When designing microwave amplifiers, stability is an important factor to consider. Stability is usually measured with the K factor. In a unilateral network, S_12 = 0, and this makes the K factor infinite.

However, we also know that being unilateral means Gamma_in = S_11, and Gamma_out = S_22. What if the network is unilateral, but either S_11 or S_22 are larger than 1? Will the amplifier be unstable despite being unilateral? Is this situation possible at all?

  • \$\begingroup\$ I've never used the term with bilateral which has a similar meaning as bipolar nor seen any stable s11>1 as this implies the feedback amplifies any input to the input. ( Return Gain not Loss) Hence unstable But I never thought of using s parms for an oscillator \$\endgroup\$ – Tony Stewart EE75 Dec 22 '19 at 18:38
  • \$\begingroup\$ @TonyStewartSunnyskyguyEE75, usually you use S-parameters to describe amplifiers, and when you design an amplifier you want to make sure you didn't accidentally design an oscillator instead. \$\endgroup\$ – The Photon Dec 22 '19 at 18:58
  • \$\begingroup\$ @ThePhoton Γ_in = S_11 is true only when the port 2 is matched, not in the general case. \$\endgroup\$ – Ali Lavasani Dec 22 '19 at 18:59
  • \$\begingroup\$ @Ali, OK, fair enough. But you could equally well talk about \$S_{11}\$ of the whole 1-port sub-system composed of the amplifier and its load. If you're going to parse the definitions of \$\Gamma_{in}\$ and \$S_{11}\$ this carefully, you should probably also give us the exact definition of "unstable" you're using. \$\endgroup\$ – The Photon Dec 22 '19 at 19:04
  • \$\begingroup\$ it will certainly be distorted if unilateral and s11 or s22>1 and not useful \$\endgroup\$ – Tony Stewart EE75 Dec 22 '19 at 19:17

It depends whether your 2-port is an arbitrary black box where you can dial in any S-parameters, or something feasible like a transistor where the values are constrained to be physical.

If the former, consider a back box with |S11|>1, and |Sxy|=0 for x,y !=1. It will be unstable for some input impedances regardless of output load, yet it's unilateral by your definition.

Computing stability circles for a port means considering the network as a whole, so for the input it involves both the S11, and the S12/21/22/load. What the ideal of unilaterality does is reduce the second term to zero. Often the |S11| is <1, and then you've automatically got stability with passive inputs. But it isn't always. Look up a Pierce oscillator for instance. It's quite easy to turn an emitter follower into a Pierce with some strays.


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