Saturday, July 3, 2010

Repeatability Specification in RF / Microwave Switches

High quality RF/microwave switches often have a “repeatability” specification. Repeatability is typically given in dB and is often confused with the insertion loss specification (also given in dB). Insertion loss is a well known spec and can be defined as the loss of signal power due to the “insertion” of the switch into the signal path. Repeatability specification is a little trickier to understand, it can be defined as the variation in insertion loss from one switch closure to the next. You may wonder why does the loss through the switch change at all since it is just two high quality flat conductors making contact? Remember at RF/microwave frequencies we are dealing with wavelengths that about the size of the signal path or shorter. This means the impedance that the signal path presents to the signal is affected by small changes in the signal paths dimensions. When the switch is cycled it never closes exactly the same way it did on the previous closure which results in a slight variation in impedance. This variation in impedance from one closure to the next is represented by the repeatability spec. The repeatability spec is only a small fraction of the switches overall insertion loss, for instance Agilent RF/microwave switches have a repeatability spec of 0.03 dB.

So why do we care about the repeatability spec? The reason we care about the repeatability of a switch is because it is a random error not a systematic error (like insertion loss) and therefore cannot be calibrated out or compensated for in measurements. If you have an RF / microwave signal path that you characterize with a network analyzer and that same path has a switch in it once you cycle that switch the insertion loss or S-parameters you measured with the network analyzer has now changed. So switches add measurement uncertainty to your characterized or calibrated signal paths and that is why it is critical to keep the number of switches in a signal path as low as possible.

Let’s say we have an RF / microwave signal path that we have characterized with two switches in it and these switches have a repeatability spec of 0.03 dB. Does that mean we would spec the signal path with a 0.06 dB uncertainty? The answer is no and the reason is because our repeatability error is random so it takes on a Gaussian distribution like the one shown in the figure.

Since repeatability error takes on this type of distribution we can use the root sum or squares (RSS) method to calculate the measurement uncertainty of the signal path. RSS is calculated using the following formula: sqrt(x1^2+x2^2+....+xn^2). Using RSS means the measurement uncertainty of our signal path with two switches in it is 0.0424 dB instead of 0.06 dB. RSS works because the repeatability is typically calculated out from the Gaussian distribution by 3 sigmas or standard deviations (see figure) so the probability that both switches are at .03 dB deviation (both on the same side of the curve) from the calibrated value is very unlikely (about 1 in 274,000).

For more info on calculating measurement uncertainty check out the NIST page on it here

Now if you’re making high precision measurements in applications where phase accuracy is critical, such as radar test, you may be wondering where the phase repeatability spec is. Unfortunately phase repeatability is not spec’d by RF / microwave switch manufacturers (or at least I have not ever seen it spec’d). This leaves you with two choices if you need to establish phase repeatability for your switches: contact the manufacturer to see if they have data on phase repeatability or calculate it yourself using Gaussian distributions and the principals of probability.

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