Advertisement

K-Factor Derivation

Click here to go to our main page on stability factor

If you are not careful, amplifier designs can oscillate easily due to feed back in the transistor or active device. In order to guarantee* stability we have to analyse the stability for all frequencies and, if not stable, insert a stabilization network.  Luckily for us, the good folks over at Microwave Labcast have provided a video that explains everything.

* There are no guarantees in life  Check out our normalized determinate function (NDF) page for another reason your amplifier can become unstable.

We originally chose the video because in the first few minutes the speaker (Professor Dr. S. F. Peik) derives the conditions for stability (Rollet's stability factor, known as "K") of an active two-port network.  But the video provides much more, if you have 51 minutes to watch the entire thing.  The video derives conditions for stability, shows how stability circles are plotted (this may be the only time in your career when you wish your S-parameters were formatted in real and imaginary parts), tells you how to test which side of the stability circle is stable, and ultimately shows K-factor and its cousins delta and mu.  Prof. Dr. Peik points out that stability does not care about your operating frequency, you have to make sure your amplifier is unconditionally stable at ALL frequencies. He uses an example transistor Infineon BFP420 (sells for $0.14 on Digikey!) showing you how to dig out its S-parameters from Microwave Office and use MWO to do the heavy lifting on stability circles and stability factors.

Near the end of the video, we learn how to stabilize a transistor using the sledgehammer method of adding pure resistors, which will reduce gain in the band you are designing for, even if the device was already unconditionally stable at your design band. In the last minute he reveals the "professional" design where the resistors are connected to reactive elements that stabilize the amplifier at low frequency without killing gain where you want it.  Bravo!

Professor Dr. S. F. Peik explains stability

This is part of a series of lectures from Microwave Labcast's "Microwave Circuits and Systems (Master Course)" playlist - He's got lots of other playlists, many in German.

Advertisement