IEEE Circuits and Systems Magazine - Q4 2020 - 19

shows the phase noise for different values of the -ratio
C1/(C1 + C2) with and without cross-coupling K, i.e.
K = 1 or K = 0. As the authors state, the oscillator is not
a Colpitts anymore, when C1 and C3 are removed, but
a class C oscillator. This oscillator will suffer from low
output amplitude.
Fig. 33 shows a noise shifting technique presented in
[42]. The idea is to relate the transistors MN2 and MN4
by a tail transistor since they are turned on only each
half period due to the cross-coupled pair. Another advantage of this technique is that the two single-ended
oscillators will have a common-mode behaviour.
Fig. 34 Shows a gm-boosted [93] version of the
noise-shifting technique presented in [42] where two
stage cross-coupling is applied. In [94], the authors put
the spotlight on the role of the feedback capacitors in

Phase Noise (dBc/Hz)

-126

the oscillator. They show that feedback capacitors C1
and C3 have double roles, i.e. on one side they increase
the positive feedback, but on the other hand they decrease the transconductance of the circuit, two effects
which in total may cancel each other. The authors propose to connect the feedback capacitors C1 and C3
to the gate instead on the drain as shown in Fig. 35.
They show that this configuration reaches a FOM
of â190 dBc/Hz/mW. The question is then if this new
circuit can still be called a Colpitts or just a modification of the Colpitts oscillator.
B. Complementary Common Gate Colpitts Oscillator
By stacking two single-ended oscillators, one PMOS on
top of a NMOS, as shown in Fig. 36, one can create a complementary push-pull oscillator. Fig. 37 shows a complementary Colpitts oscillator, where the two FBARs in
Fig. 36 are replaced by a single FBAR. This circuit offers
higher gain due to its push-pull property. This method
is presented in [84], where the authors realize the circuit

-128
-130
k=0
5 dB

FBAR

FBAR

Vout1

-132

Vout2

k=1

-134

C1

MN1

MN2

C3

MN3

MN4

C4

-136
0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
C1/(C1 + C2)

C2

MN5
Figure 32. Phase noise for different value of the ratio C1/
(C1+C2) with and without cross-coupling between the two inductors in the circuit [92].

Vout1

FBAR

FBAR
Vbias1

C1

MN1

C2

MN3

MN2

MN4

MN5

Figure 34. Common gate Colpitts topology with double
cross-coupling and single tail transistor.

Vout2

FBAR

C3

Vout1

Figure 33. Common gate Colpitts topology added a tail
transistor.

FOURTH QUARTER 2020

FBAR

MN1

MN2

C1

C4

Vbias2

Vbias2

Vout2

C3
Vbias

C2

MN3

MN4

C4

Figure 35. Modified Common gate Colpitts topology with capacitive coupling between gate and source [94].

IEEE CIRCUITS AND SYSTEMS MAGAZINE

19

IEEE Circuits and Systems Magazine - Q4 2020

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