Numerical Sheet4

NUMERICAL SHEET 4 TRANSMISSION LINES AND WAVEGUIDES 1. A transmission line with air as dielectric has z0=50Ω and a phase constant of 3 rad/m at 10MHz. Find the inductance and capacitance of the line. (L=2387.25nH/m. C=954.9 pF/m). 2. A lossy cable which has R=2.2.5Ω/m, L=1.0µH/m, C=1pF/m, and G=0 operates at f=0.5GHz. Find the attenuation constant of the line. (α=1.125x10^-3 (m^-1)) 3. A transmission line in which no distortion is present has the following parameters: zo=50α, α=0.020 m^-1, v=0.6vo. Determine R, L, G, C and wavelength at 0.1 GHz. (R=1Ω/m, L=277nH/m, G=400µ mho/m, C=111.1pF/m, λ=1.8m) 4. For a transmission line which is terminated in a normalized impedance zn, VSWR=2. Find the normalized impedance magnitude. (|zn|=2) 5. A lossless transmission line used in TV receiver has a capacitance of 50 pF/m and an inductance of 200 nH/m. Find the characteristic impedance for sections of a line 10 m long and 500 m long. (zo=63.245Ω, zo=63.2Ω) 6. A copper coaxial line has an outside tubing of thickness 1.8mm and its outside diameter is 30mm. The thickness of the inner tubing is 1.0mm and the outside diameter is 8 mm. Find the outside impedance of the line. (zo=88.79Ω) 7. If a signal of 30 MHz is transmitted through a coaxial cable which has a capacitance of 30 pF/m and an inductance of 500 nH/m. Find:(i)the time delay for a cable 1 m long (3.87ns) (ii)propagation velocity (2.5839x10^8 m/s) (iii)propagation delay over a cable length of 10m. (38.7 ns) 8. A lossless transmission line is terminated in a load impedance of 30-j23Ω. Find the phase constant and reflection coefficient of a line of length 50m. Characteristic impedance, zo=50Ω. Wavelength on the line=0.45m. (ρ=-(0.1431+j0.3071)) 9. If a wave of 6 GHz is propagating between two parallel conducting plates separated by 30mm, find the cut off and guide wavelength for TE10 mode. (6 cm, 9.05cm) 10. When a wave of 6 GHz propagates in parallel conducting plates separated by 3 cm, find the phase velocity, group velocity of the wave for the dominant wave. (5.430x10^8 m/s, 1.66x10^8 m/s) 11. When a wave of 6 GHz is to be propagated between two parallel conducting plates separated by 60 mm, find the modes that will propagate through the guide.