Page 119 - Complete Wireless Design

Amplifier Design

118 Chapter Three

1
S
2. Z Z SOURCE
IN 1
S
where Z transistor’s source (the prior stage) placed at its input (typi-
SOURCE
cally 50 ohms; written as 50 j0 for this formula). Vector algebra is used to
calculate , Z , Z , and Z .
S IN OUT LOAD
Note that all signs (±) must be strictly maintained for all calculated num-
bers. 1 will subtract 1 from the real term of , and will simply change
L L
the sign of the imaginary term.
or
equals the complex conjugate of
L S L
or respectively. In other words, just change the sign of the angle, but not the
S
magnitude’s sign (for example, 12 18° 12 18°). If
is outside a
bracket, then the answer to everything within the bracket must be converted
into this complex conjugate.
Now that we have discovered the input and output impedances of our cho-
sen device, we can begin to impedance-match its ports to obtain a simultane-
ous conjugate match for the transistor’s required source and load. So the next
step is to design the matching networks for our circuit.
As an example, the active device, a transistor, has these S parameters at 1.5
GHz and a V 10 V and an I 6 mA:
CE C
S 0.195 167.6°
11
S 0.508 32°
22
S 0.139 61.2°
12
S 2.5 62.4°
21
We will want the amplifier to run between two 50-ohm terminations. To
design an input and output matching network to maintain maximum amplifi-
er gain:
1. Calculate K. Confirm unconditional stability (K 1) by calculation or
lookup in a table, if supplied. (All negative real number results must be
used in all calculations as negative real numbers.):
a. D S S S S 0.25 61.4°
S 11 22 12 21
2
2
1 |D | |S | |S | 2
22
S
11
b. K
2|S |S |
21 12
2
2
1 (0.25) (0.195) (0.508) 2
c. K 1.1
2(2.5)(0.139)
Use vector algebra for D . Do not use vector algebra for K, use magni-
S
tudes of the S parameters.
2. Calculate MAG:
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