The discussion focuses on using a Smith Chart to determine the input impedance of an antenna modeled as a 40-ohm resistor in parallel with a capacitor (Xc = -j25) fed by a 50-ohm lossless transmission line, 0.15 wavelengths long. Participants describe two methods for calculating the input impedance: one involves normalizing admittance by dividing by 0.02 Siemens (the characteristic impedance), while the other suggests dividing by 50 directly. Both methods lead to the same conclusion, emphasizing the importance of understanding the VSWR and the process of rotating around the chart to find the normalized input impedance.
PREREQUISITESElectrical engineers, RF engineers, and students studying antenna design and transmission line theory will benefit from this discussion, particularly those looking to enhance their skills in impedance matching and Smith Chart applications.
This is how the person worked it out. First the parallel R and Xc can be expressed as admittances, by simply taking the reciprocal of each. Then they are normalised by dividing by 0.02, which is the value at the centre of the chart (it is the Zo of the line, 50 Ohms or 1/50=0.02 Siemens). Plot the normalised admittance, then notice the VSWR, which is the radial distance, and we rotate around the chart at this radius towards the generator for a distance of 0.15 lambda. This point gives the admittance at the generator, and we travel across the chart to the opposite point to obtain the normalised impedance at the generator. Multiply R and X by 50 to obtain the required values.maearnie said:
Thank you very much! i was wondering why they multiplied 50 instead of multiplying it. hahahatech99 said:
