IEEE Circuits and Systems Magazine - Q4 2020 - 16

Fig. 20 shows a MOSFET version of the gm-boosted
differential Colpitts VCO presented in [35]. [82] presents a similar circuit with gate-to-source feedback (GSColpitts), where a deeper analysis of that oscillator is
also presented. In this work, the effect of the capacitive
divider on the Colpitts behavior is discussed. In [58],
the bulk of the cross-coupled transistors are used to enhance the gain of the circuit as shown in Fig. 21. In order
to decrease the VDD the tail transistor is removed, thus
the circuit doesn't have any common mode behavior. On
the other hand, it reduces the effect of the flicker noise,
which is usually modulated to the resonance frequency
since the tail transistor acts as a mixer which up-converts this noise.
B. Complementary Common
Drain Colpitts Oscillator
In the previous section, we showed that a differential
common drain can be realized by connecting two single-ended oscillators back to back. To make a complementary version of the differential oscillator, one can
instead of connecting the single-ended oscillators back

to back, stack them. A PMOS single-ended oscillator can
be placed on top of a NMOS single-ended, as shown
in Fig. 22 and replace the two inductors with a single
one, connected between the two oscillators as shown in
Fig. 23 [83].
Similar approaches have earlier been proposed for
common gate Colpitts [84] and cross-coupled Oscillators [85], which will be presented later in this paper.
Fig. 24 shows the Small Signal Model (SSM) of the Complementary Differential Common Drain (CDCD) Colpitts
presented in Fig. 23. In the SSM we have kept the passive
components in order show that this circuit resembles
the Balanced Differential Common Drain (BDCD) Colpitts oscillator shown in Fig. 17.
In this configuration, the stacked capacitors add in
series and the resonance frequency is then given by:
ft =

	

2
(7)
L C1 C2
C1 + C2

2r

FBAR
MN1
i1

i2

MN1

i1

i2

Vout2

Vout1

MN2

MN1

MN2

C2
i3

MN3

Vbias2

i3 MN3

(a)

MN2

C3

C1

MN3

C4

MN4

Vbias2

(b)

Figure 19. Cross-coupled transistors are used to improve the
transconductance of the Colpitts oscillator. (a) shows the circuit implementation and (b) the circuits switching behaviour.

Figure 21. gm-boosted differential common drain Colpitts
topology [58].

Vbias
MP1
C1
L
MN1
Vout1

MN2
C1

C3
C3

MN3

Vout

C2

FBAR

MP2

Vout2
MN1
MN4

C1

Vout

L
Vbias

Figure 20. gm-boosted differential common drain Colpitts
topology [35], it is a combination of the differential Colpitts
shown in Fig. 18 and a cross-coupled pair.
16 	

C2

MN5

Vbias
MN2

Figure 22. Schematics of the NMOS and PMOS single-ended common drain Colpitts oscillators.

IEEE CIRCUITS AND SYSTEMS MAGAZINE 		

FOURTH QUARTER 2020



IEEE Circuits and Systems Magazine - Q4 2020

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