# Impedance Matching using Transmission line 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.

• Lots of resources out there on this topic. Search for microstrip (or stripline) impedance calculator. May 12 at 12:05

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.

• This information is very helpful. But if you do me a favor? I am editing the question and putting another picture there. There I will mention the whole circuit including the impedance matching network using transmission lines. Could you please see that and give me more detail about how I can achieve my length and width of impedance matching network using transmission lines. May 13 at 17:00
• @MuhammadAwaisQasim The author didn't go from Rzin directly to lengths and widths, he used an intermediate step where he calculated electrical lengths and impedances. You have to do the work, there is no magic. Either learn how to use a Smith chart, or to use a simulator, where you can iterate the transmission line parameters and observe the matching. Once you have electrical lengths and inpedance, then physical lengths and widths are trivial to get. May 13 at 18:55
• Thank you so much for your guidance. Actually, I used a simulator and got electrical lengths and impedance. Now I have to convert them to transmission line parameters. How can I do this? May 30 at 11:44
• @MuhammadAwaisQasim It's possibly easier to take you through a worked example than simply tell you how to do it. What are your lengths and impedances, and what sort of substrate do you want to realise them on? May 30 at 14:54

There are many tools as @SteveSh suggested, to measure impedance on stripline topology. I would suggest pcb toolkit, Saturn pcb design, since it has many other calculations other then impedance calculation. 