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Measurement Methods and Instruments for Microwave Frequencies

  • Chapter
Electrical Instruments / Elektrische Instrumente

Part of the book series: Encyclopedia of Physics / Handbuch der Physik ((PHYSIK 4,volume 4 / 23))

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Abstract

Microwaves are one form of electromagnetic radiation — that is, a wave motion associated with electric and magnetic fields — the known spectrum of which is shown in Fig. 1. Here, frequency is plotted as abscissa and free-space wavelength as ordinates, while, for future reference, the energy and equivalent temperature of corresponding photons are also included. Microwaves occupy a unique place in this spectrum because they are, as a rule, susceptibie to electrical, as distinct from purely optical, treatment, whilst requiring techniques [1] that differ completely from those used at lower, conventional radio, frequencies. This radiation is coherent, having a clearly defined frequency and spatial distribution of phase and polarization. In this respect, the field of microwave techniques has recently been extended into the infrared and visible regions and some consideration will also be given to this work.

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Abbreviations

a :

Resonant width of rectangular waveguide, m

A :

Area, m2

A e :

Effective area of antenna = (g P λ 2 /4π) m2

B :

Depth of rectangular waveguide, m

B :

Magnetic flux density = μμ 0 H webers /m2

B :

Susceptance, mhos

C :

Speed of light in vacuo = \( {\left( {{\varepsilon _0}{\mu _0}} \right)^{ - \frac{1}{2}}} \) = 2.997925 × 108m/sec

C :

Specific heat, joules/kg-deg

d :

Diameter, m

d :

Subscript denoting dielectric

D :

Distance, m

D :

Electric flux density = εε 0 E coulombs/m2

e :

Magnitude of negative charge on electron = 1.60207 × 10-19 coulomb

E :

Electric field strength, volts/m

g :

Gravitational acceleration = 9.81259 m/sec2

g :

Gain of radiator relative to an isotropic source

g e :

Free-electron g-factor= 2.002 29

G :

Conductance, mhos

G :

Gravitational constant = 6.670 × 10-11 m3/kg-sec2

h :

Planck’s constant = 6.625 17 × 10-34 joule-sec = 2π ħ

H :

Magnetic field strength, amp/m

I :

Electric current, amp

j:

Complex operator \( \sqrt { - 1} \)

J n :

Bessel function of first kind and n-th order

J :

Current density, amp/m2

k :

Boltzmann’s constant = 1.38044 × 10-23 joule/deg

l :

Length, m

L :

Numerical power insertion loss = P in /P out

L :

Self-inductance, henries

M :

Intensity of magnetization, webers/m2

n :

Refractive index = \( \sqrt {\varepsilon \mu } \) =n-jx

N :

Density of particles, m-3

p :

Pitch of periodic structure, m

P :

Subscript for power

P :

Power, watts

P :

Electric polarization, coulombs/m2

Q :

Quantity of heat, joules

Q :

Q-factor of resonant circuit

Q l :

Loaded Q-factor

Q m :

Magnetic Q-factor

Q u :

Unloaded Q-factor

r :

Subscript denoting resonance value

r :

Radius, m

r i :

Radius of inner conductor, m

r o :

Radius of outer conductor, m

r f :

Subscript denoting peak r.f. value

R :

Resistance, ohms;

Re:

Real part of;

R H :

Hall coefficient, volt-m3/ampere-weber;

S :

Poynting’s vector = \( \frac{1}{2}\left( {{E_{rf}} \times H_{rf}^*} \right) \) watts/m2;

S :

Voltage standing-wave ratio |V max|/|V min|>1;

t :

Time, sec

T :

Torque, newton-m

T :

Absolute temperature, deg K

T 0 :

Room temperature ≡(4/k) × 10-21 ≃ 290° K

U :

Volume density of electromagnetic energy = \( \frac{1}{4}\left( {D \cdot E* + B \cdot H*} \right) \) joules/m3

v :

Velocity, m/sec

v g :

Group velocity of wave= (dω/dβ) m/sec

v p :

Phase velocity of wave = (ω/β) m/sec

V :

Potential difference or voltage, volts

V :

Subscript denoting voltage

V :

Volume, m3

W :

Energy, joules

Y :

Admittance = (G + j B) mhos

Y 0 :

Characteristic admittance, mhos

Z :

Impedance =(R +j X) ohms

Z ω :

Intrinsic impedance of free space = \( \sqrt {\left( {{\mu _0}{\varepsilon _0}} \right)} \simeq 376.7304 \) ohms

Z0 :

Characteristic impedance, ohms

α :

Attenuation coefficient, nepers/m

β :

Phase-change coefficient = (2π/λ)

β g :

Coupling parameter of resonant cavity

γ :

Propagation coefficient =α + jβ

γ e :

Magnitude of magnetogyric ratio of electron µ 0 g e e/2m≃2Π×3.5218×104 sec-1(amp/m)-1

δ :

Dielectric loss angle = arc tan (ε”/ε’)

δ s :

Skin depth in a metal = \( \sqrt {\left( {{2 \mathord{\left/ {\vphantom {2 {\omega \mu {\mu _0}\sigma }}} \right. \kern-\nulldelimiterspace} {\omega \mu {\mu _0}\sigma }}} \right)} \) m

Δv :

Half-width of spectral line (from centre to half-power), c/s

Ε :

Relative permittivity = ε’ - j ε”

ε 0 :

Electric space constant = (μ 0 c2)-1 ≃ 8.854 16 × 10-12 farad/m

η :

Efficiency

η A :

Efficiency of antenna = A e /A

ϑ :

Relative temperature, deg K

ϰ :

Absorption index = α λ 0/2π

λ :

Wavelength, m

λ g :

Wavelength in waveguide, m

λ 0 :

Free-space wavelength, m

μ :

Relative permeability = μ’ - j μ’’

μ :

Drift mobility of carriers, m2/volt-sec

μ B :

Bohr’s magneton = μ 0 eh/2m 0 = 1.16 5 29 × 10-29 weber-m

υ :

Frequency, c/s

υ :

Subscript denoting value in 1-c/s interval

υ b :

Total bandwidth to half-power, c/s

υ c :

Collision frequency, c/s

v C :

Cyclotron frequency -eB 0 /2πm

υ p :

Plasma frequency = \( \left( {\frac{1}{2}\pi } \right)\sqrt {\left( {{{N{e^2}} \mathord{\left/ {\vphantom {{N{e^2}} {m\varepsilon {\varepsilon _0}}}} \right. \kern-\nulldelimiterspace} {m\varepsilon {\varepsilon _0}}}} \right)} \) c/s

ϱ :

Volume charge density=N e coulombs/m3

ϱ :

Reflection factor

σ :

Scattering cross section, m2

σ :

Conductivity = σ’ - j σ” mhos/m

τ :

Relaxation time

τ :

Transmission factor

τ 1 :

Spin-lattice relaxation time, sec

Φ :

Magnetic flux, webers

Φ :

Gravitational potential

χ :

Susceptibility = χ’ - j χ”

ω :

Angular frequency = 2 n v rad/sec

ω :

Angular velocity, rad/sec

ω C :

Cyclotron angular frequency = e B 0 /m rad/sec

o:

Subscript denoting d.c, static, or steady

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Harvey, A.F. (1967). Measurement Methods and Instruments for Microwave Frequencies. In: Pannenborg, A.E. (eds) Electrical Instruments / Elektrische Instrumente. Encyclopedia of Physics / Handbuch der Physik, vol 4 / 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46071-5_2

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