TY - CHAP
T1 - Simultaneous, multi-frequency, multi-beam antennas employing synchronous oscillator arrays
AU - Cothern, J.
AU - Heath, T.
AU - Hopkins, G.
AU - Kerr, R.
AU - Lie, D.
AU - Lopez, J.
AU - Meadows, B.
PY - 2009
Y1 - 2009
N2 - The theoretical foundations of coupled, nonlinear oscillator arrays as applied to beam forming have, almost exclusively, presumed the unit cells are well described by a Van der Pol oscillator model. In the past, a "weak" association was made between the spectral output of the differential-pair oscillator and that of an ideal Van der Pol oscillator. By applying the Method of Multiple Scales to the Van der Pol dynamical equations, one finds that only odd order harmonics are present. Moreover, one can determine the key Van der Pol parameters (i.e., the amplitude parameter, p, and nonlinearity parameter, μ) through the power contained in the first and third harmonics.
AB - The theoretical foundations of coupled, nonlinear oscillator arrays as applied to beam forming have, almost exclusively, presumed the unit cells are well described by a Van der Pol oscillator model. In the past, a "weak" association was made between the spectral output of the differential-pair oscillator and that of an ideal Van der Pol oscillator. By applying the Method of Multiple Scales to the Van der Pol dynamical equations, one finds that only odd order harmonics are present. Moreover, one can determine the key Van der Pol parameters (i.e., the amplitude parameter, p, and nonlinearity parameter, μ) through the power contained in the first and third harmonics.
UR - http://www.scopus.com/inward/record.url?scp=62849122554&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-85632-0_33
DO - 10.1007/978-3-540-85632-0_33
M3 - Chapter
AN - SCOPUS:62849122554
SN - 9783540856313
T3 - Understanding Complex Systems
SP - 395
EP - 401
BT - Applications of Nonlinear Dynamics
ER -