A Low Gain Variation LC-VCO With Mutual Inductive Tuning for K _VCO Linearity Compensation

A high‐linearity LC‐VCO with combined MOS varactors and bulk‐biased PMOS varactors for gain variation compensation

“…Compared with prior state-of-the-art works of low gain-variation VCOs in Table 1, the linearity of this work is similar to that reported in Wang et al, 20…”

“…While the control voltage V ctrl and bulk-biased PMOS varactors comply with the nominal 1.8 V supply in the 180-nm complementary metal-oxide semiconductor (CMOS) process, which may be required by other analog circuitry. 20 As shown in Figure 3B, the conventional MOS varactors are placed between the two sets of PMOS varactors, M 3 /M 4 and M 5 /M 6 , in the proposed linearity-compensation network, with layout area of only 20% compared with that of the conventional bias-shifted compensation network which is shown in Figure 3A. Furthermore, the proposed linearitycompensation network can be paralleled with more sets of bulk-biased varactors to achieve better linearity without dealing with the layout constraint of the bias-shifted topology due to the large DC-blocking capacitance, for example, two sets of PMOS varactors in this design as opposed to only one set in Peng et al 4 Figure 4A shows the C-V curves of the three sets of varactors, with bulk voltage of M 5 -M 6 biased at 0.75 V and bulk voltage of M 3 -M 4 biased at 1.4 V. The combined C-V curve of the total capacitance of the LC tank versus the control voltage exhibits a wide linear range from 0.6 to 1.4 V. As shown in Figure 4B, compared with that of the bias-shifted topology, the quality factor of the proposed capacitor network in Figure 2B is almost the same in the linear control range.…”

“…Various techniques have been proposed to improve the linearity of VCOs. [16][17][18][19][20] In Nakamura et al, 16 a mutually coupled LC-tank is added to the conventional LC-tank. However, the linear analog control voltage range corresponding to the oscillation frequency is limited to less than 0.4 V. The similar issue exists in Young-Jin et al, 17 where the capacitor array in series with variable capacitor is adopted to reduce the VCO gain variation, which killed the tuning range due to the reduced variable capacitance linear range.…”

“…Both phased‐locked loops (PLL), 7–10 and frequency modulated continuous‐wave (FMCW), 11–15 require high linearity VCOs since gain variations of VCOs directly affect the loop dynamics of the PLL as well as the accuracy of the FMCW. Various techniques have been proposed to improve the linearity of VCOs 16–20 . In Nakamura et al, 16 a mutually coupled LC‐tank is added to the conventional LC‐tank.…”

“…To resolve the above issue of the limited linear control voltage range, a pair of bias‐shifted inversion‐mode MOSFETs (I‐MOS) in parallel with conventional varactors is introduced to improve the linearity in Lim et al 18 This technique employs extra DC‐blocking capacitors and bias resistors to realize the bias‐shifted scheme, which raises the design complexity and introduces additional parasitic capacitance and resistance. Multiple pairs of I‐MOS varactors with different bulk‐bias are adopted to enhance the linearity, but with a limited control voltage range, in Karmi et al 19 A transformer is introduced in Wang et al 20 to adjust the equivalent inductance of the resonant tank by varying the current flowing into the secondary coil, achieving a wide linear control voltage range, at the cost of the deteriorated phase noise performance.…”