4.3 Matching two unequal resistive impedances
179
4.3.2 Loaded Q & Frequency Response
As we have seen in the previous section, a matching network behaves effectively like a filter
which is characterised by its own frequency response. This frequency selective behaviour is even
more pronounced in the case of parallel and series L-C resonators as shown in Figure 4.2-18 and
Figure 4.2-27. It is important to understand the frequency response of matching networks in the
context of the circuits in which they are used in i.e under loaded conditions. Such a response will be
influenced by three major factors:
1) The source resistance (R
S
)
2) The load resistance (R
L
)
3) The components Q
Depending on the complexity of the network it may be rather tricky to work out an analytical
expression for the loaded Q which takes into account all of the above factors. This is why we tend to
define the loaded Q of a circuit in terms of its frequency response as
Where
represents the centre frequency and represents the 3dB bandwidth. This is shown
in Figure 4.3-9.
Figure 4.3-9 3dB-bandwidth ( ) and centre frequency ( ) may be used to work out the loaded Q
In the example shown in Figure 4.3-9, our Loaded Q works out to be
The circuit
associated with the frequency response shown in Figure 4.3-9 is shown in Figure 4.3-10.
Gain
(dB)
f
C
f
1
f
2
Conquer Radio Frequency
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