between two inductors in the single-ended oscillators as described in [59], [89] and shown in Fig. 28. A comparative analyses of the phase noise of this circuit and a common-source cross-coupled differential pair, a Hartley and Armstrong topology is presented by [59]. The circuits were designed in 28 nm CMOS technology with an oscillation frequency of 10 GHz. Their results show that the Colpitts has the highest spectral noise in this comparison. Fig. 29 shows a similar configuration, where the tail transistors are replaced with coupled inductors. This circuit will give increased transconductance and can potentially be operated at lower voltages at high frequencies up to 60 GHz [90]. Making an accurate coupling between two inductors might be challenging in integrated circuits as inductors are usually bulky. An easier way of creating the relation between to single-ended Colpitts is by using a crosscoupled transistor pair as shown in Fig. 30 and Fig. 31. This configuration is also referred to as gm-boosting as the cross-coupled pair increases the effective transconductance of the oscillator. In Fig. 30, the cross coupling is combined with inductive coupling. In Fig. 31 the cross coupling is applied to the active devices instead of the bias transistors to improve the gm-boosting. A tunable 5 GHz PMOS version of the differential circuit shown in Fig. 30 was designed in [81]. The circuit was designed using PMOS in a 180 nm CMOS in order to reduce the flicker noise. The measurement results showed a phase noise of 120.42 dBc/Hz at 1-MHz offset and 120.99 dBc/Hz at 4.61 GHz. The power consumption of the oscillator is 3 mW, with a FOM of 189.6. The circuit in Fig. 28 is made of two independent CG oscillators and will only work as differential oscillator if there is a coupling between the two inductors, i.e. they work as transformers. This circuit cannot directly be used for driving resonators or FBARs as there is no coupling between the two single-ended oscillators. When using crystals and FBARs, a cross-coupled pair must be used as shown in Figs. 30 and 31. Different varieties of this circuit using cross-coupled transistors are reported in [81]. [92] Shows that when cross-coupling is applied, one can achieve better phase noise by removing capacitors C1 and C3 in the circuit shown in Fig. 31. Fig. 32 K12 K12 Vout1 C1 L1 L2 Vbias1 MN1 Vout1 Vout2 MN2 C3 MN4 C4 L1 L2 Vout2 Vbias1 MN1 C1 MN2 C3 Vbias2 C2 MN3 C2 MN3 Figure 28. Common gate differential Colpitts topology with inductive coupling between the two oscillators. MN4 Figure 30. gm-boosted common gate differential Colpitts topology [91]. K12 Vout1 L2 L1 Vout2 Vbias1 MN2 MN1 C1 Vout1 L3 C1 L4 C4 C2 Figure 29. Common gate differential Colpitts topology with inductive coupling between the two oscillators and replacing biasing transistor with inductors for operations up to 60 GHz [90]. 18â Vout2 C3 K34 C2 FBAR FBAR C3 Vbias C4 Figure 31. gm-boosted common gate differential Colpitts topology. IEEE CIRCUITS AND SYSTEMS MAGAZINE FOURTH QUARTER 2020