# What does Pole/Zero mean when related to capacitors and filters or Electronics in general

#### Electronic_Maniac

Joined Oct 26, 2017
253
Hi all,

I am trying to understand the feedback compensation techniques of DC-DC Buck converters. And I drift to more and more small questions which make me want to understand the basics of poles/zeroes/frequency

In general, can someone clarify me the concept of pole with filters/capacitors? Like, if someone says, there is a pole in the feedback loop, or two poles in the loop, how to understand it electrically? I don't understand the difference in circuits as I havent seen and understood.

one more question regarding this, i understand that if there is a pole, it means that oscillations will be present in the system. But the oscillations will be at what frequency? Will it be at the resonant frequency of the part or the entire systems?

It would be better if someone can provide me an analogy regarding these poles & frequency for good understanding.

Thanks.

#### Papabravo

Joined Feb 24, 2006
16,078
Without taking a deep dive, poles are the solutions to polynomial equations with real coefficients. The polynomial equations are derived from the differential equations that describe the dynamics of a system. In basic algebra we learned that polynomials can have both real and complex solutions. A real number solution to a polynomial is plotted on the real (horizontal). If the solution in negative it corresponds to a solution which decays exponentially. If it is positive it corresponds to an exponential solution that diverges to infinity. As we say: "The positive real roots disappear, or the system does". If the solution to the polynomial equations lie in the complex domain, then they must occur in complex conjugate pairs. Each complex root has a real part which corresponds to a converging or diverging exponential, and an imaginary part which corresponds to an oscillation. It is the magnitude of the imaginary part that determines the frequency multiplied by $$2\pi$$. The imaginary part is plotted on the imaginary (vertical) axis.