IEEE Circuits and Systems Magazine - Q4 2020 - 24

across the resonator one can potentially improve their
phase noise.
Recently, a new type of sensors based on oscillating structures have been reported in literature where
FBARs are used to detect small airborne particles in
Particulate Matter (PM) sensors [114]. In this type of
sensors, the mass of the particles are measured as they
are deposited on the surface of a FBAR which again
results in a change in its resonance frequency. As the
thickness of the deposited particles on the surface of
the FBARs increases, the FBARs equivalent resistance
increases and they become harder to drive and kept in
oscillation. In this case the oscillators ability to drive
the FBARs becomes an important parameter. In [115],
the authors compare the driving strength of some of
the Colpitts oscillators presented in this paper to the
increased load resistance. This comparison shows that

the push-pull common gate oscillator has the best driving capability.
Fig. 49 shows a comparison of the amplitude magnitude response of 5 different Colpitts oscillators versus
load values up to 10 K X. The differential common drain
shows the highest gain when the loading is small however, the common gate version is the most stable when
load increases. Fig. 50 shows the frequency response of
the same circuits versus increased load. In this comparison, the common gate oscillators, both the single-ended
and the complementary are stable over a larger range of
resistances compared to the others, with the common
drain with the largest variation.
Another way to compare the oscillators, is the Figure Of Merit (FOM) [56], [116] which, in addition to the
phase noise, may also include the power consumption
of the oscillator. In [116] FOM is defined as follow:

Magnitude (dB)

0
-5
-10
-15

-25

CD
CG
CS
CGComp
CDDiff

-30
10-1

100

-20

101
102
Load (â¦)

103

104

Figure 49. Magnitude of the output swing of 5 different Colpitts oscillators versus increasing load in X [115].

140

Frequency (MHz)

130
120

CD
CG
CS
CGComp
CDDiff

110
100
90
80
10-1

100

101
102
Load (â¦)

103

104

Figure 50. Frequency response of the various Colpitts oscillators versus increasing load in X [115].
24â

FM = 10Log ;`

1
E (8)
L {T~} P

In [117] a comparison of FOM, as defined above, for
different types oscillators is presented.
As the supply voltage in modern CMOS technologies
decreases due to demand for lower power consumption,
the output swing is also limited. One way to enhance the
output swing of oscillators in these technologies, is by
replacing the bias transistor in the oscillators with an
inductor as proposed in [118]. In [119] a comparison of
the FOM for different swing-enhanced oscillators is reported. The definition of FOM in this paper is different
from [116], however it also includes the power consumption and phase noise of the oscillators.
As we have discussed, making a fair comparison between various configuration of the Colpitts oscillator or
with other types of oscillators is difficult since all designs can somehow be improved using either various
techniques or technologies. In addition, a full comparison is out of scope of this paper as we only try to give
the history of the Colpitts oscillator during the last 100
years until today.
VII. Conclusion
This paper listed over 30 variations of Colpitts oscillator, which confirms the versatility of it. Colpitts
oscillators has undergone extensive improvements
throughout the last 100 years and has been adapted
to different technologies from Vacuum tube to Bipolar
and modern CMOS. Colpitts can be realized using different types of gain stages such as common source,
common drain and common gate and common emitter
and their equivalents in Bipolar technology. Various
techniques such as cross-coupling, cascading, cascoding and transformers can be used to create both

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