Laplace Transform 4.

Cuthbert Nyack

Pole Location

Transfer Function

Pole locations and transfer function for a system with 2 pairs of complex conjugate poles at a +- jb and c +- jd are shown above.

Surface Plot of Magnitude of 4 poles


If you have Netscape 3.01 or other browser with a VRML viewer, then a 3-d view of the magnitude, phase, real and imaginary parts of the Laplace Transform of a system with 4 poles can be seen by clicking on one of the links below. The values at the poles do go to infinity, but have been truncated for convenience. The +ve imag axis coincides with the +ve z-axis in the usual vrml coordinate system.
MAGNITUDE
PHASE
REAL
IMAGINARY

Impulse and Step Response for a system with 2 pairs of complex conjugate poles



Poles are at a + jb, a - jb, c + jd and c - jd. Horizontal axis is 0 to 8pi when hgain = 1. Vertical axis is 0 to 2 for step response and -1 to +1 for impulse response. Impulse response is in red and step response in orange.

Frequency Response for a system with 2 pairs of complex conjugate poles



Horizontal is 0 to 8rad/s when hgain = 1. Vertical axis for phase is -2p to +2p and 0 to 2 for magnitude when vgain is 1. Magnitude is red and Phase is green.
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Copyright 1996 Cuthbert A. Nyack.