What is the physical meaning of Pole and Zero?

[VirtuosoDracula]

Re: pole zero definition

In order to justify the invention of the complex frequency variable s - here are some additional comments:

The pole location can be marked in the complex plane. And now one can define two very important filter parameters:

1.) The value identical to the magnitude of the vector from 0/0 to the pole location is the so called "pole frequency" ωp.

2.) The angle δ between the negative-real axis and this vector is an indication of the so called "pole quality factor" Qp. The exact relation is: Qp=1/(2cosδ)

3.) Both parameters characterize the filter response and are given in relevant textbooks. More than that, both values can be measured with a frequency generator and an oscilloscop (better: network analyzer)

4.) These definitions - together with the 3D-picture as shown - reveal the relationship between pole location and magnitude response of a filter (with amplitude peaking corresponding to the pole location).

Added after 1 hours 41 minutes:

Sorry, I forgot to say someting to the zeros.

No, it is not correct that at system zeros the output "tends to zero" . This is only true for "real zeros".
In general, the slope of the magnitude function will change in the neighbourhood of zeros - nothing else.

For example, the slope of the magnitude function (BODE- diagram) goes from 0 to -20dB/dec (or from -20 to -40 dB/Dec) at the pole frequency .
In the same way the slope increases from -20 dB/Dec to 0 (or from -40 to -20 dB/Dec) caused by a complex zero.

LvW

Added after 2 hours 57 minutes:

Another addendum - perhaps helpful for somebody:

The end of the passband (corner frequency, 3-dB-frequency) is NOT identical to the pole frequency. However, both frequencies normally are not very far from each other.
(in practice: 5...10 %) .Exception: For a BUTTERWORTH response both frequencies are identical.

Hi LvW,

Can you plz clarify a little bit more on complex zeros..I'm very much clear about the significance of complex poles but my understanding about the complex zeros is bit hazy.
As in the case of complex poles when you have negeative real part your o/p decays exp with the freq,,but is the case reverse in case of complex zero and vice-versa??

plz help me out with that...

Thanks in advance.!!

 

[LvW]

As in the case of complex poles when you have negeative real part your o/p decays exp with the freq,,but is the case reverse in case of complex zero and vice-versa??

Hi Dracula, as far as I understand your question are you interested in the influence of transfer function zeros on the response in the time domain, right?
I am afraid, i cannot give a general answer because of the following reason:
The denumerator of a transfer function is identical to the characteristic polynom of the differential equation in the time domain. Thus, the roots of the denumerator function (the poles of the transfer function can be seen in the exponent of the solution in the time domain. However, something similar is not possible with the complex zeros of the transfer function because there is not such a direct relation to the time domain.

 

[erikl]

The denumerator of a transfer function is identical to the characteristic polynom of the differential equation in the time domain. Thus, the roots of the denumerator function ...

There's no such English word - LEO at least doesn't know it -- without the leading "d" it's known. I'm sure you thought of denominator ;-)

 

[LvW]

There's no such English word - LEO at least doesn't know it -- without the leading "d" it's known. I'm sure you thought of denominator ;-)

Erik, thanks.
As you will have noticed - I am getting older and older.

 

[yaqoob]

Re: physical meaning of pole and zero

physical meaning of pole and zeros

let we had calculated by different means the transfer function of a car at 60/h with temperature 50 degree etc
we we speed up , a new transfer function is created because of temperture change , or parts of car are changing position and friction etc

but
this is transfer function of the same car

so new poles will be existed

- - - Updated - - -

physical meaning of pole and zeros

let we had calculated by different means the transfer function of a car at 60/h with temperature 50 degree etc
we we speed up , a new transfer function is created because of temperture change , or parts of car are changing position and friction etc

but
this is transfer function of the same car

so new poles will be existed

 

[VirtuosoDracula]

Re: physical meaning of pole and zero

physical meaning of pole and zeros

let we had calculated by different means the transfer function of a car at 60/h with temperature 50 degree etc
we we speed up , a new transfer function is created because of temperture change , or parts of car are changing position and friction etc

but
this is transfer function of the same car

so new poles will be existed

- - - Updated - - -

physical meaning of pole and zeros

let we had calculated by different means the transfer function of a car at 60/h with temperature 50 degree etc
we we speed up , a new transfer function is created because of temperture change , or parts of car are changing position and friction etc

but
this is transfer function of the same car

so new poles will be existed

Thanks Yakoob..and with the same example how would you explain the zeroes?

 

[electrician213]

Re: complex frequency variable

I want to know what is the physical meaning of a zero or a pole in a system?
I know by using transfer function at zero the output of the system tend to zero and
at pole it tend to infinte.
but I dont know exactly what is the quality of zero or pole?
what is the nature of them?
can everybody help me?
thanks.

Hi, I guess the discussion to going to somewhere else from pole and zero...

This is what I know and have read several times...

Poles and Zeros of a transfer function are the frequencies for which the value of the transfer function becomes infinity or 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. Control systems, in the most simple sense, can be designed simply by assigning specific values to the poles and zeros of the system. (taken from wikipedia)

It is easier to understand and calculate.

Thanks!

 

[Mr_eng]

Poles and Zero's

Can you recommend a modern text book that gives a long introduction with many examples.
I have K A Strouds Further engineering mathematics and I like the way it gives many examples.

Regards

Alan

 

[LvW]

Mr_eng, perhaps a paper from the MIT suits your needs (see pdf attachement)

 

[erikl]

Re: Poles and Zero's

... a long introduction with many examples.

I like this rather practical tutorial.