phf-nrwf-dgo (2020-09-25 at 03_41 GMT-7)

Chapter 1: Introduction

  • Lossy Media

    • In lossy media, complex permittivity ((\epsilon_{rc})) replaces relative permittivity ((\epsilon_r)) to indicate loss.

    • Loss tangent characterizes material loss.

  • Lossy Dielectric Behavior

    • A very lossy dielectric behaves similarly to a good conductor.

    • The ratio of conductivity ((\sigma)) to angular frequency ((\omega)) is large in lossy materials, leading to a significant impact on wave propagation.

  • Propagation Constant

    • The propagation constant ((\gamma)) includes attenuation and phase constants.

    • For lossy materials:

      • (\gamma \approx \sqrt{j\omega \mu \sigma / 2}) when (\sigma / (\omega \epsilon_0 \epsilon_r)) is large.

  • Power Attenuation

    • Power attenuates as (e^{-\alpha z}).

    • At infinity, power approaches zero in lossy media.

    • A wave is considered to have entered the medium at a distance where power drops to 37% of its original value ((\alpha z = 1)).

    • Skin depth ((\delta)) is defined as (1/\alpha).

Chapter 2: Finite Power

  • Skin Depth

    • Skin depth is the distance where power significantly decreases in conductors, denoted as (\delta).

    • Common rule: Power remains finite up to roughly 5 skin depths.

  • High Conductivity

    • In good conductors, skin depth approaches zero. Electromagnetic fields do not penetrate conductive materials.

    • High-frequency effects result in current flowing along the surface (skin effect).

Chapter 3: Power Calculations

  • Power Density

    • Power carried by a wave can be characterized by the vector identity involving electric field ((E)) and magnetic field ((H)).

  • Integrating Power

    • Integrating the expression over a volume gives total power carried by the wave, accounting for both propagated and lost power.

Chapter 4: Real Power Flow

  • Poynting Vector

    • Poynting vector ((\mathbf{S} = \mathbf{E} \times \mathbf{H})) represents power density.

    • Indicates both power density and direction of power flow.

  • Direction of Power Flow

    • Power flows in the direction indicated by the Poynting vector.

Chapter 5: Average Power

  • Instantaneous vs Average Power Density

    • Instantaneous power density includes time-varying components; average power density is calculated over a wave period.

  • Special Case for TEM Waves

    • Average power density formulated using fields leads to expressions similar to circuit theory (e.g., ( \frac{1}{2} \frac{E^2}{\eta} )).

Chapter 6: Poynting Vector Direction

  • Power Flow in Circuits

    • Power flows externally between conductors; voltages and currents emerge as byproducts of electromagnetic field interactions.

Chapter 7: Conclusion

  • Summary of Key Concepts

    • Power does not flow through conductors but rather between them, highlighting the importance of dielectric properties.

    • The field dynamics and propagation contribute to understanding real-world electromagnetic applications.