After the last time we talked about "three minutes to understand the zero pole diagram", Roy realized that the "Extra" series was a bit noisy, and we had to talk back to the public topic, but I vaguely felt that we should strike while the iron was hot, and then talk about the "stability of op amp" related topics, gritted his teeth and stomped his feet, and simply "boring" another issue.
Last review:
Dry Goods Weekly: Understanding the Zero Pole Diagram in Three Minutes (Part I) (Extra Part 2)
Dry goods weekly: three minutes to understand the zero pole diagram (II) (extra chapter 3)
EEs who are new to the industry are often surprised by the "phase margin", "gain margin", "zero pole"... These seemingly profound words are bluffed, and when I hear "the stability of the op amp system", it is like a fish in the throat.
But in fact, if we start from an engineering point of view, it is completely easy to grasp the relevant methodology. Below, Roy uses VFB as an example to share some premature insights. Hope it helps.
Summary: Basic Concepts, Why Amplifiers Are Unstable, Specific Analysis Methods, Meaning of Zero Pole, Examples, LT-Spice Simulation.
1. A few concepts.
Open-loop gain (Aol): As the name suggests, it refers to the gain when it is placed in a feedback-free state. Aol is usually large, such as 130dB (3.16 million times). Of course, existence is reasonable, and the large open-loop gain helps us to control the output voltage more accurately and improve the performance of the circuit system.
But in the circuit world, such a large gain is also a powerful force, which can easily lead to system instability. For example, the "primitive op amp" is like the Monkey King, which is extremely powerful and difficult to restrain it.
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In order to suppress the "Monkey King", the predecessors introduced a "negative feedback network" to the op amp, which is like putting a tight spell on the Monkey King. With the blessing of negative feedback, the op amp is finally constrained, and the final effect is closed-loop gain.
Closed-loop gain (Acl): The gain (usually the actual gain of the system) exhibited by the op amp after feedback is added. It is like the Monkey King wearing a tight spell, rational and kind. At the same time, it can also adjust the circuit parameters to control the amplification of signals and noise, and retract and release freely.
Loop Buff (AF for short): The Tightening Spell. It is a negative feedback network introduced to suppress the "original op amp". Its power should not be underestimated, after all, it has single-handedly weakened the powerful open-loop buff. For example, if the open-loop gain Aol = 130 dB and the closed-loop Acl = 20 dB, then the feedback loop gain AF = Aol-Acl = 110 dB (316,000-fold weakening)
Feedback system in brief
A few simple expressions:
开环增益:Aol = Xo/Xi
反馈系数:Phi = XF/S
闭环增益:Acl = Xo/Xf = Aol/(1+Aol*F),当Aol很大时,它≈1/F
Loop gain: AF = Xf/Xi, when it >> 1, it is a deep negative feedback state.
2. Where does the stability problem of op amp come from?
In op amp systems, there are often nonlinear factors, which can cause different degrees of phase shift in the system. This is nothing, we don't need to be too sensitive, but we must be wary of the following points.
When the phase of the op amp system changes by 180°, a terrible thing can happen: the negative feedback of the system can become positive. (The original negative feedback has shifted by 180°, and if it is shifted by 180°, it will inevitably cause a feedback signal, turn around on the spot, and turn against each other)
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This can put the system in a state of instability. Specific performance: The output signal will self-oscillate, and even if there is no input, there will be an oscillation output. It is equivalent to the tight spell on Sun Wukong's head, which not only fell off, but also exploded.
Of course, it is not so exaggerated, instability requires conditions. From an engineering point of view, it is mainly reflected in two indicators: phase margin and gain margin. If the design is reasonable, there is no need to worry at all. For example, even if the negative feedback becomes positive, but the gain is << 1, then it will not make any waves.
3. Pure dry goods: analysis method for the stability of op release.
In practice, the feedback loop must have enough headroom to ensure that the system works reliably under all load conditions. In practice, we often use the intuitive graphical method, and the following takes the "loop gain curve" method as an example:
"Phase Margin" discriminant: Look at the angular difference at the intersection of loop gain = 0dB, the phase distance at the -180° phase shift, that is, PM=|180-Δ|, if the distance is far enough (e.g., ≥45°), it can be considered stable.
"Gain margin" discriminant: When looking at the phase shift of -180°, the corresponding loop gain can be considered safe if it is small enough (e.g., GM<-10dB).
Loop gain curve analysis
One thing we need to understand is that the above 45° phase margin and -10dB gain margin are only recommended values, and the larger the margin, the safer it is. For the following details:
An intuitive phenomenon: when the phase margin is insufficient, it often manifests as ringing in step response. For example, when the PM< is 45°, the number of times the clock rings up and down in the time domain usually exceeds 4 times.
Of course, there will also be people who are accustomed to using the method of "open-loop gain curve" + "closed-loop gain curve" to analyze, and the essence is the same, so we will not repeat it.
Roy had taken notes
4. Advanced: Zero-pole manipulation.
Do you remember the pull change we talked about in the previous article? Through the node equation, we get the transfer function of the op amp (containing the zero pole information), and the position of the zero pole in the gain curve also determines the change trend and characteristics of the system, which is directly related to the stability of the system.
Roy had taken notes
Space is limited, let's just talk about the methodology:
1. The negative feedback of the op amp is usually introduced by the zero pole (with a negative sign) in the left plane. At the pole position fp, there will be a 45° phase shift, and the limit of the phase shift caused by a single pole is 90° (between fp/10~10*fp), which is also the limit of the first-order system.
2. The closed-loop zero point is the pole of the loop, which will raise the closed-loop gain and press down the loop gain. Not good for stability, bad.
3. The closed-loop pole, which is the zero point of the loop, will press down the closed-loop gain and raise the loop gain, which can improve the phase/gain margin and increase the stability of the system, which is good.
4. Since the loop gain ≈ open-loop-closed-loop, the zero-pole effect of the open-loop gain is the opposite of the closed-loop gain and the same as the loop gain effect. It's all bad at the pole and good at the zero. (Good: Good for Stability)
Roy notes
When the margin is not enough, do not panic. Because we can add a phase compensation circuit to improve it, the purpose: before the phase difference reaches 180°, let the gain decrease as much as possible, or before the loop gain G drops to -10dB, do not let the phase drop too fast.
It is not difficult to see that as long as we can properly introduce the zero pole in the right place, we can manipulate the characteristics of system stability, bandwidth and response speed.
ADA4807 Closed-loop gain vs. CL in the manual
5. Examples & Simulations
Generally speaking, the output/load side of the op amp is easy to introduce the loop pole, and the input and feedback side is easy to introduce the closed-loop pole to facilitate compensation here. There are many similar examples, just to name a few:
1. The op amp output is terminated with a capacitor to ground, which introduces a closed-loop pole and may cause oscillation if the position is too low. If the output is connected in series with Rs for compensation, the zero point of the loop can be brought closer to offset the harm of the closed-loop pole.
2. In the TIA circuit, Cf and Rf introduce a closed-loop pole (i.e., the loop zero point) on the closed-loop gain curve to improve the stability of the system.
Roy had taken notes
3. Most LDOs need to be connected to the output capacitor to be stable, in fact, it is also for similar reasons.
LT-SPICE instance simulation
Let's take ADA4807 op amp as an example and use LT-Spice to actually build a simulation run to see the importance of phase compensation.
The simulated circuit is as follows:
LT-Spice simulates circuits
Thereinto:
C2 is the analog load capacitance, which brings a pole to the loop gain. When C2 is large, the amplifier becomes unstable and thus oscillates.
R3 is the phase compensation point, when R3 = 0 there is no compensation, when R3 = 50 ohms, the loop zero point will be introduced, and there is a compensation effect.
For the sake of simplicity, let's do AC simulation, directly look at the loop gain VFB/VI, and let's go:
1. When Rs=0 ohms, the op amp output is directly shorted to the ground with a 1nF capacitor, and the simulation results are:
Phase margin: When G = 0dB, the phase has slipped from 180° to -19° (it should be ≥ 45° to stabilize), there is no phase margin to speak of, if it must be said, the phase margin is negative, about -64°
Gain margin: At 180° of phase difference, the gain is still +10.3dB (it should be <-10dB to stabilize), and it is clear that there is no gain margin at all.
LT-SPICE simulation, without compensation
LT-SPICE simulation, loop gain curve without compensation
2. When Rs=50 ohms, it is equivalent to bringing the zero point of a loop in the distance closer, with the effect of phase compensation, the simulation results are:
Phase margin: When G=0dB, the phase margin is about 46°, which is stable and safe.
Gain margin: When the phase difference reaches 180°, the gain is -36dB, and the margin is sufficient.
LT-SPICE simulation, with compensation
LT-SPICE simulation with loop gain curve with compensation
Speaking of which, are you curious, what does the self-oscillation of the op amp look like? According to the different situations, its appearance is also strange, the following is a result of pressing the ADA4807, when Rs=0, the output is shorted to the ground 1nF.
As soon as you press the "Emulation" button, you know that there must be a mystery here, because the simulation speed at this time is extremely slow:
Simulation speed
After a few minutes, I finally saw the real body of "self-oscillation", ↓
One of the results of self-oscillation
It can be seen that the real signal has been heavily polluted by a high-frequency signal, and FFT was done on it, and it was found that the pollution source was around 10MHz. This means that the amplifier is self-excited here.
FFT display of self-excited frequency
In a real-world application, the phenomenon may be different, but this is only a superficial example.
Looking back, there are more than 3,000 words, let's stop first, and then set up a flag: let's talk about GMSL related content later, see you next time!
End
Roy's personal opinion, for reference only
remind
1. This article is only for engineering application/analysis, and it is from the perspective of tools, and the analysis is not in-depth.
2. Roy is not a professional, it is inevitable that there will be flaws in understanding, if the expression is inappropriate, please send a private message or leave a message.
3. There are many software tools that can be used to directly do system design/simulation. This is all well and good, but we need to be wary: relying too much on tools may make us not understand the system well and think deeply.
We will continue to update the dry goods weekly series, and the follow-up will gradually deepen and be more specific. In the "Dry Goods Weekly", there are also the following things that are kept up-to-date:
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