microwave
software®
Sceptre® User Manual
Frequency Domain Circuit Analysis Utility
APPENDIX D
The K factor of an active circuit must
be greater than one for it to be unconditionally stable. However,
although K>1 is a necessary
condition for unconditional stability, it is not sufficient.
It is also necessary that the
parameter B1 be greater than
zero.
Stability Factor
For more information on K and B1, see the book by Guillermo Gonzalez, listed as Reference 4, in Appendix G. If you click on a link to visit this appendix, please remember to use the BACK button on your browser to return here.
Early on, we had the Linvill C factor. K, also known as "Stern's Stability Factor," is its reciprocal, i.e., K = 1/C.
Sceptre will calculate both K and B1 when you use either the S1 or S2 print options. It uses the following equations:
If K is >1, the stability circles determined by use of the S2 print option will be outside the perimeter of the Smith Chart. This means that no real source or load can cause instability. On the other hand, if K<1, the circles will either overlap the perimeter of the chart, or be entirely within it. In this case, the amplifier is only conditionally stable, and certain source and/or load termination's will cause instability. A few calculations will determine whether the stable region is inside or outside the stability circle boundary.
Other causes of instability
Sadly, many engineering schools don't really tell the whole
story about stability, but instead seem to focus on only
K and B1. Another factor that may contribute to
instability, in an otherwise stable circuit, is its
operating environment, i.e., its enclosure.
Care must be taken to "size" a
housing such that it operates in a waveguide below cutoff mode,
and also does not contain a cavity resonance
within or near the operating band. If, somehow, a signal appearing at
the output terminal, radiates back towards the input, oscillation can
occur. By "sizing" the enclosure properly,
such a radiated signal will be attenuated, and stability will be
assured.
For information on how to properly "size" an enclosure containing an amplifier, or other active device, see our Utilities+ User Manual.