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Stability Considerations
When embarking on any amplifier design it is very important to spend time checking
on the stability of the device chosen, otherwise the amplifier may well turn into an oscillator.
The main way of determining the stability of a device is to calculate the Rollett’s
stability factor (K), which is calculated using a set of Sparameters for the device at the
frequency of operation. The calculations are long winded and it is much quicker to simulate
under ADS.
The conditions of stability at a given frequency are 
Γ
in
 < 1 and 
Γ
out
 < 1,and must
hold for all possible values
Γ
L
&
Γ
S
obtained using passive matching circuits. We can
∆
 to give us an indication to whether a device is likely
to oscillate or not or whether it is conditionally/unconditionally stable.
1
S
.
S
S
.
S
where
,
1
S
.
S
2
S
S

1
K
21
12
22
11
21
12
2
2
22
2
11
<
−
=
∆
>
∆
+
−
=
The parameters must satisfy K > 1 and

∆
 < 1 for a transistor to be unconditionally
stable. Once we have calculated the K factor and find the device to be unconditionally stable
we can calculate the Maximum available gain (MAG):
(
)
1
K

K
S
S
G
2
12
21
MAX
−
=
Where K is on the limit of unity the above equation reduces down to:
12
21
MAX
S
S
G
=
In this case the MAG is known as the maximum stable gain MSG.
In the case of the design we need to calculate the stability factor at 4 & 6GHz, however it is
important to check the stability factor from low frequencies up to the f
T
of the device as
instabilities may occur at other frequencies even though the device is stable within the pass
band.
()
(
)
()
( )
0.26615
and
0.5159
2
.
131

0.5159
33957
.
0
38845
.
0
tan
33957
.
0
0.38845

polar
to
convert
j0.33957

0.38845

j0.1266

0.15094

j0.46617

0.23751

n
subtractio
for
cartesian
to
convert
130
0.19707

153

0.5232
97)
33x2.986
(0.066

61)

92x0.607

0.862
(
S
.
S
S
.
S
4GHz
at
K
of
Evaluation
2
1
2
2
21
12
22
11
=
∆
=
∆
∴
∠
=
⎟
⎠
⎞
⎜
⎝
⎛
−
−
∠
−
+
=
=
=
∠
∠
=
∠
∠
∠
∠
=
−
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()
()
()
0.39
0.394
0.1551
)
130
197
.
0
(
2
0.26617
0.368

0.743

1
97
986
.
2
33
066
.
0
2
26617
.
0
607
.
0
0.862

1
S
.
S
2
S
S

1
K
2
2
21
12
2
2
22
2
11
=
=
∠
+
=
∠
∠
+
−
=
∆
+
−
=
x
Therefore, at 4GHz the transistor is conditionally stable as K < 1 and therefore, we
will have to be careful in the way the transistor is matched.
Similarly the K factor at 6GHz was calculated to be 0.585 and 
∆
 = 0.42.
Now that it is known that the transistor is conditionally stable it is now necessary to
calculate and plot the corresponding stability circles on a Smith chart so that the nogo areas
for matches can be highlighted.
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This note was uploaded on 01/07/2011 for the course ECE 166 taught by Professor Staff during the Spring '08 term at UCSD.
 Spring '08
 staff
 Amplifier

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