It means; at that perticular frequency the output is zero even the input is present. To make the better undertanding, think of small signal model where the output current going to load and coming out of load is equal and finaaly current valus eis zero.
thanks
-Bharat

Bharat,
H(s) = 1 + as
H(-1/a) = 1 - 1 = 0

When you evaluate these s-domain functions, you have to fill in the actual s-value and then take the magnitude.

In the attached plot, there is a a zero at s = -4.  i.e., H(s) = 1 + s/4  

The point s=-4 does go to zero, but the slice of this 3d plot along the imag axis is what we look at for the frequency response, as just recently discussed in another post.

Hope this helps!

That plot didn't get saved so well...

Here is the Matlab code (I found on the web) which you can modify to plot whatever.  Modify the num and den vector...these are the transfer function co-efficients.

%      Figure 3.2
%      
%      BM Mar 98

clear
clf
colordef(1,'black')

rx = -5:0.1:5;
ix = -5:0.1:5;
[rrx,iix] = meshgrid(rx,ix);
xx = rrx + j*iix;

num = [0.25 1];
den = [ 1 ];
z = zeros(size(xx));
nn = max(size(rx));
for jj = 1:nn
     z(:,jj) = polyval(num,xx(:,jj))./polyval(den,xx(:,jj));
end
h = surf(rx,ix,20*log10(abs(z)));hold
plot3([-1 -1 ],[ -2 -2 ],[-30 10 ])
plot3([-1 -1 ],[ 2 2 ], [ -30 10 ])

xlabel('real')
ylabel('imag')
zlabel('magnitude (dB)')
view([50,40]);
fprintf(1,'Figure 3.2: press return to rotate\n')
pause

rotvec = 50:5:90;
ss = max(size(rotvec));
step = 30/(ss-1);
hvec = 40:-step:10;
for ii = 1:length(rotvec)
     set(gca,'View',[rotvec(ii) hvec(ii)] )
     drawnow
     pause(2);
     end

A zero represents differentiation of the input signal, while a pole integrates it. From a control theory perspective, a zero makes for a 'PD' controller which, like the proverbial hare, responds fast but with steady state error. OTOH a pole corresponds to a 'PI' controller that, like the tortoise, is slow to get there but does so with zero steady state error.

Here's a physical picture: say you're designing an elevator for a high rise building. You leverage a zero to get quick response but it won't do for the elevator to stop three feet short of the opening to a particular floor. Likewise you use poles for a slow but precise 'Driving Miss Daisy' ride that will align the door to the opening with millimetric precision (and leave passengers wishing they'd taken the stairs). The golden mean corresponds to a balance between haste and precision - it's called a PID controller and is non-trivial to design.

Non-linear circuits can be very different. A flip-flop regenerating its own input is like a snake chasing its tail. The unstable transient response takes off like a rocket, reaching steady state nirvana by saturating against one of the rails. If you design fighter aircraft you want 'em to whip around like that, but also not spin out of control or make Top Gun pass out. So you do an elaborate balance of linear and non-linear control. Even PID design is kid stuff compared to non-linear aircraft control amidst turbulence and countermeasures.

M.G.Rajan
www.eecalc.com

Croaker, you are right about the phase difference between right and left half zeros. The RHP zero is kinda funny - for a step input it tries to cancel the proportional term with a negative going impulse. That means the rise time will increase, so it actually behaves like a pole!? This intuition is borne out mathematically, since for small s

1/(1+αs) ≈ 1 - αs

One place we naturally come across a RHP zero is the (g_m - sC_μ) term in the numerator of the collector/drain voltage gain transfer functions derived from the hybrid-Pi small signal model of transistors. You can derive it using the following circuit for a common-emitter amplifier (Spice netlist in lieu of a diagram).

vs 1 0 ac
cpi 1 0 {small or zero}  *doesn't matter since it's charged neat by an ideal voltage source
cmu 1 2 cmu
g 2 0 1 0 gm
rl 2 0 rl

The physical significance of this zero is that even with the base/gate driven with zero source or contact resistance (R_s, r_bb etc = 0) the displacement current through the drain-gate capacitance acts like an inertia. Kind of trying to cause an 'fT effect' if you will.

M.G.Rajan
www.eecalc.com

mg777 wrote on Jan 19^th, 2007, 2:31pm:


Are you sure about that?  The transit time is related to the diffusion capacitance of a BJT.  Cb = gm * τ...maybe you are confusing Cb with Cu.  

Unless  you're relating the change in base charge over the change in base-collector voltage to transit time in a way I don't see.

I don't understand what you mean by an inertia and fT effect.

In my mind, the main problem with that zero in the CS amp is that it makes the phase margin worse if not dealt with somehow.

mg777 wrote on Jan 19^th, 2007, 2:25pm:


Rajan,

Could you please elaborate more into this?

Regards,