Conventional techniques for realizing filters and oscillators at video
frequencies are –TRANSCONDUCTANCE-C, SC and SI.
But these approaches are not applicable for circuits at radio
frequencies particularly in the GHz range due to the noise and
parasitics associated with active devices at such frequencies of
This results in LIMITED DR, OPERATING FC and LARGE
A means to overcome this is to employ LC tuned circuit for the
Due to the passive nature of such passive L and C components
which produce much less noise, parasitics and distortion, we can
have an IMPROVED DR, OPERATING FC at relatively LOW
The main problem associated with this realization is a method to
tune the LC resonantor’s center frequency.
Why need the LC tuned circuit to be tunable.
So that the designed circuits can be compensated for process
spreads and temperature variations.
Also, in some applications, this tuning capability can help reduce
The most widely used tuning technique for LC tanks is the C
TUNING based on the impedance multiplication scheme.
In this configuration, the EFFECTIVE CAPACITANCE can be
tuned via the current gain alpha of the current amplifier.
This particular technique has been successfully employed to
implement TUNABLE BANDPASS FILTER and OSCILLATOR.
A viable alternative recently introduced is the mutual L TUNING
TECHNIQUE which employs two mutual inductors and a current
Again, the EFFECTIVE INDUCTANCE value can be adjusted via
the current gain alpha.
This has been used to implement an RF filter with a rather limited
tuning range. But so far, there has been no report on oscillator
circuit using the scheme.
In order to know the advantage and disadvantage of those two
main tuning techniques, we then have to analyse and compare
Here, we focus on the performance in terms of the TUNING
ABILITY and the ‘Starting’ QUALITY FACTOR of both the tuning
The word ‘STARTING’ Q-factor means the Q-factor of the overall
LC circuit after being made tunable with no active circuitry to
enhance the Q.
In this analysis, important non-idealities are included and these are
1) RESISTIVE LOSS in L,
2) CURRENT AMPLIFIER’s INPUT RESISTANCE and 3)
PARASITIC CAPACITANCE associated with the output of the
current amplifier and L.
To simplify the calculation, we assume that the current amplifier
has INFINITE BANDWIDTH and the inductor has no SUBSTRATE
This seems to be reasonable as these effects are beyond the
operating frequency range of the LC tanks
From the circuits in the last slide, we have derived their equivalent
parallel RLC circuits by removing the current amplifier and these
can be shown here on the RIGHT and LEFT.
By inspection, we can see that the current amplifier introduce more
loss to the original LC tank via the input resistance ri.
By defining omega_o, as the center frequency and Q_o as the Q-
factor of the original LC tank, we can express the center frequency
and Q-factor of the C-tuning resonator and mutual-L tuning
resonator by these equations.
Notice that n is the ratio between Co and C and the center
frequency in both the resonators can be adjusted via the variable
Also, indicated by the equations is that the starting Qs in both
circuits also depend on alpha.
Based on the equations on the last slide, we can then generate a
plot of the tradeoffs between the Q-factor at alpha=0 normalized to
Q_o and the frequency tuning range defined here as the ratio of
the highest center frequency to lowest center frequency when
alpha sweeps from -1 to one, of the two tunable LC tanks.
We assume that ri=26ohms, rL=15ohms and the coupling
coefficient in the mutal-L tuning is 0.9.
First, the effect of Co is to lower the frequency tuning range in both
the tuning techniques
Secondly, we can see from this plot that at the same n the mutual
L tuning exhibits slightly less frequency tunability compared to C-
tuning. But the difference is less at higher n at higher Co.
The third point is quite important because the plot shows that the
mutual-L tuning technique exhibit a better tradeoffs between the
achievable tuning range and Q. The benefit is more evident at
Even more striking is the ability to possess Q-factor even larger
than Q_o while still providing tuning ratio larger than 1.5.
In practice, higher starting Q will translate to circuits with lower
power requirement, filters with better dynamic range, oscillators
with lower phase noise
To demonstrate the feasibility of the mutual-L tuing technique in
practice, a GHz range VFO has been designed based on such
technique using 0.8um BiCMOS process with ft=12GHz.
The circuit schematic can be shown in this slide.
The current amplifier is based on the translinear gain cell.
The mutual inductor is made from two inter-wound on-chip spiral
The negative resistance circuit to compensate for the loss for
oscillation is a cross-coupled amplifier with a capacitive feedback.
For simulations, a free program for electromagnetic analysis of
spiral inductors called ASITIC from UCB was used to generate an
equivalent circuit model for the spirals,
Here is the simulated tuning range where you can see that for
alpha in the range between –1 and 1, we obtain around 600MHz
frequency tuning from 1.4GHz to 2.0GHz.
The simulated phase noise performance is shown in this plot at
1MHz offset frequency. The best phase noise is -107dB/Hz at
1.65GHz and the phase noise is better than –100dBc/Hz for the
entire frequency range.
Other simulated performances include min o/p power of 4.5dBm,
power disspation of 28mW.