Page 133 - Complete Wireless Design

Amplifier Design

132 Chapter Three

Figure 3.30 Canceling the load’s stray reactance.

3. Simplify by combining both of the inductors we now have (Fig. 3.31) with a
single inductor by (Fig. 3.32):
L L
2
1
L
NEW L L
1 2
or 2.22 nH L
NEW
The 50-ohm source is now perfectly matched to the complex load.
Pi and T network matching. Three-element impedance matching (pi or T) net-
works are popular in narrowband applications. The narrowband popularity is
due to the higher Q over that which L networks possess, yet pi and T networks
also permit almost any Q to be selected. Nonetheless, T and pi circuits can
never be lower in Q than an L network. The Q desired for a particular appli-
cation may be calculated with the following formula, assuming the utilization
of high-Q inductors:
f
c
Q
(f f )
2 1
where Q loaded quality factor of the circuit
f center frequency of the circuit
C
f upper frequency that we will require to pass with little loss
2
f lower frequency that we will require to pass with little loss
1
Employ the guidelines below to design a pi network capable of matching two
different pure resistances (Fig. 3.33). With the following design methodology,
consider the pi network as two L networks attached back to back, with a vir-
tual resistor in the center; which is used only as an aid in designing these net-
works, and will not be in the final design:

1. Find “R”, the virtual resistance, as shown in Fig. 3.34. (Note: In this exam-
ple, the Q of the pi network is chosen to be 10):

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