Design of Low Power Active Inductor

The realization of inductances L3 and L4 is based on the active inductor with a feedback resistor proposed in [56]. Fig. 4.19 (a) and (b) illustrate circuit schematic and the corresponding equivalent circuit. Through a simple derivation, the components of the equivalent circuit can be obtained as

( ) ( )

(a) (b)

Fig. 4.19 (a) Schematic and (b) equivalent circuit of the active inductor with a resistor in the feedback path.

4

p gs

C ≈ C

with Cgsi, gdsi, and gmi being the gate-source capacitance, output conductance, and transconductance of the corresponding transistors, respectively. In general, the quality factor of the active inductor can be promoted by decreasing the values of Gp

and Rs. From (4.26), the use of the feedback resistor RF does reduce the value of the parallel conductance Gp by introducing the factor (1+ gds4RF). In addition, a larger gm7gm4 is required as shown in (4.27) to get lower value of Rs. However, this will increase the whole dc power consumption in the active inductor since gmi is proportional to the current of transistors. To overcome this drawback, here we modify the active inductor circuit by using the gain-boosting technique [57] to achieve a small amount of dc current while maintaining a sufficient Q value. This is accomplished by

Fig. 4.20 Complete schematics of the proposed second UWB LNA.

using a cascode stage M4 and M6 to replace the only common-source transistor M4, resulting in a new active inductor configuration as shown in the complete schematic of the second UWB LNA in Fig. 4.20. The voltage gain in (4.27) can thus be substantially augmented and the value of Rs will be obtained as

( )

7 4 6 4 6 7 4 6

1 ( ) .

s m v v ds ds m m m

R ≈ g A A = g g g g g

Therefore, a low-power active inductor is easily accomplished due to the use of the cascode gain-boosting stage with a feedback resistor. On the other hand, the transistor component, which exists the parasitic effect such as a Miller parasitic capacitor will

2.0 2.4 2.8 4.8 5.2 5.6 6.0 0

200 400 600 800 1000

L

L

Quality Factor

Frequency (GHz)

Fig. 4.21 Simulated quality factor of the proposed active inductors L3 and L4.

common-gate amplifier) not only has less influence on its Miller parasitic capacitor, but also facilitates to reduce the Miller effect of the transistor M4. As a consequence, the proposed low-power active inductor is attractive and suitable in the nowadays microwave integrated circuits for the excellent high-frequency performance. Fig. 4.21 illustrates the simulated Q factor of the proposed active inductor, which shows that the active inductor exhibits a Q factor larger than 1000 at both 2.4 GHz and 5 GHz bands. These high-Q inductors undoubtedly provide a larger attenuation at the interferer frequencies, as can be observed from Fig. 4.18. Only 0.55 mA (for L4) and 0.8 mA (for L3) dc currents are required in the second UWB LNA circuit shown in Fig.

4.20, which are smaller than those in the previously literatures [56]–[58].

Moreover, it is obvious in (4.25) that the inductance of an active inductor is related to the transconductances, and thus the bias currents, of the transistors.

Consequently, the notch frequencies will be effectively tuned by adjusting the bias

5.0 5.2 5.4 5.6

Fig. 4.22 Inductance of an active inductor is related to the bias voltages of the transistors.

currents of the active inductor. The externally controlled bias voltages VG1 and VG2 in Fig. 4.20 are designed here for adjusting the bias currents to compensate the frequency shift due to the process variation, as can be observed from Fig. 4.22. The quality factor Q of the active inductor is necessary to further adjust after tuning the notch frequencies. The quality factor Q also can be modified by the bias voltages VG1

and VG2. As is clear from (4.25), the value of the equivalent inductor Leq is inversely proportional to gm4gm7. To avoid the notch frequency drifting more, the quality factor Q must be tuned by gradually increasing gm4 with a decrease of gm7, as can be observed from Fig. 4.23. By this way, the quality factor Q will be swept to optimize the maximum attenuation of the notch filter while maintaining a similar notch frequency.

On the other hand, a feedback mechanism, which has been adopted and

5.0 5.2 5.4 5.6 0

2 4 6 8 10 12 14 16

Frequency (GHz)

L

Inductance (nH) ₁₀₀

1000

g

=2.29 mS, g

m7b

=82 uS g

=2.36 mS, g

m7b

=80.3 uS g

=2.45 mS, g

m7b

=78.8 uS

Quality Factor

Fig. 4.23 Adjustable quality factor Q of an active inductor while maintaining a similar inductance value.

Fig. 4.24 Principle of the feedback technique for setting the notch frequency.

demonstrated in [43]-[44] and [59]-[60], is necessary to precisely set the notch frequency. The circuit architecture of the feedback technique is shown in Fig. 4.24. To

Fig. 4.25 Microphotograph of the fabricated UWB LNA. Die area is 0.9×0.85 mm².

begin with, a test signal such as 2.4 GHz is transmitted to the input of the LNA, and the output power at the node Vout can be measured with the received signal strength indicator (RSSI), which is a device available commonly in any wireless receiver. In addition, the RSSI output can be used to adjust the externally controlled bias voltages VG1 and VG2, so as to assure the detected test signal strength is minimum. As we can see, the notch frequency drift due to the process variation will be calibrated as long as a feedback mechanism is utilized. Consequently, the narrowband interferers can be effectively attenuated in order to coexist with other wireless technologies for UWB communication.

4.3.4 Simulation and Experimental Results

For the second UWB LNA shown in Fig. 4.20, the components values of the active inductors are as follows: M4a = 60 μm, M5a = 4.5 μm, M6a = M7a = 37.5 μm, M8a = 1.5 μm, M4b = 16.5 μm, M5b = 2.1 μm, M6b = 31.5 μm, M7b = 35 μm, M8b = 2.7 μm, RFa = 125 Ω ,and RFb = 1.1 kΩ. A die microphotograph of the second LNA is shown in Fig. 4.25 and the die area including pads is 0.9×0.85 mm².

1 2 3 4 5 6

Fig. 4.26 Measured and simulated power gain (S21) and input return loss (1/S11) of the second UWB LNA.

Fig. 4.27 Measured and simulated noise figure of the second UWB LNA.

The total dc power of the second UWB LNA without output buffer is 5 mW, drawn from 0.9 and 1.8 V power supply. The simulated and measured results of power gain and input return loss are depicted in Fig. 4.26. The measured peak gain is 15 dB from 3 to 4.8 GHz and the input return loss is better than 10 dB in the operation frequencies while the maximum rejections at 1.8, 2.4, and 5.2 GHz are 55, 48, and 45 dB, respectively. The simulated and measured noise figures are depicted in Fig. 4.27 and the measured minimum noise figure is 3.5 dB at 3.9 GHz.