Nonsense said:Hi, all,
Why does the quality factor of the on-chip spiral inductor have a peak? I mean what dominate the loss at low freq. and what at high freq.?
wlcsp said:Of course it has a peak since it's not a perfect inductor, instead it has many parasitic effects. At low freq, substrate loss and ohmic loss dominate, while at high frequency major loss mainly comes from the eddy current loss i.e. skin effect and proximity effect.
rautio said:At low frequency, resistance is a constant and inductive reactance goes to zero, so Q goes to zero.
At high frequency, there is inter-turn capacitance and capacitance to the substrate. This capacitance is in parallel with the inductor. At the frist self resonance (S sub RF) we have a parallel resonant circuit (C in parallel with a series RL). If you sit down and calculate the imaginary part of that impedance and divide it by the real part of that impedance, you find that the capacitance acts to decrease the Q. For R small, Q goes to zero at close to (but not quite equal to) the self resonant frequency.
With Q zero at low frequency and zero near the self resonant frequency and larger than zero in between, it must see a maximum at some frequency below the self resonant frequency.
The equation for Q in this case is:
Q = ωL/R - (ω²L²+R²)ωC/R
Note that a non-zero C decreases Q even though there is no resistance at all associated with the C in this case.