I know I have been asked not to provide video links and ask questions.
But I have no proper guide/mentor or anyone who can provide me better answers other than users in this site. So, please pardon me for this. I rely on this site for answers which can Solve my queries and help me with my understanding.
If you seen my previous questions, you would notice that a majority of my questions would have been related to control loop stability analysis of a dc-dc converter. I was not able to grasp the concept of zeroes with respect to electrical components. All I understood is that, If I have a pole, it means the electrical component will oscillate (at some frequency) and the system will be unstable. But what happens when a component provides a zero instead of a pole? How does one understand or find whether a component will provide a zero or a pole? What effect will that zero have in the system?
So, I am trying to learn it by watching questions and answers in this site, reading app notes, watching lectures and so on to get clarity.
In this Video, around 3:08 , he says that when the capacitance magnitude matches the resistance magnitude, we get a zero.
I don't understand that. Can you tell me :
- Is he meaning that at some frequency, the capacitance impedance will be equal to the resistor's resistance? If so, at this point, what will the combination of the resistor and the capacitor connected to ground look like? And when he says zero, what effect will it have on the system?
Please do not think that I am asking multiple questions. If anyone can provide the answer which can help me clear my doubt regarding the poles and zeroes in an electrical circuit (in simple electrical terms for a beginner to understand) and how one can figure that this component will provide a pole or a zero, then that answer would solve all my questions.
Would be really grateful.
Best Answer
Ok newbie, i've read your questions and comments and have a gauge of your understanding level. what classes have you taken pertaining this subject?
If you're designing a DC-DC converter for stability using bode plots (poles and zeros), you received great answers already. You need to make it a goal of understanding them.
This is a pretty good read: https://web.stanford.edu/class/archive/engr/engr40m.1178/reader/chapter7.pdf
It boils down to what another answer alluded to:
Poles/Zeros zeros have +20db/decade gain and poles have -20db/decade attenuation. You asked why in a comment? At the stage of PSU design you should have learned it, follow the math in my link. Simply, in an RC circuit, as the frequency goes up, the impedance of C will become lower and lower, and the ratio of R - C will drop/increase and this rate happens to be at 20dB/decade. Or thinking in the time-domain instead of frequency domain, the capacitor takes time to charge, so any fast changes in voltage will not be relayed with attenuation.
There is also phase. +/-90 degrees for a single zero/pole (respectively), 180 degrees for double pole/zero. The phase transitions quickly at the R+C or L+C crossover/corner frequency.
Multiple poles/zeros will have Nx20db/decade gain. so 2 pole will have 40db/decade (on average), roughly. With higher order yet poles/zeros other things come into play involving phase, and for real accuracy s-diagrams are needed. This link describes them in great detail: https://web.mit.edu/2.14/www/Handouts/PoleZero.pdf It's not critical to understand this all for PSU design, as it's usually a combination of passive poles or at most a 2 pole LC, but it's good to understand the basics.
With this information you should know how to draw a bode plot. Good link: https://pages.mtu.edu/~tbco/cm416/bodestab.html
Intuitively, this means a pole "slows down" the response of the system, because higher frequencies are attenuated. This often, but not always, has a stabilizing effect. A real-world example of a pole is heating up a pot of water to exactly 90C. You can crank it on "HIGH" (high input power) but the temperature (output voltage) takes like 5 minutes to warm up. The circuits have their own physical limitations that limit their speed, described w/ poles/zeros.
By inverse logic a zero "speeds up" the response of a system, by applying gain to higher frequencies which is more likely to have a destabilizing effect. Intuitively this makes sense: if an "ideal" zero will have more and more gain as frequency increase, then at some absurd 2.4GHz I will have +100dB of gain. So any teeny tiny interference from a wifi-router will cause the output voltage to change by an incredible amount. bad.
Both poles and zeros affect phase and gain, which affect stability.
There's a final point about the gain part of the bode plot: the gain level is usually set externally by an R+C and includes factors like the gain of the amplifier, any R-dividers, and so on. It's a variable that can be changed to affect the stability, where generally lower gain will mean a slower but more stable response.
Stability Critereon Why is this gain/phase behavior of poles/zeros important?
A good read: https://pages.mtu.edu/~tbco/cm416/bodestab.html But basically, one things need to occur for sustained oscilaltions (instability): +When PHASE reaches -180 degrees, there is greater than unity gain ( A > 1V/V, A > 0dB) +Or, described inversely: when gain approaches unity (0.001dB), there is 180 degrees of phase shift
In reality, you don't want to approach anywhere near 0dB at 180 degrees phase shift, so the concepts of "gain margin" and "phase margin" as described in the link arise. As you "approach" this unstable point, you may have "DC stability" where your DC level will be correct, but a sudden shift in the DC operating point (say a step change in the load) will cause decaying oscillations at frequencies near the 0db/180degree point.
Gain margin is how much gain you have to spare when the phase reaches the trechearous 180 degrees. You want it to be well below the 0db threshold, maybe like -20dB. Phase margin is how much phase you have to spare when gain hits 0dB. You want about -45 degrees for damped performance.
Intuitively, this stability critereon makes sense: If you have GAIN while having 180 degree inversion, your system went from negative feedback to positive feedback. Having 180 degree inversion (and thus some positive feedback) is fine if it's gain is <0dB, because it won't accumulate. But having >0dB gain and positive feedback means a positive feedback loop that will grow as it oscillates. Even if gain is only 1.001 or like +0.1dB, it will gain until it reaches some other physical limitation.
So, you asked for intuition instead of tough math about poles/zeros, I hope this helps.
To bring it to your original question, why does a C on the output cause instability? A big capacitor right at the output is an R+C zero in some converter topologies, and L+C in others.
It generally has a stabilizing effect on DC-DC converters, but can also cause instability. It depends on what this RC did to the bode-plot and whether it ruined the gain/phase margin of the converter.
Thinking about it in the time-domain, a super large C will cause the output voltage to change SLOWLY. This, like i said, usually stabilizes the output voltage, but you have to consider what the PSU system is doing. Basically, will the PSU patiently increase the current to charge the cap, or will it "accelerate" too quickly and dump huge current into the cap, overshooting. In the 90C pot of water example, you'd hope your control scheme would turn the power down a bit from HIGH as the pot of water approaches 90C, lest we overshoot and accidentally boil the water. This rationale can be applied to any aspect of the PSU, they all have bandwidth/gain--i think of it as inertia as in the pot of water. The output voltage (capacitor) can only gain voltage so fast. The inductor can only increase current supplied so fast. The amplifier only has so much gain at high frequencies. Bode plots allows us to quantify it.
There are also empirical ways to categorize a PSU (or any) control system. By applying a "Step" change to the input voltage or output load, the converter closed loop response can be characterized, and stability inferred.