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RF Electronics Chapter 8: Amplifiers: Stability, Noise and Gain Page 282 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. Cadence AWR DE allows stability circles to be plotted. Figure 8.6 shows the input and output stability circles for the following S parameter values: S 11 = 0.96 – j0.26, S 21 = 0.34 – j0.06, S 12 = 0.58 + j0.28 and S 22 = 0.84 + j0.5. The blue circle is the Input Stability Circle and the Red circle is the Output Stability Circle. For Input Stability Circles if |S 22 | >1, then the area outside the Input Stability Circle is unstable. If |S 22 | <1, the area inside the Input Stability Circle is unstable. For the Input Stability Circle of figure 8.6, |S 22 | = 0.978 so that the inside of the circle is unstable. Similarly for the Output Stability Circle of figure 8.6, |S 11 | = 0.989 <1 and the unstable region is inside the Output Stability Circle. In figure 8.6, the different regions are labelled as Stable or Unstable. The region outside both circles, where both the input and output are stable covers most of the Smith Chart with ||<1. Stability circles will thus allow the input and output matching to be arranged to ensure that an amplifier is stable under normal operation. Unconditional Stability An amplifier is unconditionally stable if 1 in and 1 out , for all passive load and source impedances. For many MMIC's, measured S parameter are provided and those can be used to determine the stability of those devices. If the stable region of the Input and Output Stability Circles cover the whole Smith Chart with ||<1, then the device is unconditionally stable. Conditional Stability An amplifier is conditionally stable if 1 in and 1 out , only for certain load and source impedances. As an example, the early version of the MAR8 amplifier was only conditionally stable and both input and output reflection coefficients had to be less than 0.5. For conditional stability, unstable regions of either or both the input and output stability circles partially lie inside the region of the Smith Chart with ||<1. Stability Factors: Measures of Stability When wide-band operations are required, as shown in figures 8.9, 8.23 and 8.29a, it is sometimes difficult to see if an amplifier is stable at a specified frequency. Stability factors provide a simple indication of an amplifier's stability versus frequency. There are different stability factors the as shown below. The Rollet's stability factor, K is defined as: 21 12 2 2 22 2 11 2 1 S S S S K Where 21 12 22 11 S S S S Eqn. 8.18 In addition, the auxiliary stability factor is defined as: 2 2 22 2 11 1 S S B Eqn. 8.19 For unconditional stability K > 1 and B > 0. Both equations involve the input and the output equally, so the Rollet's stability factor applies to the whole amplifier. The Geometric Stability Factor, µ is defined as: � � ��|� �� | � | � �� ��� �� ∗ | �|� �� � �� | Eqn. 8.20 RF Electronics: Design and Simulation 282 www.cadence.com/go/awr