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Stability

 

A stable circuit is a circuit that does not oscillate.

Oscillations can take the form of either spurious signal generation or noise generation, and are commonly accompanied by changes in DC operating point (bias level). They can be brought on by changes in source or load impedance (reflection oscillator), changes in bias, or improper grounding.

An unconditionally stable device has the property that it will not oscillate as a consequence of changes in source or load impedance. Unconditional stability is frequency and bias dependent. Mathematically, it corresponds to having k>1 and a non-negative determinant, where

k is Rollett's stability factor,

k = { 1 - |S11|^2 - |S22|^2 + |D|^2} / {2 |S12| |S21| }

and D is the Determinant,

D = S11 S22 - S12 S21

Many HP gain block ICs are unconditionally stable; and the k factor is often shown with the S-parameter table. Unconditional stability is important because it implies that a device can be used in cascades and with filters without worrying about oscillations.

A conditionally stable device (one with k<1) has the property that there are some source or load impedances that will cause the device to oscillate. Care must be taken to avoid incorrectly loading such a device.

Any device with gain can be made to oscillate if feedback is added. Feedback may be either shunt (output-to-input) or series (inserted between the circuit and ground). Since poor grounding adds series feedback, it can cause even an unconditionally stable device to oscillate. Poor grounding is the most common cause of oscillation in RF components.
 

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