Page 146 - Complete Wireless Design

Amplifier Design

Amplifier Design 145

height of the forward wave. Most values of , however, will contain both mag-
nitude and phase, instead of simply magnitude as above. These reflection coef-
ficients are an indicator of the quality of the match between one impedance
and another, or V /V , with a perfect match equaling zero and the worst
REFL FWD
match equaling 1. They can be expressed in rectangular ( R ± jX) or polar
( P ±0) forms.
Nevertheless, calculating just the magnitude ratio will allow the computa-
tion of the return loss and mismatch for any circuit.

Return loss: RL (in dB) 10 log 2
10
2
Mismatch loss: ML (in dB) 10 log (1 )
10
Conversions. There may be occasions when we will need to convert from the
old Y parameters (another way to characterize a transistor) into the newer S
parameters, even though this is rarely required today.

11 (1 S ) (1 S ) S S 21 1
12
22
11
Y
(1 S ) (1 S ) (S S )
11 22 12 21 50
12 2S 12 1
Y
(1 S ) (1 S ) (S S )
11 22 12 21 50
21 2S 21 1
Y
(1 S ) (1 S ) (S S )
11 22 12 21 50
(1 S ) (1 S ) S S
1
12
22
21
11
Y
21 (1 S ) (1 S ) (S S ) 50
22 11 12 21
Use full vector values of S (Z ±0°) in calculations (for example, S 0.35
11
45°).
We will have many instances when we have to convert from rectangular (Z
R ± jX) to polar (Z R ) notation, and back, when designing amplifiers.
The manual technique below—good only for positive real numbers—is one
method. However, a simple scientific calculator performs the job much faster
and more accurately.
1. To convert rectangular into polar form (R ± jX to Z ):
a. Z R X 2
2
b. tan 1 X/R (Note: tan 1 arc tangent)
2. To convert polar into rectangular form (Z to R ± jX):
a. R Z (COS )
b . X Z (SIN )

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