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- 7-5 Electromagnetic Boundary Conditions
- E1tE2t, always.
- B1nB2n, always.
- For PEC, the conductor side H20, E20.

(7.66a)

(7.66b)

(7.66c)

(7.66d)

(7.68)

- 7-6 Wave Equations and Time-Domain Solutions
- Retarded scalar and vector potentials are the

solution - to the non-homogeneous wave equation (7-65) and

(7-63), - respectively
- where is the propagation velocity,

and

(7.77)

(7.78)

- In contrast to the static case of instantaneous
- response of
- The wave nature of (7.77) and (7.78) shows the
- retarded response to the source.

(3-61)

(6-23)

- 7-6.2 Source-Free Wave Equations
- In a region, where ,

Maxwells equations - becomes

(7.79a)

(7.79b)

(7.79c)

(7.79d)

- Taking both sides on (7.79a),
- Hence,
- In the same fashion,

(7.80)

(7.82)

- 7-7 Time-Harmonic Fields
- 7-7.1 Phasors
- Phasor (frequency domain) converts the ordinary

differential equations (ODEs) into algebraic

equations. - Let I(t)I(w)cos(wtj) where I is the magnitude,

w2pf. - Circuit
- where e(t) E cos wt is the electromotive force

(emf). - In the phasor form (taking the Fourier

transform), - or

(7.84)

(7.91)

- Example 7-6 Convert a time domain expression
- into the phasor form (complex exponential)
- Solution
- In comparison with (7.92a),
- Therefore,

(7.92a)

- The complex form
- And the phasor form, after dropping the time

conversion ejwt is

- Rules
- From phasor to time-domain
- From time-domain to phasor
- See the example
- 3. Similar to the Laplace transform

- 7-7.2 Time-Harmonic Electromagnetics
- Using the rule
- We have the Maxwells equations in phasor form

as - The Lorentz gauge

(7.94)

(7.98)

- The nonhomogeneous wave equations
- where
- The wavenumber
- The phasor solutions

(7.95)

(7.96)

(7.97)

(7.99)

(7.100)

- Note
- Wavenumber

(7.102)