Microwave transmission lines include coaxial cables, waveguides, and strip lines. Strip lines have configurations like microstrip lines, parallel strip lines, coplanar strip lines, and shielded strip lines. Microstrip lines use a conducting strip separated from a ground plane by a dielectric substrate. They have quasi-TEM mode transmission and characteristic impedances typically between 50-150 ohms. Power losses in microstrip lines include ohmic, dielectric, and radiation losses. The document derives equations for microstrip line characteristic impedance and propagation properties, and discusses sources of loss and quality factors.

1. STRIP LINES

2. Microwave transmission lines
• Coaxial cables
• Waveguides
• Striplines
– Microstrip lines
– Parallel strip-lines
– Coplanar strip lines
– Shielded strip lines

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

14. • Coplanar striplines
• Shielded striplines

15. THANK YOU!