Strip Lines
15
STRIP LINES
description
strip lines-transmission lines for microwave
Transcript of Strip Lines
STRIP LINES
Microwave transmission lines
• Coaxial cables
• Waveguides
• Striplines
– Microstrip lines
– Parallel strip-lines
– Coplanar strip lines
– Shielded strip lines
Microstrip lines
•Microwave solid-state device can be easily fabricated as a semiconducting chip•Very less volume of the order of 0.008-0.08mm3
•Mode of transmission-quasi TEM, hence the theory of TEM-coupled lines is approximated.
Deriving Zo of microstrip lines
Comparison method
Comparing with a wire over ground,
For a wire over ground,
Changes for microstrip lines,The effective permittivity will be
Other relation will be t/w<0.8
[derived by Assadourian]
The velocity of propagation of microwaves in microstrips,
Propagation time constant is,𝑇𝑑 = μ ϵ
=3.333 ϵ𝑟 𝑛𝑠/𝑚
LOSSES IN MICROSTRIP LINES• Ohmic Losses• Dielectric Losses• Radiation Losses
Typically, Zo is in between 50Ω to 150Ω
Power losses in Microstrips
• The power carried by a wave travelling in z direction is given by
• The attenuation constant α can be expressed as
• Power dissipation per unit length can be calculated as
• Hence,
Dielectric loss
from first unit,
Attenuation constant, ∝=σ
2
μ
ε
Phase constant,𝛽 = 𝜔 μϵ
Here,
∝ 𝑑 =σ
2
μ
ε
Np/m
Np/m
Dielectric attenuation constant,
Substituting
We get, [Welch and pratt’s equation]
Modified equation by Pucel,
dB/m Where,
We usually express ∝ 𝑑 in dB/λg
Where,
Ohmic loss
• Because of the resistance in path• Mainly due to irregularities in conductors• Current density mainly concentrated in a sheet with a thickness equal to skin depth• Current distribution in a microstrip is as in diagram,
• Exact expressions for conducting attenuation constant can not be determined.
• Assuming current distribution is uniform,
dB/m
Above relation holds good only if w/h<1
Radiation losses
• Depends on substrate’s thickness, its dielectric constant and its geometry.
• Some approximations:– TEM transmission
– Uniform dielectric
– Neglecting TE field component
– Substrate thickness<<free space λ
• The ratio of radiated power to total dissipated power is
Where,
Quality factor
• Quality factor of the striplines is very high, but limited by radiation losses of the substrates.
• Qc is related to conductor attenuation constant by,
• Substituting, dB/λg
• 𝑄𝑐 = 3.95𝑋10−6 ℎ
𝑅𝑠𝑓
• Substituting Rs and 𝜎 = 5.8𝑋107mho/m for copper assuming stripline is in air,
𝑄𝑐 = 15.14ℎ 𝑓
• Similarly, Qd related to dielectric attenuation constant is given by,
approximating,
Parallel strip lines
• Two perfectly parallel strips separated by a perfect dielectric slab of uniform thickness.
• Considering w>>d,
some parameters are
Attenuation losses
• The propagation constant of a parallel strip is,
The attenuation constant will be
• Coplanar striplines
• Shielded striplines
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