# LNA Quiets 3.1 To 10.6 GHz

Ultrawideband (UWB) communications systems can operate with a variety of modulation formats in the bandwidth allocated by the United States Federal Communications Commission (FCC) from 3.1 to 10.6 GHz. In all cases, a broadband low-noise amplifier (LNA) is essential to the receiver, with low DC power consumption. One solution is a low-voltage variable-gain CMOS design capable of 14-dB gain from 3.1 to 10.6 GHz with minimal noise figure of 3.2 dB.

Although different wideband pulse shapes and pulse modulation schemes have been proposed for future UWB transmission systems, two major proposals are now the candidatures for the IEEE 802.15.3 standard^{1}: the direct sequence (DS)-UWB2 approach and the multi-band orthogonal frequency- division-multiplex (OFDM) UWB approach.^{3} A wideband LNA is an important building block in an UWB receiver. A number of low-noise designs have been developed based on silicon CMOS device technology.^{4-8}

However, conventional UWB LNAs cannot provide the variable-gain function. A variable-gain LNA (VG LNA) not only can prevent a receiver from saturation when the input signal is relatively large, but also can mitigate the linearity requirement of the following mixer and maximize the dynamic range of the overall system.^{9} A number of UWB VG LNAs have been reported in the literature. For example, several researchers proposed a distributed VG LNA.^{10} The main advantages of the distributed amplifier are its intrinsic broadband characteristic, good input and output matching, however, the power consumption is high and the chip area is relatively large. Other researchers proposed a VG LNA with broad bandwidth and good gain flatness, however, the gain and gain-variable range was limited and the power consumption is relatively high.^{11}

To meet the conditions for broadband impedance matching from 3.1 to 10.6 GHz with adequate variablegain range, an amplifier was designed based on a common-gate transistor as the input stage. The LNA uses a modified cascade structure aimed at low power consumption. The commongate stage and its associated small-signal circuitry^{9} is shown in * Fig. 1*. Source inductor L

_{S}is placed between the source of the metal-oxide-semiconductor (MOS) transistor to form an inductive-capacitive (LC) resonator with gate-to-source capacitance, C

_{gs}. As reference 12 points out, the finite output resistance of the transistor also influences LNA performance, since the load impedance of the commongate stage and the input impedance of the next stage degrade impedance matching and noise performance due to the short-channel MOS transistor's low output resistance, about 500 O for an 0.18-μm CMOS process.

^{13}

From ref. 9, the input impedance can be written as Eq. 1:

where Z_{S}(?) and Z_{0}(?) are given by Eqs. 2 and 3, respectively,

where Z_{L} = the impedance of the load,

Z_{in2} = the input impedance of the next stage, and

g_{m1} = the transconductance of the MOS transistor in a common-gate configuration.

Assuming that both Z_{S}(?) and Z_{0}(?) are composed of high-quality-factor (high-Q) inductors and capacitors and thus can be regarded as purely reactive within the frequency band of interest:

and Eq. 1 can be rewritten by substituting in Eqs. 4 and 5 to get Eq. 6.

The term 1/X_{S}(?) in Eq. 6 dominates the imaginary part because g_{m1}R_{0}X_{0}(?)

<< R^{0}_{2} + X^{0}_{2}(?) throughout the UWB frequency band. Given that g_{m1}X_{0}(?)

<< R^{2}_{0} + X^{2}_{0}(?), the real part in the denominator will remain constant across the 3.1-to-10.6-GHz range.

As is well known, lowering the supply voltage is an effective way to reducing power consumption. Still, it is difficult to reduce the power supply of a cascade topology to under 1 V.^{5,8} To meet requirements for high gain, low noise figure, and low power consumption, the classical cascade topology has often been modified.^{14} In the current report, the structure has been modified from a narrowband circuit to one for use in ultrawideband applications.

When the cascade configuration is changed to a parallel topology, the current is no longer reused by the common- gate stage and common-source stage. This lack of reuse will result in an increase in DC power consumption. In order to minimize the use of bias current, a current mirror is added to the common-source stage. At the same time, a resistor is added to the source of the common-gate stage to control the DC current.

In the cascode topology, the common- gate transistor (M3 in * Fig. 3*) can be used to improve power gain and achieve variable gain control without influencing input and output match. The common-gate configuration is also used to enhance the reverse isolation and high-frequency response, and restrain the Miller effect. The power gain for this stage is expressed as Eq. 7, where

g_{m2} = the transconductance of M_{2};

g_{m3} = the transconductance of M_{3}; and

C_{D3} = the total parasitic capacitances at the drain of transistor M_{3}.

Equation 7 shows that the gain is proportional to g_{m2}. g_{m2} and I_{D} can be written as Eqs. 8 and 9:

where

K = a transconductance parameter;

W = the width of M_{2} and M_{3};

L = the length of M_{2} and M_{3};

I_{D} = the DC drain current of the second stage;

? = the channel length modulation parameter of transistors M_{2} and M_{3};

V_{ds2} = the drain-source voltage of transistor M_{2}; and

V_{gs2} = the gate-source voltage of M_{2}.

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In fact, transistor M_{3} can be seen as the load of transistor M_{2}. It has impedance of Zds3. When VC is increased, from Eqs. 8 and 9 it can be seen that I_{D} would increase because impedance Z_{ds3} would decrease as VC increases and V_{ds2} is also increased; thus transconductance gm2 is also increased. From these relationships, it can be concluded that gain can be controlled by varying V_{C}**see Fig. 2(a)**>.

For a cascade system, the noise figure of the first stage is critical to the whole circuit, especially when the common-gate stage is employed for UWB input matching. The commongate configuration is generally noisier than narrowband matching techniques such as inductive source degeneration. The noise factor of the common-gate stage can be written as^{12}:

where c = the correlation coefficient,

and theoretically c = -0.395j for longchannel devices. Additional parameters, a and d, are process constants.

As *g _{m1}* appears in the denominators of all noise components, it can be increased (by reducing R

_{ref1}in

**) to improve the overall noise performance. However, the input matching degrades as**

*Fig. 3**g*increases

_{m1}*>.*

**see Fig. 2(b)** In the circuit design, a large (1-pF) capacitor (C_{1} in * Fig. 1*) is placed between the gate of transistor M

_{1}and ground, for two reasons. This ensures good AC grounding and bypasses the noise contributed by the biasing circuit. Also, with the drain-gate capacitance of transistor M

_{1}, this forms a noiseless capacitive divider as a feedback network.

^{15}The design of the proposed variable-gain LNA is based on an 0.18-μm RF CMOS process from TSMC. All transistors employ the minimum gate length of 0.18 μm for minimum parasitic capacitance. According to ref. 16, the optimized gate width for transistor M

_{1}is 100 μm. Simulations show that the best input matching impedance is achieved with a source inductance, L

_{S}, of 6.9 nH.

In the circuit, current mirrors have been added for M_{2} and M_{4}. By adjusting the value of reference resistor R_{ref2}, bias current is set to 2 mA. The gate widths of transistors M_{2} through M_{5} are also set to 100 μm. A resistance of 200 O is chosen for source resistor RS so that currents of M_{2} and M5 are both set to 2 mA. The gate width of M_{9} and M10 is selected as 10 μm. A buffer is added at the output to drive output test equipment and also output pad capacitance. It is composed of transistors M_{6} and M_{7}. The output impedance is designed to be 50 O for desired output impedance matching. The parasitic capacitance of M_{4} serves as the load of the UWB LNA, which emulates the input impedance of the connected mixer in the system. The gate widths are 30 m for M_{6} and 60 m for M_{7}. M_{6} was sized at one-half the size of M_{7} to save DC current.

Computer-aided-engineering (CAE) software from Cadence Design Systems was used to simulate the circuit, as shown in * Figs. 4* through

*. The input and output reflection coefficients were maintained below -10 dB from 3.1 to 10.6 GHz (*

**7***).*

**Fig. 5***and*

**Figures 4***show the pre-layout and post-layout simulation results for forward transmission, S*

**5**_{21}. The results show that S

_{21}dropped from 20 dB to 14 dB, within 0.4 dB, from 3.1 to 10.6 GHz. This is because the parasitic resistors and capacitors degrade the power gain, especially at higher frequencies. The minimum noise figure is 3.2 dB (

*), while S*

**Fig. 6**_{12}drops below -75 dB in the UWB band, indicating good reverse isolation (

*). The average noise figure is 5.8 dB. The LNA has a 1-dB compression point of -37 dBm for a die size of 1.3 x 0.73 mm, including pads and guard ring. DC power consumption is 10 mW, including the buffer, for a supply voltage of +0.85 VDC. The table compares this LNA with recently reported LNAs.*

**Fig. 7**ACKNOWLEDGMENTS

This work was supported by the Open Fund Project of the Key Laboratory of Hunan Universities, Hunan, China, (grant No. 09K011) and in part by the National Natural Science Foundation of China (grant No. 60776021).

REFERENCES

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