Analysis of Transmission Line Load at 900MHz

[athi.muffin]

Figure below shows a load made up of a 50 W resistance, a 15 nH inductance and a 22 pF
capacitance connected in series. The load is terminated to a two-wire transmission line with
characteristics impedance of 50 W.



(i) Determine the load reflection coefficient at an operating frequency of 900 MHz, from
the Smith chart.

(ii) Calculate the standing wave ratio on the transmission line.

(iii) Determine the input impedance at 0.15 l away from the load using the Smith chart,
where l is the wavelength at the operating frequency.

Help me answer this question :shy:

 

[NateD]

(i) The reflection coefficient at 900 MHz can be determined from the Smith chart. At this frequency, the inductance and capacitance form a resonant circuit, whose impedance is equal to the series combination of the resistance and the reactance of the inductor. This can be represented by a point on the Smith chart. The reflection coefficient is then calculated using the formula: Γ = (ZL-Z0)/(ZL+Z0), where ZL is the load impedance and Z0 is the characteristic impedance of the transmission line, which is given as 50 Ω. (ii) The standing wave ratio (SWR) is calculated as the ratio of the maximum voltage to the minimum voltage on the transmission line. It is given by the formula: SWR = (1 + |Γ|)/(1 - |Γ|). (iii) The input impedance at 0.15l away from the load can be determined from the Smith chart. The input impedance is calculated as the ratio of the incident wave to the reflected wave, which is given by the formula: Zin = Z0(1 + Γ)/(1 - Γ).