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# Strip lines

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### Strip lines

1. 1. STRIP LINES
2. 2. Microwave transmission lines • Coaxial cables • Waveguides • Striplines – Microstrip lines – Parallel strip-lines – Coplanar strip lines – Shielded strip lines
3. 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. 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. 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. 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. 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. 8. Modified equation by Pucel, dB/m Where, We usually express ∝ ������ in dB/λg Where,
9. 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. 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. 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. 12. Parallel strip lines • Two perfectly parallel strips separated by a perfect dielectric slab of uniform thickness. • Considering w>>d, some parameters are
13. 13. Attenuation losses • The propagation constant of a parallel strip is, The attenuation constant will be
14. 14. • Coplanar striplines • Shielded striplines
15. 15. THANK YOU!