Understanding the LHP zero?

I started to use LHP zero with the basic miller compensation including a capacitor and a resistor in series to build a left half plane zero for good stability.

From the theory, zero makes the transfer function to zero value, and zero produces +20db gain and positive or negative 90 degree phase shift.

But somehow I can't correspond and understand the theory with the practice together on the zero. For example, how do feedback signals in the time domain change with positive or negative zero.

I also get to know that two paths with the same phase in parallel can generate a LHP zero, if the compensation path has higher gain or faster than the main path.
Could someone also explain this?

Thanks a lot!

Hi thomas,

From the theory, zero makes the transfer function to zero value, and zero produces +20db gain and positive or negative 90 degree phase shift.

I think, your understanding of the meaning of the complex frequency variable s is not yet good enough - and the difference to the real-world frequency w (omega). Remember: The transfer function H(s) turns into the so called frequency response H(jw) if you replace s by jw.
You are right the transfer function H(s) can go to zero for a certain value of s. For example, think of a simple highpass of 2nd order. Buth this does not mean that you can measure zero volts with a function generator. The zero is located in the left hand part of the complex plane. Only if the zero is placed directly on the jw axis it is identical to a "real" zero because H(jw)=0.
Secondly, a complex zero does not "produce" a gain of +20 dB.( It produces a slope increase in the BODE plot that has an asymptote of +20 dB/decade.) Correction: It produces a slope change in the bode plot by an asymptotic value of +20 dB/decade.

LHP zero contributes 90 degree phase increase while RHP zero leads to 90 degree phase decrease.

leo_o2 said:

LHP zero contributes 90 degree phase increase while RHP zero leads to 90 degree phase decrease.

Click to expand...

....phase increase as far as the asymptotic behaviour is concerned.
For example, the zero of a PD-T1 controller (lead-lag) may enhance the phase as much as 10 or 20 deg only.

LvW,
Do you mean it is influenced by other pole?
I didn't understand. Please explain more.
Thanks.

leo_o2 said:

LvW,
Do you mean it is influenced by other pole?
I didn't understand. Please explain more.
Thanks.

Click to expand...

OK, best explanation with an example:
PD-T1 controller: H(s)=Ho(1+sT1)/(1+sT2) with T1>T2 (that means: zero<pole).
For very low and very high frequencies the phase approaches 0 deg.
In between (above zero but below the pole frequency) the phase goes to positive values due to the zero influence , but never reaches +90 deg. (due to the beginning pole influence). The maximum pos. phase excursion (perhaps 10, 20, 30 deg) depends on the distance between the zero and the pole.
In the BODE diagram the gain and phase response can be easily approximated by some asymptotes. And - as far as the phase is concerned - one of these asymptotes is constant at +90 deg. However, as mentioned before, the actual phase never reaches this value.

I understand your meaning. Maybe my description is not strict.
Thanks.