Real Meaning of Poles and Zeros in Frequency Domain ?

poles and zeros

Hello Guys,

I have read a lot about Poles, Zeros, S-plane, transfer function and I am just wandering to know,

1. what is real and intuitive meaning of it in physical life ?

2.how it is useful in amplifier?

3. Pole shoot up the response and zero shoot down the response. then what happen if we do not have both in systems transfer function?

if you have any paper on it then please share with me. some one suggest me to look for book i.e Poles and zeros in electrical and control engineering by robin maddock. if you have it. then please provide me link

concept of poles and zeros

OK, I´ll trty a short explanation:
1.) The "normal" frequency in measurement and simulation is f or ω.
2.) However, to describe the behaviour of filters with a transfer function it is advantageous not to use ω but extend it into the complex plane s=σ+jω.
(But remember: Just for easy and comfortable formulation, because in reality s does not exist).
3.) By doing this, one can define two parameters which very good describe the filter behaviour (pole frequency and pole Q). Both can be measured also very easily.
3.) As a consequence a quadratic term in an 2nd order denominator of a transfer function can become zero at a certain value of s (that is the pole of the transer function!)
4) Look at Fig. 2b and 4a of the enclosed document and you will see the function approaching infinite.
5.) But interestingly, for "real" frequencies with σ=0 (shown as a cut area in the picture) in the vicinity of the pole , the amplitude goes DOWN.
6.) For zeros something similar applies (analogous to the pole).
_____________
Summary: The complex frequency s is a fiction, but a very good means to describe and to show in a picture the properties of a transfer function.
Regards
LvW

poles zeros

Hi,
Thanks LvW for sharing your thought.. I have understood your points. i have known it. but i just want to know that, i want to relate this concept of poles and zero with physical life or you can say a daily life example. so that we can visualize this things more intuitively... :|

understanding poles and zeros

girih192002 said:

Hi,
Thanks LvW for sharing your thought.. I have understood your points. i have known it. but i just want to know that, i want to relate this concept of poles and zero with physical life or you can say a daily life example. so that we can visualize this things more intuitively... :|

Click to expand...

I don´t know if I understood your question completely, however, as the complex frequency variable s cannot be produced in real life. also a complex pole does not exist in "real life".

understanding frequency domain

A very simple analogy for poles and zeros is:

Pole's are like Pole's that support a tent (think of a 3 ring circus, 3 poles)
Then the Zero's are the spikes that hold the tent down.....
(The "tent" represents the output power of the frequencies you uses).

Poles are where the filter/Amp has the best thru-put or gain and the Zeros are
were the filter/Amp has the the most impermanence in the thru-put path.

poles and zeros of transfer function

girih192002 said:

Hello Guys,


1. what is real and intuitive meaning of it in physical life ?

2.how it is useful in amplifier?

3. Pole shoot up the response and zero shoot down the response. then what happen if we do not have both in systems transfer function?

if you have any paper on it then please share with me. some one suggest me to look for book i.e Poles and zeros in electrical and control engineering by robin maddock. if you have it. then please provide me link

Click to expand...

If you want to visualize the effects of poles and zeros , then you can better do that by understanding the fact that in case of amplifiers, they come from the presence of inductances and capacitances in the amplifier ckt.

In the transfer function of the amplifiers (ex CMOS in CS stage), if suppose you have a capacitance in the output node, then if you write the transfer function of the amplifier, you will find a pole created by this capacitance, due to which there is a decrease in the gain of the amplifier with increase in frequency. Now, if you want to visualize this phenomena rather than writing the transfer function, then you can note that at higher frequencies, that particular output node capacitor will short the output node to ground, thereby reducing the output voltage to zero, and hence reducing the gain to zero.

If there are no poles and zeros in the transfer function, then it signifies that there are no inductances or capacitances in the amplifier ckt, so its gain is always constant and thus independent of the frequency.

poles and zeros of a transfer function

Thanks LvW, Eleement_115 and shivam Dwivedi for you reply. now i got the clear visual understanding of Poles and Zero.

Thanks a Lot..

explanation about poles and zeros

hello,

are you sure you have an understanding of what a pole and zero is?

There is a saying...

"The time domain is for explanation but the frequency domain is for calculation"

in other words....only the time domain can really be understood analogously..........poles and zeros are in the frequecny domain...a domain in which we do not live, but made up just so we could do calculations more quickly.

I doubt there is such thing as an analogy for a pole or a zero..........you only know what they help you to calculate.

Re: poles and zeros

girih192002 said:

Hello Guys,

I have read a lot about Poles, Zeros, S-plane, transfer function and I am just wandering to know,

1. what is real and intuitive meaning of it in physical life ?

2.how it is useful in amplifier?

3. Pole shoot up the response and zero shoot down the response. then what happen if we do not have both in systems transfer function?

if you have any paper on it then please share with me. some one suggest me to look for book i.e Poles and zeros in electrical and control engineering by robin maddock. if you have it. then please provide me link

Click to expand...

Hi,
Though i am too late here, let me put my views on this for those who come across this later on.
1. The hierarchy is like that: From Real world-Physical Circuits > Cauer & Foster Forms (This realizes R,L,C circuit in mathematical form) > Transfer function > Story of pole zeros.
2. I hope it's quite clear now that pole zeros are integral part of any circuit dealing in frequency domain.
3. As a simple example, in band pass/reject filter, we want some frequencies to be boosted and other to be suppressed. Hence we need both poles and zeros at appropriate locations.

There are many books giving inside view on pole and zeros. you can refer any analog filter design or in general analog circuit design book.

Re: understanding frequency domain

Element_115 said:

A very simple analogy for poles and zeros is:

Pole's are like Pole's that support a tent (think of a 3 ring circus, 3 poles)
Then the Zero's are the spikes that hold the tent down.....
(The "tent" represents the output power of the frequencies you uses).

Poles are where the filter/Amp has the best thru-put or gain and the Zeros are
were the filter/Amp has the the most impermanence in the thru-put path.

Click to expand...

I like that one.

Another way to think of it:
For open loop systems: Poles are lowpass "elements" where gain drops 20 dB/decade for each pole. Zeros are like highpass elements, where gain rises 20 dB/decade for each zero.
For closed loops systems: too many poles can make a system unstable (because each pole eventually adds -90 degree of phase shift to the open loop gain), and adding zeros (at the right frequency) can partially compensate for that and make the system "conditionally stable"

Refer the book "Linear Systems and Signals" written by B.P.Lathi...
The book is very intuitive. Time domain, frequency domain and complex plane are very well explained.