fundamentals of engineering supplied-reference handbook - Ventech!

AC Machines
The synchronous speed ns for ac motors is given by
ns = 120f/p, where
f = the line voltage frequency in Hz and
p = the number of poles.
The slip for an induction motor is
slip = (ns – n)/ns, where
n = the rotational speed (rpm).
DC Machines
The armature circuit of a dc machine is approximated by a
series connection of the armature resistance Ra, the armature
inductance La, and a dependent voltage source of value
Va = Kanφ volts, where
Ka = constant depending on the design,
n = is armature speed in rpm, and
φ = the magnetic flux generated by the field.
The field circuit is approximated by the field resistance Rf in
series with the field inductance Lf. Neglecting saturation, the
magnetic flux generated by the field current If is
φ = Kf If webers
The mechanical power generated by the armature is
Pm = VaIa watts
where Ia is the armature current. The mechanical torque
produced is
Tm = (60/2π)KaφIa newton-meters.
ELECTROMAGNETIC DYNAMIC FIELDS
The integral and point form of Maxwell's equations are
� ∫ E ·dl = – ∫∫S (∂B/∂t)·dS
� ∫ H ·dl = Ienc + ∫∫S (∂D/∂t)·dS
∫∫
∫∫
SV
SV
D ⋅ dS
= ∫∫∫ ρ dv V
B ⋅ dS
= 0
∇×E = – ∂B/∂t
∇×H = J + ∂D/∂t
∇·D = ρ
∇·B = 0
The sinusoidal wave equation in E for an isotropic homogeneous
medium is given by
∇ 2 E = – ω 2 µεE
The EM energy flow of a volume V enclosed by the surface
SV can be expressed in terms of the Poynting's Theorem
− ∫∫
S
V
( × H)
E ⋅ dS = ∫∫∫V J·E dv
+ ∂/∂t{∫∫∫V (εE 2 /2 + µH 2 /2) dv}
172
ELECTRICAL AND COMPUTER ENGINEERING (continued)
where the left-side term represents the energy flow per unit
time or power flow into the volume V, whereas the J·E
represents the loss in V and the last term represents the rate
of change of the energy stored in the E and H fields.
LOSSLESS TRANSMISSION LINES
The wavelength, λ, of a sinusoidal signal is defined as the
distance the signal will travel in one period.
U
λ =
f
where U is the velocity of propagation and f is the frequency
of the sinusoid.
The characteristic impedance, Z0, of a transmission line is
the input impedance of an infinite length of the line and is
given by
Z
0
=
L C
where L and C are the per unit length inductance and
capacitance of the line.
The reflection coefficient at the load is defined as
ZL−Z0 Γ=
ZL+ Z 0
and the standing wave ratio SWR is
1+
Γ
SWR =
1−
Γ
2 π
β = Propagation constant =
λ
For sinusoidal voltages and currents:
Voltage across the transmission line:
V(d) = V + e jβd + V – e –jβd
Current along the transmission line:
I(d) = I + e jβd + I – e –jβd
where I + = V + /Z0 and I – = –V – /Z0
Input impedance at d
ZL+ jZ0tan βd
Zin ( d ) = Z0 Z + jZ tan βd
+
–
0
L
0
( )
( )