RF Electronics Chapter 8: Amplifiers: Stability, Noise and Gain Page 281
2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0.
Stability Circles
Setting |
in
| = 1 in equation 8.4, allows it to be solved for the values
load
that form the
border between stable and unstable regions of the amplifier operation. When plotted on
the Smith Chart, this border forms a circle, which shows the output impedances that cause
the instability. This is called the Output Stability Circle [5, 6].
It has a centre
�
�
��
��
���
��
∗
�
∗
|�
��
|
�
�|�|
�
Eqn. 8.13
And a radius
�
� |
��
��
�
��
�
|�
��
|
�
�|�|
�
| Eqn. 8.14
Where �
�� ��
�
�� ��
Eqn. 8.15
Similarly, Setting |
out
| = 1 in equation 8.5 allows it to be solved for the values
source
that
form the border between stable and unstable regions of the amplifier operation. When
plotted on the Smith Chart, this is a circle and is called the Input Stability Circle [5, 6].
It has a centre
�
�
��
��
���
��
∗
�
∗
|�
��
|
�
�|�|
�
Eqn. 8.16
And a radius
�
� |
��
��
�
��
�
|�
��
|
�
�|�|
�
| Eqn. 8.17
Figure 8.6. Input and output stability circles.
These stability circles show the border between stable and unstable regions. Depending
on the values of the s parameters, the centre of these stability circles can be inside or
outside the unit circle. For the input Stability Circle, if S
22
is <1, then the outside of the
Stability Circle is stable. If S
22
is >1, then the inside of the Stability Circle is stable.
However, that corresponds to reflection from port 2 to be larger than the incident voltage
and that is unlikely in practical cases. Similarly, for the output Stability Circle, if S
11
is
>1, then the inside of the Stability Circle is stable and if S
11
is <1, then the outside of the
Stability Circle is stable.
RF Electronics: Design and Simulation
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