Here is the magnitude plot for a system.
*****INSERT FIGURE
vCan you determine what the transfer function is
       for this system?

vWARNING:  This is a trick question!

       It is very tempting to make the following claims.

vThe system has zero db gain at DC.
       You can't deny that.

vThe system is 3 db down at f = 159 Hz.

vThat 3db point implies a corner frequency
       of 159 Hz

       or w = 1000 rad/sec.

vSo the transfer function is:

              G(jw) = 1/(jwt + 1)

                or G(s) = 1/(st + 1)

       How could these conclusions be wrong?

vYou are making an assumption that the phase plot looks like the one we saw earlier - the one shown here.
*****INSERT FIGURE
vThe actual phase plot does not look like this one.

vHere is the actual phase plot.
*****INSERT FIGURE
vThe phase starts at 0^o at low frequencies.

vThe phase goes to -270^o at high frequencies.

Whoa!

vThe phase is -135^o at a frequency of 159 Hz - the corner frequency.

How can that be?

        Looking at the phase plot, you are surely tempted to believe that there are three poles in the system because the phase goes to -270^o at high frequencies. So let's examine the magnitude plot again.

vIf there are three poles in the system,
       then it should drop off at -60 db/decade
       at high frequencies.

vIt doesn't! It falls off at -20 db/decade.
       What's happening? Can you imagine
       a transfer function with these properties?

        Here's the transfer function that we have been using to befuddle you.

vIt has a zero in the right half plane. We haven't emphasized that possibility.

vIt is the transfer function for a stable system, so it's not something totally off the

wall.

vThe transfer function has two factors that always act to give unity gain - but with

phase shift. Here are the two factors.

        Consider this claim about this form.

vThe magnitude of the numerator and denominator of these two factors always

have the same magnitude.

vConsider: | -.001jw + 1| = | .001jw + 1|

since, when s = jw, the numerator and denominator are complex conjugates!

vOn the other hand, the angles are equal but of opposite sign, so they add up when

one is in the denominator and the other is in the numerator.

vThat's how you can get an extra 180^o into the phase shift and get the phase plot we have.

        Is it possible to build systems like this. The answer is "You betcha!". There are some simple operational amplifier circuits that you can use to build a system with a zero in the right half of the s-plane - if you want to build a system with that property.

This kind of system - not limited to, but including systems with right half plane zeroes - is called a non-minimum phase system. Systems with time delays - which do not actually have zeroes in the right half plane - are non-minimum phase, and they appear often in real physical situations. Finite order models of time delay systems often use models with right half plane zeroes.