3. 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.
4. 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]
5. Typically, Zo is in between 50Ω to 150Ω
The velocity of propagation of microwaves in microstrips,
Propagation time constant is,
������������ = μ ϵ
=3.333 ϵ������ ������������/������
LOSSES IN MICROSTRIP LINES
• Ohmic Losses
• Dielectric Losses
• Radiation Losses
6. 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
7. • Hence,
Np/m
Np/m
Dielectric loss
from first unit,
σ μ
Attenuation constant, ∝= 2 ε
Phase constant,������ = ������ μϵ
Here,
σ μ
Dielectric attenuation constant, ∝ ������ =
2 ε
Substituting
We get, [Welch and pratt’s equation]
8. Modified equation by Pucel,
dB/m Where,
We usually express ∝ ������ in dB/λg
Where,
9. 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
10. 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,
11. 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
ℎ
• ������������ = 3.95������10−6 ������
������������
• Substituting Rs and ������ = 5.8������107 mho/m for copper assuming stripline is in air,
������������ = 15.14ℎ ������
• Similarly, Qd related to dielectric attenuation constant is given by,
approximating,
12. Parallel strip lines
• Two perfectly parallel strips separated by a perfect dielectric
slab of uniform thickness.
• Considering w>>d,
some parameters are
13. Attenuation losses
• The propagation constant of a parallel strip is,
The attenuation constant will be
