Page 116 - Complete Wireless Design

Amplifier Design

Amplifier Design 115

our frequency and bias of interest over all impedance variations. This stability
should also be maintained over a very wide region of frequencies, both low and
high, for wide-ranging stability.
The K stability formula is

2
2
2
1 (|D | |S | |S | )
11
S
22
K
2|S |S |
21 12
where
D S S S S
S 11 22 12 21
As explained below, vector algebra is used to calculate D , while scalar quan-
S
tities (magnitudes only) are used to calculate K.
Thus, if K 1, then the active device will be unconditionally stable for all
Z and Z presented at its ports. This is by far the easiest transistor to
IN OUT
design an amplifier with. But if K 1, then the device is potentially unstable.
If this is so, Z and Z must be very cautiously selected. Alternatively, you
IN OUT
can pick a different active device with a K 1, or opt for another transistor
bias point that will give a K 1, or use a neutralizing circuit, or place a low-
value resistor at the amplifier’s input (to decrease gain).
The following is an example of how to rapidly calculate whether a chosen
transistor will be stable at 1.5 GHz, with a V 10 V and an I 6 mA.
CE C
1. The S parameters at that particular frequency and bias point are found to
be (by looking at its S parameter file):

S 0.195 167.6°
11
S 0.508 32°
22
S 0.139 61.2°
12
S 2.5 62.4°
21
*
2. First calculate D :
S
D (0.195 167.6° 0.508 32°) (0.139 61.2° 2.5 62.4°)
S
0.25 61.4°
†
3. Then calculate K :
2
2
1 |0.25| |0.195| |0.508| 2
K 1.1
2|2.5|0.139|
*Use full vector algebra (Z ± 0°) in S-parameter calculations (for example, S 0.35 45°).
How to multiply, subtract, divide, and add vectors is explained below. 11
†Do not use full vector algebra; employ only the S-parameters’ magnitudes (for example, S
0.35). |S | means to ignore the sign of the magnitude, and always make it positive. 11
11
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