# I cannot understand why oscillations happens at gain less than 1?

Thread Starter

#### TarikElec

Joined Oct 17, 2019
45
Hello Everyone,
As I am reading the book of Op Amp for Everyone, chapter feedback theory. I come across this paragraph that I could not understand well:
Stability is determined by the loop gain, and when Aβ = –1 = |1| ∠–180° instability or oscillation occurs. If the magnitude of the gain exceeds one, it is usually reduced to one by circuit nonlinearities, so oscillation generally results for situations where the gain magnitude exceeds one. Consider oscillator design, which depends on nonlinearities to decrease the gain magnitude; if the engineer designed for a gain magnitude of one at nominal circuit conditions, the gain magnitude would fall below one under worst case circuit conditions causing oscillation to cease

so my confusions is that how can the oscillation happens (bold writing) when the gain Magnitude greater than 1 an also gain magnitude under 1!!???
I am sure that oscillations happens when Aβ = –1 = |1| ∠–180°, because Vout/Vin=A/(1+AB), since AB would be -1, which create infinite gain

Op Amp for Everyone

#### Delta Prime

Joined Nov 15, 2019
1,022
Hello there it is good to have a schematic of a unity gain operational amplifier also called voltage follower this way you can apply different values to various components. If you don't understand bode plots for an operational amplifier you might have some difficulty. Grab yourself a datasheet of the operational amplifier anyone except the 741, it is total garbage.
Beta(β) = This is called the feedback fraction and is a ratio of the impedances used in the feedback loop. To keep it simple it is the ratio of the feedback resistors commonly placed around the loop to reduce the gain.
Loop gain (Aβ)
This is a special gain and is the most important one which is an indication of the stability of an op-amp. Loop gain in the case of an inverting amplifier is the (-Aol*Beta) and is written as (-Aβ). This is important because if loop gain ever equals +1 with a phase shift of –360 ˚ the circuit could oscillate
.This is Aol /1+(Aβ) and is the classic closed loop gain formula. This is derived from the open loop gain and the feedback fraction. For the case of an inverting amplifier this is Aol/(1-Aβ).
This is the highest frequency (bandwidth) of the op-amp where the gain is reduced to 1 (output is the same magnitude as the input) or 0dB also called the unity gain bandwidth.
Noise Gain(NG)
It is the inverse of the feedback factor which defines stability. (Sometimes, this expression is called noise gain) . It is NG= (R1/R2)+1
Signal Gain(SG)
This is the gain formed by the closed loop of the op-amp. For an inverting amplifier it is R1/R2
For a non inverting amplifier it is (R1/R2)+1
Open Loop Gain(Avol) = This is the gain that an unloaded op-amp with no feedback will give you, feedback is when a percentage of the output signal in fed back into the input.
Feedback stabilizes the DC operating point only. Dynamic stability is degraded ! The bandwidth of the opamp unit remains unchanged.
However, the closed-loop bandwidth of the amplifier with feedback is larger than the open-loop bandwidth.
Why do they give us this gain on the data sheet, simple reason is, this is how you get the part, they don’t know what you are going to do with it

Last edited:
• TarikElec

#### BobaMosfet

Joined Jul 1, 2009
1,776
Hello Everyone,
As I am reading the book of Op Amp for Everyone, chapter feedback theory. I come across this paragraph that I could not understand well:
Stability is determined by the loop gain, and when Aβ = –1 = |1| ∠–180° instability or oscillation occurs. If the magnitude of the gain exceeds one, it is usually reduced to one by circuit nonlinearities, so oscillation generally results for situations where the gain magnitude exceeds one. Consider oscillator design, which depends on nonlinearities to decrease the gain magnitude; if the engineer designed for a gain magnitude of one at nominal circuit conditions, the gain magnitude would fall below one under worst case circuit conditions causing oscillation to cease

so my confusions is that how can the oscillation happens (bold writing) when the gain Magnitude greater than 1 an also gain magnitude under 1!!???
I am sure that oscillations happens when Aβ = –1 = |1| ∠–180°, because Vout/Vin=A/(1+AB), since AB would be -1, which create infinite gain

Op Amp for Everyone
Title: Understanding Basic Electronics, 1st Ed.
Publisher: The American Radio Relay League
ISBN: 0-87259-398-3

The Art of Electronics 3rd Ed.
Author(s) Horowitz & Hill
ISBN-10: 9780521809269

• TarikElec

#### BobTPH

Joined Jun 5, 2013
3,318
I have no idea what you are talking about, the bolded text does not say that it oscillates with a gain of less than one, it says the opposite, that oscillation ceases, meaning stops, when the gain is less than one.

Bob

• TarikElec

#### LvW

Joined Jun 13, 2013
1,247
In short:
* The oscillation condition (it is a necessary one only !) requires that the LOOP GAIN is "1" at one single frequency only (closed-loop poles on the imag. axis of the s-plane).
* Due to unavoidable tolerances this cannot be achieved with 100% accuracy. Therefore, we design the circuit for a loop gain slighly greater than "1" (rising oscillation amplitudes). This enables a safe start of oscillations.
* In addition, we add some non-linearities to bring the loop gain back to "1" before the amplitudes are clipped. To be more exact: Due to unavoidable delays withinthe loop the loop gain will be for certain time slots slightly smaller than "1" (decaying amplitudes).
* That means: The closed-loop poles will periodically swing around the imag. axis.

• TarikElec

#### Hugh Riddle

Joined Jun 12, 2020
78
Worth noting that emitter follower circuits can quite easily oscillate or ring, particularly when their lead/tracks exhibit appreciable inductance due to poor design or layout. Although the emitter follower exhibits an overall voltage gain of just below one, the voltage gain between its base-emitter and collector-emitter circuits will be much greater than one.

• TarikElec

#### LvW

Joined Jun 13, 2013
1,247
Worth noting that emitter follower circuits can quite easily oscillate or ring, particularly when their lead/tracks exhibit appreciable inductance due to poor design or layout.
The oscillation principle based on an emitter follower (gain<1) can ensure the required loop gain >1 due to resonant properties of the L-C feedback path (Colpitt-, Hartley principles).

• TarikElec

#### vanderghast

Joined Jun 14, 2018
55
because Vout/Vin=A/(1+AB), since AB would be -1, which create infinite gain

Op Amp for Everyone
On resonnance too, the theorical amplitude goes toward infinity, but that is NOT an unstability.
It is unstable because it goes from having a goal to go toward + infinity to go toward - infinity within a very small variation. That could easily create the feedback to stimulate overshoot and undershoot.

• TarikElec

#### jeffl_2

Joined Sep 17, 2013
45
Actually ANY kind of voltage follower, either discrete or op-amp, will usually oscillate if you connect the output directly to one end of a small diameter piece of coax a few inches long, and at least one input is unterminated. I recall we always used to need to "build out" the output lines of our op-amps with a small resistor (maybe 33 ohms) to stop this. The output will "echo" out of the open end of the coax and back in again, and the coax will all by itself "find" some frequency at which the voltage gain around the loop exceeds unity and the phase relationship will sustain oscillation, it generally doesn't take much to make it happen.

• TarikElec
Thread Starter

#### TarikElec

Joined Oct 17, 2019
45
I have no idea what you are talking about, the bolded text does not say that it oscillates with a gain of less than one, it says the opposite, that oscillation ceases, meaning stops, when the gain is less than one.

Bob
Yes you are right. it ceases when it is less than one. but oscillate when it is more than one, which I do not see in the equation of feedback loop

#### LvW

Joined Jun 13, 2013
1,247
Yes you are right. it ceases when it is less than one. but oscillate when it is more than one, which I do not see in the equation of feedback loop
May I ask you - where did you see (in this thread) such an "equation of feedback loop"?

#### Papabravo

Joined Feb 24, 2006
16,165
If you look carefully you will see that there is more to it than gain. In addition to the gain requirement there is also a phase requirement. You have to think about AC circuits differently than DC circuits.

• TarikElec
Thread Starter

#### TarikElec

Joined Oct 17, 2019
45
Hello there it is good to have a schematic of a unity gain operational amplifier also called voltage follower this way you can apply different values to various components. If you don't understand bode plots for an operational amplifier you might have some difficulty. Grab yourself a datasheet of the operational amplifier anyone except the 741, it is total garbage.
Beta(β) = This is called the feedback fraction and is a ratio of the impedances used in the feedback loop. To keep it simple it is the ratio of the feedback resistors commonly placed around the loop to reduce the gain.
Loop gain (Aβ)
This is a special gain and is the most important one which is an indication of the stability of an op-amp. Loop gain in the case of an inverting amplifier is the (-Aol*Beta) and is written as (-Aβ). This is important because if loop gain ever equals +1 with a phase shift of –360 ˚ the circuit could oscillate
.This is Aol /1+(Aβ) and is the classic closed loop gain formula. This is derived from the open loop gain and the feedback fraction. For the case of an inverting amplifier this is Aol/(1-Aβ).
This is the highest frequency (bandwidth) of the op-amp where the gain is reduced to 1 (output is the same magnitude as the input) or 0dB also called the unity gain bandwidth.
Noise Gain(NG)
It is the inverse of the feedback factor which defines stability. (Sometimes, this expression is called noise gain) . It is NG= (R1/R2)+1
Signal Gain(SG)
This is the gain formed by the closed loop of the op-amp. For an inverting amplifier it is R1/R2
For a non inverting amplifier it is (R1/R2)+1
Open Loop Gain(Avol) = This is the gain that an unloaded op-amp with no feedback will give you, feedback is when a percentage of the output signal in fed back into the input.
Feedback stabilizes the DC operating point only. Dynamic stability is degraded ! The bandwidth of the opamp unit remains unchanged.
However, the closed-loop bandwidth of the amplifier with feedback is larger than the open-loop bandwidth.
Why do they give us this gain on the data sheet, simple reason is, this is how you get the part, they don’t know what you are going to do with it
Thank you Sir for the excellent explanation. I could not understand the Noise gain and how you did get the formula. it seems for me it is the closed loop gain

Thread Starter

#### TarikElec

Joined Oct 17, 2019
45
I have no idea what you are talking about, the bolded text does not say that it oscillates with a gain of less than one, it says the opposite, that oscillation ceases, meaning stops, when the gain is less than one.

Bob
I agree, I read it wrong. I got it now. Thanks

Thread Starter

#### TarikElec

Joined Oct 17, 2019
45
Actually ANY kind of voltage follower, either discrete or op-amp, will usually oscillate if you connect the output directly to one end of a small diameter piece of coax a few inches long, and at least one input is unterminated. I recall we always used to need to "build out" the output lines of our op-amps with a small resistor (maybe 33 ohms) to stop this. The output will "echo" out of the open end of the coax and back in again, and the coax will all by itself "find" some frequency at which the voltage gain around the loop exceeds unity and the phase relationship will sustain oscillation, it generally doesn't take much to make it happen.
Thanks for your answer. WHat you said seems interesting. so we add a R=33ohm to the output of the Opamp so stop oscialltion but I dot not understand that theoritically