Simulations

Validity of the proposed distortion reduction technique and low distortion active inductors are confirmed by HSPICE simulations. 0.18 $\rm\mu m$ CMOS process BSIM3 parameter sets are used in the simulations.

At first, the proposed active inductor shown in Fig. 8 is designed. Sizes of MOSFETs are summarize in Table I. Frequency characteristics are shown in Fig. 11. The active inductor acts as an inductor from 60 MHz to about 1 GHz. In this frequency range phase shift of the input voltage becomes more than 75 degree. Inductance of active inductor becomes about 15.7 nH. These values can be estimated by Eq. 17, however, they deviate slightly from the estimation.

Table I: Channel width and length of MOSFETs for Fig. 8

	M$_{1}$	M$_{2}$	M$_{3}$	M$_{4}$
W [$\rm\mu m$]	30	12	30	48
L [$\rm\mu m$]	0.36	0.36	0.36	0.36
	M$_{5}$	M$_{6}$	M$_{7}$	M$_{8}$
W [$\rm\mu m$]	1	1	5	11
L [$\rm\mu m$]	0.18	0.18	0.18	0.18

Figure 11: Frequency characteristics of the active inductor shown in Fig. 8

Figure 12 shows impedance controllability of Fig. 8. Even when the proposed distortion reduction technique is applied to the active inductor inductance of the active inductor can be controlled by $V_{g7}$. Its inductance is controlled from 13 nH to 24 nH. The series resistance $R_s$ and parallel resistance $R_p$ also changes as $V_{g7}$ varies because they are also function of $g_{m2}$.

Figure 12: Impedance controllability of Fig. 8

Effects of the proposed distortion reduction technique is shown in Fig. 13. Total harmonic distortion (THD) of an active inductor using the proposed distortion reduction technique and that of Fig. 4 is shown in the same figure for the comparison. THD of Fig. 8 is much smaller than that of conventional one. It becomes larger as input voltage becomes larger, however, it is kept below 2.5 % even when input voltage is 20 mV. On the other hand, THD of Fig. 4 increases rapidly. When input voltage is 20 mV its becomes more than 17 %. The propose distortion reduction technique can reduce the distortion of input voltage (or current) drastically.

Figure 13: Total harmonic distortion of the proposed active inductor (Fig. 8) and Fig. 4

Figure 14: Bandpass filter using proposed low distortion active inductor

As an application of the proposed low distortion active inductor, a 2nd order balanced bandpass filter shown in Fig. 14 is designed. The input signal and output signal of Fig. 14 are $v_{in1}-v_{in2}$ and $v_{out1}-v_{out2}$. The bandpass filter consists of two active inductor shown in Fig. 9, capacitor and input transconductor. A negative resistor circuit realized by MOSFETs are connected in parallel with the $LC$ resonator to enhance $Q$, however, the negative resistors is omitted in Fig. 14 for simplicity.

Figure 15: AC characteristics of bandpass filter shown in Fig.14

Frequency characteristics of Fig.14 is shown in Fig.15. Its center frequency is set to 1 GHz and its $Q$ is controlled by $V_{G3}$, $V_{G4}$ and the negative resistance circuit. Its center frequency deviate from 1 GHz slightly when $Q$ is controlled because this bandpass filter cannot control its center frequency and $Q$ separately. THD of the Bandpass filter is 0.26 % and this value is less than half of that of conventional one.