Low-noise-amplifier (LNA) design requires tradeoffs, often among such goals as noise figure, gain, linearity, and stability. In addition, portable applications call for low power consumption. But through the use of a common- gate (CG) architecture for input impedance matching and reduced power consumption through currentreuse techniques, an RF CMOS LNA was developed with 15.5-dB forward gain and 1.68 dB noise figure at 2.4 GHz. With its excellent input and output impedance matching, it consumes only 1.05 mW power.

Low-voltage and current-reuse design approaches can effectively decrease power consumption,^{1-9} including the use of cascode amplifier configurations.^{1-4} With the currentreuse topology, desirable gain can be achieved with relatively low current consumption. However, due to the use of multiple transistors, it employs increased supply voltage. To lower the supply voltage, a folded topology has been proposed.^{5,6} The required supply voltage is reduced by one transistor compared with that of a cascade amplifier. Unfortunately, with more than one gain stage, the total current consumption of a CMOS LNA may not be minimized. A current-reuse, two-stage common-source (CS) topology can provide high gain at low supply voltage and power consumption, although at somewhat elevated noise levels.^{7-9} With a current-reuse, two-stage CG topology, however, both high gain and low noise figure can be achieved at low voltages and power consumption.

The inductor-degenerated CS topology is a popular LNA choice for narrowband applications; it provides both high gain and relatively low noise figure. But it provides low noise figure via high power consumption and/or high-quality-factor (high-Q) off-chip inductors. The noise figure of these structures increases sharply as the power consumption is decreased. ^{13} For a low-power receiver, an LNA based on a CG approach is the preferred topology.^{11} At 2.4 GHz, CG LNAs typically offer lower noise figures than CS LNAs for power consumption below 3.1 mW.^{12} Compared to CS LNAs, CG LNAs feature broadband input match and better linearity and stability.^{13} To achieve a low noise figure with low power consumption, a CG LNA input structure was used (* Fig. 1*); by tuning input inductor LS and capacitor C1, the noise figure can be reduced to minimum. In addition, this structure's current-reuse two-stage topology provides relatively high gain with reduced power consumption.

In * Fig.1*, CS MOS transistors M

_{1}and M

_{2}represent the first and second stages, respectively, of the LNA. They share the same DC bias current flowing through L

_{1}to reduce power consumption. The amplified RF signal from M

_{1}is directed to the gate node of M

_{2}through coupling capacitor C

_{4}. Capacitor C

_{3}is the RF bypass for M

_{2}. Inductor LS and capacitor C

_{1}help to obtain simultaneous power and noise matching for the input stage, while output matching is provided by Ld, C

_{2}, and C

_{5}. The LC network L

_{1}-C

_{4}between the gain stages is used for interstage matching.

The proposed LNA topology is basically a two-stage amplifier (* Fig. 2*). The overall transconductance is equal to the multiplication of the individual transconductances of devices M

_{2}and M

_{2}. Therefore, it has a comparable power gain to the cascaded CS amplifier topology.

The input of the LNA must be matched to the output of the filter following the antenna to minimize reflections between the LNA and the antenna. The proposed LNA is treated as a two-stage amplifier, with simplified circuit model in * Fig. 2*. The conditions for input matching7 are shown in Eqs. 1-3:

where Z_{source} is the impedance seen at the gate of M_{1} when looking toward the antenna,

Zin,1 is the input impedance of M1, and ZL is the load impedance.

A simple, small-signal equivalent circuit of the first gain stage is illustrated in * Fig. 3* where RS is the source impedance, and gm represents the transconductance of the MOSFETs. In

*, the input impedance of M1, Zin, is expressed by Eq. 4:*

**Fig. 3**From Eq. 4, the input impedance matching to a 50-Ohm system can be achieved by

From Eqs. 5 and 6, the operating frequency, ?0, can be derived as

From the input matching conditions described in Eqs. 1-3, the effective transconductance of the first stage, g_{M1,eff}, can be written as:

where s = j?_{0} and g_{M1} is the transconductance of M1. From Eqs. 1-3, it is possible to also know the effective transconductance of the second stage, g_{M2,eff}, as

where g_{M2} is the transconductance of M_{2} and C_{gs2} is the gate-to-source capacitance of M_{2}. The overall effective transconductance is equal to the multiplication of the individual transconductance of M_{1} and M_{2}. Therefore, two cascaded stages are employed in the proposed LNA topology to boost the amplifier gain for ultra-low-voltage operation.

As the first active building block in an RF receiver, the LNA is required to provide sufficient gain such that the noise contributed from the following stages can be effectively suppressed. In a cascade amplifier, the total noise figure can be expressed^{14} by Eq. 10:

where NF_{n} and G_{n} are the noise figure and gain of the nth stage, respectively. According to Eq. 10, the noise figure and gain of the first stage are both very important for total noise figure contribution. Thus, the first stage should be carefully designed to achieve a good input matching and to make a tradeoff among gain, noise figure, and power consumption.

The noise factor of a two-port network, such as the LNA, can be expressed^{1} as Eq. 11:

where F_{min} is the minimum noise factor, Gn is the equivalent noise conductance, Z_{source} = R_{source} + jX_{source} is the impedance seen at the input of the LNA when looking toward the antenna, and Z_{opt} = R_{opt} + jX_{opt} is the optimum source impedance. Although Fmin can be minimized by properly choosing the width of the MOS device, this is not a good choice for constant DC current. To minimize the NF, , it is crucial to design the matching network of the LNA such that the second term in Eq. 14 is close to zero, which in turn means that Z_{source} should be close to Z_{opt}.

The matching conditions for minimum noise figures of the cascaded gain stages7 are given by Eq. 12:

with the matching conditions specified in Eqs. 1-3 and 12 resulting in

From Eq. 13, this yields

From * Fig. 2*, the relations of Eqs. 16 and 17 can be found:

According to the definition of a matching network, the noise and power matching of the LNA are achieved when Eqs. 14 and 15 are satisfied. Therefore, when R_{opt} is larger than R_{in,1}, there is a tradeoff between the noise figure and S11. Using a CS LNA configuration with inductive degeneration for input matching, power and noise matching cannot be obtained simultaneously at low current bias, thus the noise figure could be potentially high for low-power applications. For a low-power LNA, a CG LNA is the preferred topology.

In the proposed LNA, even when the MOSFET's R_{opt} is larger than R_{in,1}, from Eqs. 16 and 17, it is possible to adjust the sizes of M_{1}, LS , and C_{1} to achieve optimum input matching and noise matching simultaneously. In addition, a value of S_{11} of less than -10 dB is adequate for an LNA in most applications.^{1} Therefore, the value of R_{source} can be brought much closer to the value of R_{opt} by altering the values of L_{S} and C_{1} for better noise matching, while S_{11} is less than -10 dB. Noise figure responses with various values of L_{S} and C_{1} are shown in * Figs. 4(a)* and

*, respectively, indicating that is it possible to reduce the noise figure as low as possible by adjusting the values of L*

**4(b)**_{S}and C

_{1}. With shunt capacitance C

_{1}, the value of L

_{S}can be decreased to a level suitable for on-chip integration.

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Circuit simulations for the proposed design were performed with the Advanced Design System (ADS) suite of software tools from Agilent Technologies. Measured S-parameters are shown in * Fig. 5* for comparison. The maximal power gain is 15.5 dB at 2.4 GHz, S11 is -10.5 dB at 2.4 GHz, and S

_{22}is -12.3 dB at 2.4 GHz. The measured noise figure reaches 1.68 dB at 2.4 GHz. The LNA's measured input third-order intercept (IIP3) is -6.5 dBm. The DC power consumption is only 1.05 mW from a 0.9-V supply.

A commonly used figure of merit (FOM) for comparing low-power LNAs is the ratio of power gain to DC power consumption (gain/DC power). A more meaningful FOM includes the effects of amplifier gain, noise figure, linearity (IIP3), operating frequency (f0), and DC power consumption (Pdc)15 as shown in Eq. 18.

The table shows data from a number of low-power CMOS LNAs. It shows that this ultra-low-power LNA can provide better overall performance in terms of gain, noise figure, linearity, DC power consumption, and frequency of operation. The LNA was fabricated with a standard 0.18- m CMOS technology and offers the best gain to DC power ratio and overall FOM among recently published low-power CMOS LNAs.

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