Microwave Engineering : Introduction to Microwave Engineering and EM Wave Propagation

• Electric flux & enclosed charge
• Magnetic flux & enclosed charge
• EMF induced ∝ time varying magnetic flux
• DC current flow generates H.flux
• D=εE; B=μH; J=σE
• Behavior of EM fields/wave
• Static Electric field (char. capacitor)
• Static Magnetic field (magnet/DC ‘I’)
• E.field->M.field->E.field->.
• Potential function in charged region & free-space
• Force between charged particles
• Force between Magnetic  Poles
• Magnetic Potential function due to current distribution.
• Time varying fields/waves
• Linear resistor law
• Voltage and current law
• Linear reluctance law
• Magnetic flux & MMF laws
• Time harmonic fields/waves

Maxwell's Equation

• For Static fields (δ/δt=0) Maxwell’s equations are:
  • D = ρ
  • ∇•B = 0
  • ∇ × E = 0
  • ∇ × H = J
  • where, D = ε E and B = μ H (ρ, J are the charge, current Densities)
• For Time varying fields Maxwell’s equations are:
  • ∇•D = ρ
  • ∇•B = 0
  • ∇×E = -δB/δt
  • ∇ × H = J + δD/δt
  • Faraday's Law (∇ × E = – δB/δt) shows that time-varying magnetic field (δB/δt) is a source of the electric field (E).
  • Ampere’s Law (∇ × H = J + δD/δt) shows that both electric current (J) or time-varying E-field (δD/δt) are sources for the magnetic field (H).
• Thus, in the source-free region (ρ = 0 and J = 0), time-varying electric and magnetic fields can generate each other.
• Consequently, EM fields are self-sustaining, thus predicting the phenomenon of EM wave propagation.

Electromagnetic (EM) Signal spectrum

• Signal wavelength, λ=λ₀/√(ε_rμ_r);
• λ₀=c/f ; velocity, v = c /√(ε_rμ_r) and
• β = ω/v

RF/MW versus DC/Low – AC signals: MW Engineering

• In LF, mostly l<<λ, thus I & V are constant in line. (l = device length)
• In HF, mostly l >> λ, thus I & V are not constant in the line.
• Unwanted HF effects of component insulating-shell & wire-lead
• Current distribution within the conductor [Skin Depth, δ_s = √(2/ωμσ) and Surface resistance, Rs = 1/(δ_sσ) = √(ωμ/2σ)]

A few reasons for using RF/Microwaves

• Wider bandwidth due to higher frequency
• Smaller component size leading to smaller systems
• More available frequency spectrum with low interference.
• Better resolution for radars due to smaller wavelengths
• High antenna gain possible in a smaller space

Some Disadvantages in using RF/Microwaves

• More expensive components
• Existence of higher signal losses
• Use of high-speed semiconductor devices

RF/Microwave Applications

• Medical: Imaging, selective heating, sterilization etc.
• Domestic/industrial:  Cooking, traffic & toll management, sensor
• Surveillance: Electronic warfare, security system etc.
• Radar: Air defense, guided weapon, collision avoidance, weather
• Astronomy & Space exploration: Monitor and collect data.
• Communication: Satellite, Space, Long distance telephone, etc

Introduction to RF/Microwave Communication

• In 1960’s: Microwave was 1stused for wireless communication between Europe and America. It required repeater stations for approximately every 30 to 50 miles .
• In 1970~1980’s: Fiber-optic link was introduced and repeaters were used for approximately every 2000 miles.
• In 1990’s: Microwave Satellite links were introduced. The High-orbit and Low-orbit satellites were used since then.

Guided Transmission Media

• Coaxial TL : Low radiation, freq. range up to3GHz, support TEM mode
• Two-wire TL: Low radiation, freq. up to300 MHz, support TEM mode
• Waveguide: For high freq./power signals, Support TE/TMmodes.
• Microstrip: Losy, quasi-TEM modes, high bandwidth, easy integration
• Stripline: Less losy, TEM, high bandwidth, low power capacity, Fair’’

   

         

 

TEM: Electric & Magnetic field comparatively are perpendicular to each other and also to the direction of proportional.

More on guided Transmission Media

• Suspended-substrate stripline, easy for device integration.
• Slot line: very useful for specific applications.
• Coplanar line: Conductor and GND is in the same plane

 

 

Free space propagation (Plane Waves)

• Plane wavefronts (circular, spherical or rectangular plane)
• Uniform Plane wave; E & H fields are uniform in plane-wave-front.
• Plane Wave conditions; δE/δx = δE/δy = δH/δx = δH/δy= 0 (as prop in z-dir)
• The solution of Maxwell's equations for a uniform plane wave in source-free-region results in the expressions of E & H field intensities as: E_x = E_o e^(jωt-γz) = E_o cos(ωt-βz) OR H_y = H_o e^(jωt-γz) = H_o cos(ωt-βz) ; where E_o & H_o are E & H field magnitudes; γ= α+jβ= jω√εμ{as α=0}
• Plane waves in air/vacuum (ε_r = μ_r = 1); the phase constant βo=ω√εoμo; the intrinsic wave impedance ηo = Eo/Ho = √μo/εo = 377Ω{λo = 2π/βo = c/f}

Basic characteristics of the uniform plane wave in a source free region

• There is no E or H field component along the direction of proportional (z).
• Two pairs of the E & H fields {(E_x, H_y) OR (H_x, E_y)} produces two independent plane waves, which can exist and propagate by itself.
• E and H field components are always ⊥to each other; (E_x, H_y) or (H_x, E_y)
• Ratio of E and H field components are constant (intrinsic wave imp)
• If reflection of the wave occurs due to some obstacles in the propagating path.
• Standing wave is generated from the incident and reflected waves.

Polarization of waves

• Polarization of wave depends on magnitude and phase relationship between existing E-field components (E_x and E_y)
• Linear polarization occurs when E_x and/or E_y are in phase regardless of their relative magnitudes (direction of L.P. wave is the same as E-field)
• E-field of a L.P. EM wave: E(z,t) = [A a_x + B ay] cos(ωt -βz-φ)
• Circular polarization occurs when E_x & E_y are out of phase by 90° but both components have equal magnitude.
• E-fields of an L.P. EM wave are: E_x = A cos(ωt + f_y + π/2 + βz) and E_y = A cos(ωt + f_y + βz)
• Elliptical polarization occurs when E_x and E_y are out of phase by 90° and both components have different magnitudes.
• E-fields of E.P. wave: E_x = A cos(ωt+ f_y + π/2 + βz) and E_y = B cos(ωt + f_y + βz)
• Example: use a probe to measure E & H fields of L. polarized EM wave

EM wave propagation and attenuation

• Use two horn antennas, one connected with the source (mW power and 9GHz) and the other one is connected with a speaker (load). By moving the receiving Horns, we can show the power radiation pattern of the load (attenuation and main-lobe)
• Reflection of EM wave: Microwave reflects from metal plates with a reflected wave angle equal to the incident wave angle. This is due to the acceleration of the free electrons in the metal (caused by the incident EM wave), which in-turn produce an EM wave traveling away from the metal plate (called reflected EM wave). Since in a semiconductor material, a number of free electrons are less, less amount of reflection occurs and more incident EM wave is absorbed.
• Interference in EM wave propagation: The constructive and destructive interference in the receiver is shown (~height of the receiver)
• Guided EM wave propagation: In the rectangular waveguide: correct guide size is important for guiding EM waves properly.

Microwave Integrated Circuits (MICs)

 

Microwave Frequency bands Designation frequency range

• L-band 1 to 2 GHz
• S-band 2 to 4 GHz
• C-band 4 to 8 GHz
• X-band 8 to 12 GHz
• Ku-band 12 to 18 GHz
• K-band 18 to 26.5 GHz
• Ka-band 26.5 to 40 GHz
• Q-band 30 to 50 GHz
• U band 40 to 60 GHz
• V-band 50 to 75 GHz
• E-band 60 to 90 GHz
• W-band 75 to 110 GHz
• F-band 90 to 140 GHz and D band 110 to 170 GHz

Thanks.

Team Gradeup.