Page 117 - Complete Wireless Design

Amplifier Design

116 Chapter Three

Since K is greater than 1, we see that we have a stable transistor at 1.5 GHz
with the transistor’s bias conditions as stated in the S-parameter file. For ease
of design, it is always recommended that, if at all possible, we exploit only
unconditionally stable transistors in our amplifier circuits.
For the calculation of maximum available gain to be valid, K must be
greater than 1, or unconditionally stable. Thus, if K is over 1 for a transistor,
we can proceed to the MAG calculation to see if the transistor will give us the
gain value we desire. MAG is, of course, never attained in practice, so only
when the MAG is 20 percent or more above our required gain would we want
to work with that particular transistor.
To calculate the MAG of the transistor, or the maximum gain that the tran-
sistor can attain when perfectly matched:

1. Calculate

2
2
B 1 |S | |S | |D | 2
1 11 22 S
2. B determines whether or will be adopted in the MAG equation in step
1
3. If B returns a negative answer, use the sign after K; if B is positive,
1 1
utilize the (negative) sign after K.
|S |

21
3. MAG 10 log 10 log (|K K 1|)
2
|S |
12
In the equations for B and MAG, do not use full vector algebra; employ only
1
the S-parameters’ magnitudes (for example, S 0.35). |S | means to ignore
11 11
the sign of the magnitude, and always make it positive.
As an example of a MAG calculation:
2
2
2
1. B 1 |0.195| |0.508| |0.25| 0.717
1
2. Since B has returned a positive number, the sign after K (1.1) in the equa-
1
tion below will be negative.
3. Complete for MAG:
|2.5|

2
MAG 10 log 10 log (|1.1 1.1 1 |)
|0.139|
12.56 ( 1.92) 10.63dB
Thus, the amplifier will supply a maximum available gain of 10.63 dB.
After finding that the transistor has a K greater than 1 at our desired fre-
quency, and with a MAG greater than 20 percent of that required for our appli-
cation, the actual Z and Z of the transistor can then be calculated. These
IN OUT
impedance calculations will take into account the reflected impedances caused
by S , the transistor’s value of isolation in the reverse direction, since only if
12
S has a value of zero will it have no effect on the transistor’s individual Z
12 IN

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