Hi all,

I guess i have a very foolish question.

We have all learned that poles and zeros are contributed by capacitor either parasitic or external. Poles tend to increase the gain to infinity and zero to 0.
I have learned that in most cases the output load capacitance , or in the case of Op-amp the capacitance at the output of first stage, is the dominant pole.

The capacitance impedance decreases as the frequency increases. Suppose F0 be the frequency of the dominant pole. when f > F0, the dominant capacitance tend to decrease its impedance, hence the quantum of voltage dropping across it reduces.

Hence according to the above explanation the gain should decrease and that's what happens when u see the Bode plot.

Then why is that poles are defined as those which increase the gain to infinity.


Please correct me.


Thanks

ARJ

Hello ARJ !

The answer of RFICDUDE is totally correct. However, perhaps it is not quite understood by you as it is pure theory. Therefore I recommend a very illustrative application note which shows the effect of a transfer function pole.

Here is the reference: www.maxim-ic.com/appnotes.cfm/appnote_number/733/ - 65k  

(look at Fig. 4)

Perhaps this can help as well.

Lutz

I appreciate this discussion on the basics.  To revive this thread and embarrass myself by exposing my limited understanding...

I've been trying to make sense of the Laplace Transform method.  I can follow the math, but not the meaning.  In particular,
when transforming from t  to s spaces, one is going from one-dimensional (time) to two-dimensional (sigma, omega) spaces.
So what is the physical meaning of sigma?  What constrains its value when transforming from t to s? What (if any) information is lost
when transforming from s to t?  Does my question even make sense?  I don't know...

Hello joel,

here is a rather clear and evident interpretation of "sigma" and "omega" in the s-plane:

Take a simple RLC-circuit and stimulate it with a step function. Than calculate the step reponse in the time domain. The solution of the corresponding differential equation is a time function exp(s*t). By introducing the presently unknown factor "s" (which has the dimension (1/sec) into the characteristic equation the solution shows that "s" consists of two parts: one is real (called "sigma", with a negative sign) and the other one is pure imaginary (jw). The latter one - if substituted back into the e-function - has to be interpreted as a sine function : exp(jwt).
Therefore, the real part exp(sigma*t) determines the amplitude of the sinus, which decreases continuously with increasing time. So we have a frequnecy with a decaying amplitude.
Thus, the solution of the differential equation of a system leads directly to a parameter which is called the complex frequency variable "s=sigma+j*omega".

Perhaps this can help to understand the physical meaning of "s".
Regards
Lutz
   

Hi joel.

I cannot recommend any specific textbook in english since I am familiar with german textbooks only.
However, any good textbook on analog active filter circuits should explain the meaning of the complex frequency variable since the LAPLACE transform is used extensively in filter theory.
For example, the application note  

http://www.maxim-ic.com/appnotes.cfm/appnote_number/733/

explains in a nice manner the difference between "s" and "j*omega". Of course, in the real world only "omega" exists, however, the use of "s" opens a very elegant way to describe filter responses with poles in the complex s-plane. Here, the pole location can be described by two specific parameters (pole-Q and pole frequency), which appears also in the filter transfer function - if "s" instead of "omega" is used.
Regards
Lutz