Table of Contents

## What is a pole zero doublet?

Pole-zero doublets arise in a variety of circumstances. An active-loaded differential input stage introduces a pole-zero pair separated by an octave in the open-loop response of an op amp [1]. Other examples include frequency-compensation schemes such as feed forward, input lag, and feedback lead compensation [2].

### What is a pole in frequency response?

A pole frequency corresponds to a corner frequency at which the slope of the magnitude curve decreases by 20 dB/decade, and a zero corresponds to a corner frequency at which the slope increases by 20 dB/decade.

#### What happens if there is pole zero cancellation in a system?

CTM: Pole/Zero Cancellation. When an open-loop system has right-half-plane poles (in which case the system is unstable), one idea to alleviate this problem is to add zeros at the same locations as the poles, to cancel the unstable poles. Unfortunately, this method is always unreliable.

**What are the effects of the addition of pole and zero on time domain response specification?**

Adding a RHP zero to the transfer function makes the step response slower, and can make the response undershoot. Adding a LHP pole to the transfer function makes the step response slower. those dominant poles and zeros.

**What is the difference between a zero and a pole?**

Definition: Poles are the roots of the denominator of a transfer function. Zeros are the roots of the nominator of a transfer function.

## What does pole-zero plot tell us?

Pole-Zero plot is an important tool, which helps us to relate the Frequency domain and Z-domain representation of a system. Understanding this relation will help in interpreting results in either domain. It also helps in determining stability of a system, given its transfer function H(z).

### How can we justify pole zero cancellation?

When an open-loop system has right-half-plane poles (in which case the system is unstable), one idea to alleviate the problem is to add zeros at the same locations as the unstable poles, to in effect cancel the unstable poles.

#### How do you know if a pole is unstable?

We can factor L(s) to determine the number of poles that are in the right half plane. Since we know N and P, we can determine Z, the number of zeros of “1+L(s)” in the right half plane (which is the same as the number of poles of T(s)). If Z>0, the system is unstable.

**What are Effect of zeros and poles in the response of a system?**

Poles and Zeros of a transfer function are the frequencies for which the value of the denominator and numerator of transfer function becomes zero respectively. The values of the poles and the zeros of a system determine whether the system is stable, and how well the system performs.

**How do you calculate poles and zeros?**

In this equation the constant k=b0/a0. The zi terms are the zeros of the transfer function; as s→zi the numerator polynomial goes to zero, so the transfer function also goes to zero….So the pole-zero representation consists of:

- a constant term, k=3,
- zeros at s=-1 and s=-2, and.
- polese at s=-1+j, s=-1-j and s=-3.