Page 118 - Complete Wireless Design

Amplifier Design

Amplifier Design 117

and Z ; however, this is never the case. So we will want to perform a simul-
OUT
taneous conjugate match to prevent the matching of the input port from chang-
ing the matching of the output port, and vice versa.
To begin the calculation of the transistor’s input and output impedances:

1. Determine the value of C , which is used in one of the following equa-
2
tions, by:
C S (D S
) D S S S S
2 22 S 11 S 11 22 12 21
(S
equals the complex conjugate of S . In other words, just change the sign
11 11
of the angle, but not the magnitude’s sign, of the S value (for example, S
11
11
12 18°, so S
12 18°). C and D are calculated as vectors.
11 2 S
2. Calculate B , which is also used in one of the following equations:
2
2
2
B 1 |S | |S | |D | 2
2 22 11 S
3. Then calculate the magnitude of the load reflection coefficient ( ), which is
L
the value of the impedance that the transistor must see at its output to be
perfectly matched:

B ± |B | 4|C | 2
2
2
2
2
| |
L 2|C |
2
Note that the sign used for B ± is the opposite of that obtained in the B
2 2
calculation of step 2. This formula supplies magnitude.
4. The angle is the same as that calculated in step 1 for the C angle, but sim-
2
ply reverse that answer’s sign.
Now, to calculate the output impedance of the transistor (Z ). Use the fol-
OUT
lowing formula [all signs (±) must be strictly maintained for all calculated
numbers. 1 will subtract 1 from the real term of , and will simply
L L
change the sign of the imaginary term, while 1 will add 1 to the real term
L
of and ignores the imaginary number completely]:
L

1
L
Z Z LOAD
OUT (1
L
where Z transistor’s load placed at its output (typically 50 ohms; writ-
LOAD
ten as 50 j0).
To calculate the value of the transistor’s input impedance (Z ) for the tran-
IN
sistor’s output impedance as calculated above:
S S S L
12
21
1. S
11
1 ( S )
L 22
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