Hi! I was looking at this research paper for Energy Harvesting through Rectanna and I stuck with this thing. The author, first, calculated the Rzin of the rectifier circuit. He had a source resistance of 50 ohms. Then he calculated the length and width of the transmission line which he was using for impedance matching. My question is how he calculated this? is there any formula or relation for finding these parameters? In the paper, there is nothing mentioned about this. Please let me know if anybody has knowledge about this. Thank you.
Impedance matching goes in several stages.
First, you have to select a general method. Options are transformer, lumped component network, or transmission line network. These would be applicable in increasing order of frequency.
Assuming you chose a transmission line topology, then you would need to compute the electrical lengths and impedances to use. One option is to use the Smith Chart, which is a graphical method of doing the complex number calculations. It's a bit like a slide rule, so unknown to most youngsters, but very fast and intuitive in the hands of an expert. These days you would tend to use a simulator to iterate to a solution, or an optimiser to design the network for you.
Finally, turn the impedances into a physical realisation. There are many calculators, many of which are free online, to allow you to get from target impedance and substrate material to dimensions. To give you one easy to remember data point, line width = twice substrate thickness gives you roughly 50 Ω on FR4 microstrip, when the substrate thickness is much much greater than that of the metalisation.