## S21 curves for SMD resistors

09.11.2020 20:19

Some time ago I've stumbled upon the following figure that appears in the Building VNA Calibration Loads video by W0QE. The discussion about it starts around the 13:42 mark. It supposedly comes from some work done at CERN. The "Fig 2" in the caption suggests it appears in a paper, but after searching for it I've failed to find a public source.

Image by W0QE

What this measurement shows is how the impedance of surface mount resistors of different values change with frequency. If the resistors would be ideal all values would have perfectly parallel horizontal lines. However at high frequency the plots for high value resistors curve upwards. The line that they approach asymptotically is one of a 50 fF parasitic capacitor that appears across the resistor. On the other hand, the line for a 0 Ω resistor curves downwards due to parasitic inductance. W0QE discusses the resistor model in more detail, so watch the video for the full explanation.

According to this result the 100 Ω resistor is best at maintaining constant S21 towards high frequencies. This is the base of the argument that making a 50 Ω termination with two parallel 100 Ω resistors is best, and more accurate than using a single 50 Ω resistor or four 200 Ω resistors.

Some thoughts on this: the caption says that S21 curves shown are for 1206 size resistors. Very likely they look differently for other sizes since the parasitics will change with physical dimensions. Hence the optimal choice of a termination resistor might be different if using other sizes.

Another thing that W0QE doesn't mention is that the lines also curve towards the low frequency end of the scale. I suspect this is some kind of a measurement error. I see no reason why a resistor would not have the correct value at DC. This feature also does not appear in W0QE's simulation that is also shown in the video alongside this experimental result.

Anyway, the whole video is well worth a watch. I just wanted to give some more visibility to this particular figure and also have it here for my reference. Since it only appears in a video it's kind of hard to search for it. I already forgot where I saw it once and it's frustrating not to be able to find a thing I know I've seen somewhere when I want to refer to it.

Posted by | Categories: Analog

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