Page 181 - Electrical Engineering Dictionary

A(i), B(i), Q(i), R(i) are, respectively, sys- most common types are termed fused taper
temandweighting, stateandinputmatricesin and dichroic.
the mode i, and q ij is the transition rate from (2) a device inserted into an optical fiber
mode i to j. If the system is stochastically communications link that is used to insert ad-
√
stabilizable and the pairs (A(i), Q(i)) are ditionaloptical energy or signalsontothe link
√
observable for all i where Q(i) = C(i) and/or tap off some of the energy or signal
0
such that C(i) C(i) = Q(i), then the solu- on the link to another optical fiber. A cou-
tion K(i, t) is finite for each i and pler may also be used to combine power from
two or more input fibers into one output fiber
ˆ
lim K(i, t) = K(i) or to distribute the combined input power to a
T −t→∞
number of output fibers. Couplers are made
ˆ
where K(i) is the set of solutions to the cou- in1×N, N×N, andN×M (input)×(output)
pled algebraic Riccati equations: configurations where N and M are the num-
s ber of fibers. The power combining and/or
X
0 ˆ ˆ ˆ splitting ratios can vary from 50%/50% (a 3
A(i) K(i) + K(i)A(i) + q ij K(j)
dB coupler) in a symmetric 2 × 2 coupler to
j=1
> 99%/< 1% in an asymmetric coupler.
0
+ Q(i) − K(i)B(i)R(i) −1 B(i) K(i) = 0
ˆ
ˆ
coupling capacitor voltage transformer
Coupled Riccati equations are also used in
(CCVT) a potential transformer that uses
N-person linear quadratic games. In this
the impedance of a small capacitance to re-
case i = 1, 2,...,N is the number of the
duce the power line voltage to measureable
player and the set of coupled differential ma-
levels.
trix equations has the following form:
0
K(i, t) + A K(i, t) + K(i, t)A + Q(i) coupling factor in a coupler, the ratio of
˙
power in the coupled port to that applied at
j=N
X
0
− K(i, t) BR(j) −1 B K(j, t) = 0 the input port.
j=1
coupling efficiency the efficiency to
for i ∈{1, 2,...,N}, t ∈[0,T ] and termi- which a signal can be coupled from one trans-
nal condition K(i, T ) = 0 where A, B are, mission line or resonator to another.
respectively, state and input matrices in the
state equation, Q(i), R(i) are weighting state coupling field a region of interaction
and input matrices for the i-th player, and its where energy is transferred between systems.
solution defines the gain in a Nash equilib- The energy may be transferred between sys-
rium in the game. tems of a similar nature (i.e., electrical–
electrical) or between systems of a different
coupled wave equations a special case nature (i.e., electrical–mechanical).
of Maxwell’s equations describing the prop-
agation of two interacting electromagnetic coupling loss measure of the power dis-
fields in a nonlinear material. For example, sipated as a result of coupling a signal from
in four wave mixing or optical phase conju- one transmission line or resonator to another.
gation, the probe and conjugate fields often
obey coupled wave equations. covariance Theexpectationoftheproduct
of two mean-removed random quantities:
coupler (1) a passive, wavelength-
h i
insensitive, fiber optic component that com- T
C fg (t 1 ,t 2 ) = E f(t 1 )g(t 2 )
bines all inputs and distributes them to the
T
outputs with a defined splitting ratio. The − E[f(t 1 )]E[g(t 2 ) ].

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2000 by CRC Press LLC