Radio Frequency Integrated Circuit Design - Webs

The Use and Design of Passive Circuit Elements in IC Technologies
In this case, the substrate capacitance and resistance from both halves of
the inductor are in series. When the inductor is excited in this mode, it ‘‘sees’’
less loss and will give a higher Q. Thus, the differential Q is usually higher than
the single-ended Q. The self-resonance of the inductor in this mode will also
be higher than the self-resonance frequency looking from either side to ground.
Also, the frequency at which the differential Q peaks is usually higher than for
the single-ended excitation. Care must be taken, therefore, when optimizing an
inductor for a given frequency, to keep in mind its intended configuration in
the circuit.
Important note: Every inductor has a differential Q and a single-ended
Q regardless of its layout. Which Q should be used in analysis depends on how
the inductor is used in a circuit.
5.16 Some Notes About the Proper Use of Inductors
Designers are very hesitant to place a nonsymmetric regular inductor across a
differential circuit. Instead, two regular inductors are usually used. In this case,
the center of the two inductors is effectively ac grounded and the effective Q
for the two inductors is equal to their individual single-ended Qs. To illustrate
this point, take a simplified model of an inductor with only substrate loss, as
shown in Figure 5.18. In this case, the single-ended Q is given by
and the differential Q is given by
Q SE = R
�L
Q diff = 2R
�L
117
(5.22)
(5.23)
Now if two inductors are placed in series as shown in Figure 5.19, the
differential Q of the overall structure is given by
Figure 5.18 Simplified inductor model with only substrate loss.