than a gain of say 5 amplifier?

As explained above, the unity gain amplifier does not have the AGC.

Ratch