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i1
i2
Inductor
Capacitor
Partial differential equations
Recall the wave equation
from Physics 231?
v=f(z-vpt) is the general solution
to this lossless, dispersionless
wave equation.
Run the extra mile: Prove this.
The shape v=f(z-vpt) will propagate
i.e. translate, as long as the medium
is lossless and dispersionless.
(6/E)
pp. 54 in 7/E
(if the excitation is single-frequency)
(arbitrarily take phase as 0 w/o loss of generality)
+φ0+
+φ0
-
Complex numbers, including phase information
V0+ =|V0+ |e j φ0
+
with
Ordinary differential equation
Again, complex numbers, including phase information
z
From circuit,
z
explicitly frequency dependent
no explicit frequency dependence
1+Γ
1−Γ
Z0
One-to-one mapping between gamma and impedance.
ZL
=
The
implication
of this is ...
See Wikipedia Standing Wave
https://en.wikipedia.org/wiki/Standing_wave