Intrinsic impedance of a medium

Question

I am trying to understand what the intrinsic impedance of a medium means. I understand the mathematical definition of it, but it doesn't speak much about the concept to me. What does intrinsic impedance mean conceptually? All I understand is that the electric field intensity is going to be much higher than the magnetic field intensity if the intrinsic impedance is high. Do conductors have higher or lower intrinsic impedance than lossless dielectric? My guess is that at high frequency, conductors have high intrinsic impedance whereas lossless dielectrics have high intrinsic impedance at low frequency, and vise versa. Am I correct on this?

Also, why is the wave impedance called "impedance"? From what I know, it is merely a ratio between an electric field intensity and a magnetic field intensity. It says nothing about the material's ability to "impede" something. Is it a misnomer?

Answer 1

For all practical purposes when a medium can sustain a TEM (transverse electromagnetic) wave then the wave impedance is the ratio of the corresponding electric and magnetic field components, that is $\mathcal Z_0 = \frac {E_x}{H_x}=\frac{E_y}{H_y}$ where I assume that wave front is in the $xy$ plane. In free space and using MKS SI units $\mathcal Z_0 = \sqrt{\frac{\mu_0}{\epsilon_0}}=120\pi [\rm{\Omega}] $. In linear material medium characterized by permittivity and permeability $\mathcal Z_m = \sqrt{\frac{\mu_r\mu_0}{\epsilon_r\epsilon_0}}$

The concept can be extended to a waveguide filled with a linear medium. For TEM wave to exist the waveguide must have at least two conductors and is important that the medium fill the guide completely and uniformly. The presence of metal will change the ratio $E/H$ from $\mathcal Z_m$ that is dependent on the medium only to something that represents the ratio of the inductance per unit length and capacitance per unit length within the medium.

In general, one can define impedance parameters for other propagating waveguide modes, such as TE or TM. The corresponding impedances are related to the transmission line representation of the waveguide propagation; this has mostly theoretical use. Instead, one uses scattering matrix $\mathbf S$ with which if desired one can associate an impedance matrix $\mathbf Z= (\mathbf I +\mathbf S)(\mathbf I -\mathbf S)^{-1}$. Unlike impedance the scattering parameters *always* exist and finite, and one can measure them directly. In fact, at microwaves one always measures the scattering parameters and never that of impedance.

(Impedance means something that impedes, here current being impeded at a given voltage, but its historical origin have no import in practice.)

Answer 2

Also, why is the wave impedance called "impedance"? From what I know, it is merely a ratio between an electric field intensity and a magnetic field intensity. It says nothing about the material's ability to "impede" something. Is it a misnomer?

Historically, the concept of characteristic impedance (or intrinsic impedance) was first invented in the context of transmission line theory. Originally, transmission lines were just electric cables. For an infinite and lossless transmission line, its characteristic impedance is given by:

$$ Z_0 = {V \over I} = \sqrt{L \over C} $$

It's named "impedance" because it's a ratio between voltage and current, in other words, a literal electrical impedance. Since voltage and current are physical quantities that can be directly measured in a cable, this definition is used as it's both straightforward and practical.

Later, waveguides were invented and used as transmission lines, too. Since the transmission and reflection of electromagnetic waves still take place in waveguide, a definition of "impedance" would be extremely useful. However, unlike cables, voltage waves and current flows don't always exist. Thus, the characteristic impedance of a waveguide is defined as:

$$ Z_0 = {E_x \over H_y} $$

Rather than a ratio of voltage and current, it's now a ratio between electric and magnetic field. In this context, it's usually known as "wave impedance", as this impedance is frequency-dependent for non-TEM waves.

In TEM mode when the electric and magnetic fields are perfectly orthogonal:

$$ Z_0 = {E_x \over H_y} = \sqrt{\mu \over \epsilon} $$

Similarly, rather than a ratio between the square root of inductance and capacitance, it's now a ratio between permeability and permittivity.

Since it's possible to define an "impedance" in terms of E&M fields in waveguides, from here, it's natural to generalize the concept of characteristic impedance further to unguided E&M waves in vacuum itself and different mediums. This is the motivation behind the concept of "intrinsic impedance" (at least from a microwave engineering perspective). It's also possible to define this generalization experimentally - loosely speaking, the impedance of free space can be defined to be the wave impedance of an open-ended waveguide, if pointed to free space, does not reflect electromagnetic waves back to the source.

Thus, one can say the origin of the term "intrinsic impedance" came from the generalization of a concept on electrical impedance in transmission line theory from cables to waveguide, and later to vacuum and mediums. The roles of electric and magnetic fields are seen as analogues to voltages and currents in cables.