Mathcad - ee217projtodonew2.mcd

100
10
1
0.1
0.01
0.01 0.1 1 10 100
| S11 |
| S21 |
| S12 |
| S22 |
Fig. 8: S Parameters vs. Frequency
Stability Analysis
Often it happens a designer designs an amplifier, but he gets an oscillator in return. This
scenario typically occurs at frequencies out of the desired band, where the source and load
impedances can be unknown. If the out of band source and load impedances are unknown it is
desirable to make the amplifier stable for all source and load impedances. This is known as an
unconditionaly stable amplifier. If the out-of-band source and load impedances are known it is
possible to design a conditionally stable amplifier design. Usually conditionally stable amplifiers
can acheive higher performance levels than unconditionally stable amplifiers. This is becuase
the amplifier performance must be degraded some with form of ballasting resistor to make it
stable.
It is desirable to make the stability factor greater than one for another reason other than
stability. With a K factor greater than one it is possible to simultaneously conjugate match the
input and output impedance of the amplifier. Conjugate matches are desirable, because the
filters connected to the amplifier require a conjugate impedance to provide their specified
frequency response.
For a K factor of one, the real part of the matching impedances is zero ohms, so it is
impossible to match with practical matching networks. For this same reason it is desirable to
make the K factor some value significantly larger than one.
KS ( ) ∆ S .
1, 1
S 22 ,
S .
12
,
S 2,
1
1 ( ∆ ) 2 2
S 1, 1
2. S .
1,
2
S 21 ,
2
S 2, 2
K Sparam N, I C , s = 1.016
The mu factor is often a more desirable parameter to use for stability than K factor. This is
because the K factor must be specified with other conditions, such as ∆. In this sense the µ
factor is easier to use, because it does not require any other parameters to guarantee
unconditional stability. Although the K factor and µ factor curves are different, their values are
equal for the transition point between unconditionally stable and conditionally stable regions
(K=µ=1). µ S
.
, , s = 1.102
( ) ∆ S .
1, 1
S 22 ,
S 12
S 1 1
,
S 2,
1
2
1 S 22 ,
,
∆ . S 2,
2
S .
2 1
,
S 12 ,
µ Sparam N I C