Stability (Poles and Zeros) + Capacity load + Phasors

[cborrero2000@hotmail.com]

Hi Everybody,

Can somebody explain me the basis of stability (zeros and poles), also how capacity loads have a big impact in the circuit stability and finally what role phasor plays when analyzing the stability of the system and one practical example of this if possible

Thank you

Carlos

[AndyC_772]

Hi Carlos

This sounds like something my 3rd year control theory course took about 6 months to explain - and what you're asking sounds like an exam question that I might have been able to answer about 15 years ago, though sadly not any more.

If you'd like a real world example, try looking at the data sheets for a switched mode power supply controller. These devices usually allow for an external compensation network which has to be designed to give adequate phase margin across all operating conditions, and can be quite tricky to get right. There's a reasonable worked example here:

http://www.ti.com/lit/ds/symlink/lm3075.pdf

...page 15, section beginning 'loop compensation'.

I'll leave the explanation of poles, zeros and phasors to someone with a less frazzled brain than mine.

[PSR B1257]

the basis of stability (zeros and poles)

http://en.wikipedia.org/wiki/Nyquist_stability_criterion

Besides, this is a huuuuge theme, and therefore almost impollible to explain it in a few sentencis.

[Mechatrommer]

the basis of stability (zeros and poles)

http://en.wikipedia.org/wiki/Nyquist_stability_criterion

http://en.wikipedia.org/wiki/Bode_plot bode plot can do as well. dont ask, i'm also having trouble with it.

[sorin]

read a book

[poorchava]

That's one of the areas where i think all of the EE-related students have a hard time. I guess its on par with high speed pcb layout, advanced magnetic field theory, analog filter design and advanced DSP in terms of 'level of VOO-DOOness'.

[cborrero2000@hotmail.com]

Thank you All for your responses,

After your inputs I realized I needed to go deep into the books and internet (Wikipedia, ti buck controller ds, etc) as suggested...

I have been reading, not continuously,  for about 20 hrs about this topic and yes, it's very extensive and finally I am just starting to understand some of the concepts and how they are related to each other...   Specially how phase has a big impact in the voltage and currents of each element in the circuit, so that not a simple voltage divider will be an accurate answer, that's why we need to use phasors to make the calculations of voltages and currents in the elements of the circuit considering the phase shift in each case. Also Transfer Function Phase tells if the circuit is unestable or not based on the gain by constructing and looking the Bode Plot out of the Transfer function specially evaluating db gain whether it is greater or lower of 0db (1) at the frequency where Phase shift is 180 degrees in a negative feedback loop configuration which will produce positive feedback and also by determined the phase margin of the circuit. Also very important to take into account the phase shift introduced by the internal capacitance of the OPAMP in use plus the added capacitance of the pcb and how to overcome this by adding zeros  with high pass filters for example. Also how a capacitive load will produce inestability by adding overshoot, ringing with positive or negative exponential component, defining in which of the 4 quadrants poles and zeros lay by looking at the pole-zero plot.

 I guess after 40 more hours of reading I'll be satisfied with my search and I'll review if my concepts are clear and right


I appreciate all your responses which guided me through this road.

Regards,

Carlos

[sorin]

http://pcbheaven.com/wikipages/PID_Theory/?p=0