CHAPTER 4 - Impedance Matching
182
As explained in section 4.2.6, the losses of an inductor may be modelled by a series resistor (Figure
4.2-29) and the losses of a capacitor with a shunt resistor (Figure 4.2-30). The L-C resonator in Figure
4.3-12 when losses are included would therefore look as shown in Figure 4.3-14.
Figure 4.3-14 Resistors may be added to model the losses in non-ideal capacitors and inductors
We can use parallel to series conversions formulae (4.2.7) for the series R-L above so as to have all
elements in parallel.
Figure 4.3-15 Equivalent parallel conversion for the circuit in Figure 4.3-14
In the schematic of Figure 4.3-15, R
LP
may be calculated by using the conversions formulae in Table
4.2-1 as
(
)
Where
is the inductor Q which is equal to
Also
remember that the Q of the capacitor
is equal to
Now
recall how the Q is directly proportional (eq. (4.3-3)) to the equivalent parallel
resistance seen by the resonator (Figure 4.3-13). Now if R
CP
or R
LP
are small, they will considerably
decrease the overall equivalent parallel resistance R
P
since the resistance of a parallel must be lower
than lowest of the resistors that such a parallel comprises of. A poor component Q may therefore
decrease the circuit Q considerably.
In most cases the Q of the inductor alone must be included in calculations since the Q of capacitors,
and hence their equivalent shunt resistance is quite high and hence can usually be neglected.
L
R
LS
C
R
CP
L
C
R
CP
R
LP
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182 www.cadence.com/go/awr
