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Unformatted text preview: Amplifiers Exploiting Thermal Noise Canceling: A Review
Eric A.M. Klumperink1, Federico Bruccoleri2, Peter Stroet3, Bram Nauta1
1 University of Twente, MESA+ Research Institute, IC Design group, PO box 217, 7500AE Enschede, The Netherlands, 2 Catena Microelectronics BV, Delft, The Netherlands 3 Linear Technology, Milpitas, USA Abstract — Wideband LNAs suffer from a fundamental tradeoff between noise figure NF and source impedance matching, which limits NF to values typically above 3dB. Recently, a feedforward noise canceling technique has been proposed to break this tradeoff. This paper reviews the principle of the technique and its key properties. Although the technique has been applied to wideband CMOS LNAs, it can just as well be implemented exploiting transconductance elements realized with other types of transistors. To examplify this claim, measurement results on a bipolar amplifier exploiting noise cancellation will also be presented. instability problems [2,3,4]. In earlier work [5,6], LNA circuits with partial noise cancellation have been found, via systematic circuit topology generation [7]. However, those circuits still have constraints on NF upon ZIN=RS. In contrast, the technique presented in this paper can, at least in principle, achieve arbitrarily low NF, at the cost of power consumption. This paper reviews the basis of the technique and discusses its key properties. Furthermore several examples of circuits exploiting full or partial noise cancellation will be given. NEF for a long channel MOSFET is theoretically 2/3, but for a practical deepsubmicron MOSFET between 1 and 2, whereas resistive degeneration of a transconductor results in NEF=1. Thus, such wideband MOSFET LNAs are limited to F>2 or NF>3dB, even for high gain. To be best of our knowledge, only amplifiers exploiting global negative feedback (shuntfeedback) can break this tradeoff between NF and impedance matching, but they are prone to instability [1]. In contrast, we propose a feedforward thermalnoise canceling technique enabling low NF and source impedance matching, without 12th GAAS Symposium  Amsterdam, 2004 I. INTRODUCTION Wideband LowNoise Amplifiers (LNAs) are used in receiving systems where the ratio between the bandwidth and its center frequency can be as large as two, for instance in analog cable TV (50850 MHz), and satellite (9502150 MHz) or terrestrial digital (450850 MHz) video broadcasting. Moreover, a wideband lownoise amplifier can replace several LCtuned LNAs in multiband or multimode narrowband receivers. A wideband solution saves chiparea and fits better to the trend towards flexible radios with as much signal processing (e.g.: channel selection, image rejection, etc.) as possible in the digital domain (towards “software radio”). Highsensitivity integrated receivers require LNAs with sufficiently large gain, noise figure NF well below 3dB, adequate linearity and source impedance matching ZIN=RS. The latter is to avoid signal reflections on a cable or alterations of the characteristics of the RF filter preceding the LNA, such as passband ripple and stopband attenuation. Fig.1ad shows wellknown wideband amplifiers capable of matching a real source impedance RS. These amplifiers suffer from a fundamental tradeoff between their noise factor F (NF=10log10(F)) and impedance matching, ZIN=RS. Assuming large gain, low F requires a large gmi or Ri. However, impedance matching demands a fixed gmi=1/RS or Ri=RS. Modeling transistors as a transconductance gm, and assuming current noise spectral density 4kT⋅NEF⋅gm, analysis renders [4]: (1) FLNA ≥ 1 + NEF Fig. 1. Wellknown wideband LNAs capable of impedance matching for Ri =Rs or gmi=1/Rs (biasing not shown). The paper is organized as follows. Section II reviews the principle of the noise canceling technique, while section III discusses its key properties and limitations. Section IV shows some practical examples of amplifiers exploiting noise cancellation. Finally, section V draws conclusions. II. NOISE CANCELING PRINCIPLE To understand the principle of noise canceling, consider the amplifier stage of fig. 1c redrawn in fig. 2. Its input impedance is ZIN=1/gmi and the voltage gain is AVF,MS=VY/VX=1gmiR where the index “MS” refers to the matching stage in fig.1c. For ZIN=RS its F is larger than 1+NEF, as discussed in the previous section. Let’s now analyze the signal and the noise voltages at the input node X and output node Y, both with respect to ground, due to the noise current In,i of the impedance matching MOSFET. Depending on the relation between ZIN=1/gmi and RS, a noise current (RS,gmi)·In,i, flows out of the matching MOSFET through R and RS (fig. 2a), with 0< <1. This current causes two instantaneous noise voltages at nodes X and Y, which have equal sign. On the other hand, the signal voltages at nodes X and Y have opposite sign (fig. 2b), because the gain AVF,MS is negative, assuming gmiR>1. This difference in sign for noise and signal makes it possible to cancel the noise of the matching device, while simultaneously adding the signal contributions constructively. This is done by creating a new output, where the voltage at node Y is added to a scaled negative replica of the voltage at node X. A proper value for this scaling factor renders noise 371 canceling at the output node, for the thermal noise originating from the matching device. splitting its noise current In,Ri in two correlated sources to ground, at the output node Y and the input node X. The former is cancelled for Av=Av,c, the latter is not. R RS + VS X gmi Y + In,i Av Ampl. “A” a)
“A” plus adder Fig. 2 Matching MOSFET noise (a) and signal (b) voltage at nodes X and Y for the amplifier in fig. 1c (biasing not shown). R Y In,i gm3 ZY gm2 Output ZL Fig. 3a shows a straightforward implementation using an ideal feedforward voltage amplifier “A” with a gain –Av (with Av>0). By circuit inspection, the matching device noise voltages at node X and Y are: VX ,n ,i = α (RS , g mi ) ⋅ I n ,i RS = α ⋅ I n ,i RS (2) VY ,n,i = α ⋅ I n ,i (RS + R ) The output noise voltage due to the noise of the matching device, VOUT,n,i is then equal to: VOUT ,n ,i = VY , n ,i − V X ,n ,i ⋅ Av = α ⋅ I n ,i (R + RS − Av R S ) (3) Output noise cancellation, VOUT,n,i=0, is achieved for a gain Av equal to:
A v ,c = VY , n , i VX , n , i =1+ R RS X + VS CIN gmi b)
Fig. 3. (a) Wideband LNA exploiting noisecanceling, (b) Elementary implementation of amplifier “A” plus adder (biasing not shown). III. PROPERTIES AND LIMITATIONS We will now discuss some key properties of noise cancellation, starting with the achievable noise factor. A. Noise factor The noise factor F of the LNA in fig. 3a can be written as: (6) F =1 + EFMD + EFR + EFA where the “excess noise factor” EF is used to quantify the contribution of different devices to F, and index MD refers to the matching device, R to the resistor R, and A to amplifier “A”. For the implementation in fig. 3b, expressions for EF for ZIN=RS, assuming equal NEF, and cancellation for Av=Av,c become:
EFMD , c = 0 EFR , c = − EFA = 2 A VF , c = RS R (4) where the index “c” denotes the cancellation. On the other hand, signal components along the two paths add constructively, leading to an overall gain (assuming ZIN=1/gmi=RS and Av=Av,c): V R R (5) A = OUT = 1 − g R − Av, c = −g R − = −2
VF,c VX mi mi RS RS From equation (4), two characteristics of noise canceling are evident: 1. Noise canceling depends on the absolute value of the real impedance of the source, RS (e.g.: the impedance seen "looking into" a terminated coax cable). 2. The cancellation is independent on (RS,gmi) and on the quality of the source impedance match. This is because any change of gmi equally affects the noise voltages VX,n,i and VY,n,i. Fig. 3b shows a simple implementation of the noisecanceling LNA in fig. 3a. Amplifier “A” and the adder are replaced with the commonsource stage M2M3, rendering an output voltage equal to the voltage at node X times the gain Av=gm2/gm3. Transistor M3 also acts as a source follower, copying the voltage at node Y to the output. The superposition principle renders the addition of voltages with an overall gain AVF=1gmiRSgm2/gm3. Note that any small signal that can be modeled by a current source between the drain and source of the matching device is cancelled too (e.g.: 1/f noise, thermal noise of the distributed gate resistance and the bias noisecurrent injected into node Y and even distortion terms). However the noise of R is not cancelled. This can be seen (7) NEF 1 3 2R S + + g m2 R S R R 2 The noise factor at cancellation, Fc, is thus only determined by EFA,c and EFR,c, which are both not constrained by the matching requirement. EFA,c can be made arbitrarily smaller than 1 by increasing gm2 of its input stage, at the price of power dissipation. The minimum achievable Fc is now determined by EFR,c. The latter can also be significantly smaller than 1 when the gain AVF,c is large, which is desired anyhow for an LNA. In practical design, Fc can be lowered below 2 (i.e. 3dB) by increasing gm2RS until it saturates to Fc,min=1+EFR,c=1+RS/R. B. Robustness for component spread The noise canceling technique is relatively robust to device parameter variations. The cancellation depends only on a reduced set of device parameters. For instance, 372 12th GAAS Symposium  Amsterdam, 2004 the impedance from node Y to ground ZY (e.g.: gd of the matching device), the load ZL (e.g.: gd and gmb of M3) and gmi of the matching device in fig. 3b do not affect the cancellation because they “load” the two feedforward paths in the same fashion. On the other hand, any deviation of the source resistance RS and the gain Av from their nominal values RS,NOM and Av,c affect the cancellation, as shown by equation (3). For a typical practical case with NEF=1.5 and Av,c=7, δRS/RS,NOM and δAv/Av,c as large as ±20% are needed in order to rise EFMD to only 0.1 [4], one tenth of the contribution of the input source. Thus, the sensitivity to variations of RS and the gain Av is low. C. Advantages compared to negative feedback As shown in the previous section, the noise canceling technique is capable of NF well below 3dB upon ZIN=RS. Similar noise performance could also be achieved exploiting shuntfeedback. However, noise cancellation offers several advantages: • It is a feedforward technique free of global feedback, so instability risks are greatly relaxed. • To first order, ZIN depends only on gmi. Thus, ZIN is less sensitive to process spread. • Implementing variablegain at ZIN=RS is more straightforward due to the orthogonality between the gain AVF and ZIN (changing the value of R and Av changes the gain, but not ZIN). Furthermore, it can be shown [3] that simultaneous noise and power matching is achieved. D. Frequency dependence of noise cancellation Parasitic capacitors not only limit the signal bandwidth but also degrade noise cancellation at high frequencies. The simplified case of fig. 3b with CY=CL=0 appears to be adequate to model the main trend. Here, CIN accounts for the parasitic capacitance contributed to the input node mainly by the matching device and amplifier “A”. This simple model is realistic because: (a) CY and the load CL in fig. 3b do not affect the cancellation and (b) CL does not affect the F of the LNA standalone. The noise current α·In,i flowing out from the matching device “sees” a complex source impedance ZS(f)= RS/(1+j2πfCIN) as shown in fig. 3b. In this case, the output noise due to the matching device, VOUT,n,i(f), is obtained replacing RS with ZS(f), resulting in a frequency dependent noise factor, Fc(f), which can be written as: 2 Fc ( f ) = Fc + ( Fc − 1 + NEF ) ⋅ ( f / f 0 ) (8) where Fc is the lowfrequency noise factor as given in (6) and f0=1/(π·RS·CIN) is the input pole. For Fc smaller than 1+NEF, Fc(f)Fc increases with f/f0 mainly because the cancellation degrades. IV. PRACTICAL CIRCUIT EXAMPLES A. Wideband Noise Cancellation LNA A wideband LNA according to the concept of fig. 3b was designed in a 0.25µm standard CMOS process. Table 1 summarizes the achieved performance and fig.4 shows the simulated and the calculated noise figure using formula (8). The measured NF is below 2.4dB over more than one decade (1502000 MHz) and below 2dB over more than 2 octaves (2501100 MHz). At low frequency, NF rises due to a ACcoupling highpass filter. Fig. 4. Noise Figure [dB] as a function of frequency for the CMOS LNA [2,4]. Table. 1. Performance summary of the CMOS LNA [2,4]. B. Other Noise Cancellation Configurations The concept of noise canceling can be generalized to other circuit topologies according to the model shown in fig. 5a. It consists of the following functional blocks: (a) An amplifier stage providing the source impedance matching, ZIN=RS. (b) An auxiliary amplifier sensing the voltage (signal and noise) across the real input source. (c) A network combining the output of the two amplifiers, such that noise from the matching device cancels while signal contributions add. Fig. 5b shows one of the possible implementations [3]. Noise cancellation occurs for R1=gm2RSR2, while low F requires high gm2. Fig. 5. Generalized noise cancellation concept and one possible alternative circuit implementation. 12th GAAS Symposium  Amsterdam, 2004 373 C. Bipolar LNA As stated in the previous subsection, noise cancellation can also be exploited in other technologies. To exemplify this claim, a bipolar LNA will be discussed. The LNA was designed in a 15GHz industrial bipolar process, aiming for IFapplications in the 10100MHz range. Fig. 6 show the core of the LNA and table 2 summarizes its performance. Measurements were done using two singleended amplifier to create a quasibalanced amplifier, where transformers were used as baluns. The loss of the transformers degrades noise performance slightly, but still a noise figure below 2dB is achieved. LNAs operating at the same gain. Detailed analysis [5,7] shows that this is due to (partial) noise cancellation of the noise of the common gate device (note that there are again two paths to the output, one via the common gate device Ma, one via the common drain device Mb). Moreover, the noise figure is almost independent of the gain, which is useful in LNAs requiring variable gain. Measurements on an LNA realized in a 0.35µm standard CMOS process show NF<4.4dB for 611dB gain, very good linearity (IIP3=15dBm) at only 1.5mA current consumption [6]. V. CONCLUSION In this paper, noise canceling was reviewed as a circuit technique, which is able to break the tradeoff between noise factor F and source impedance matching. This is done placing an auxiliary voltagesensing amplifier in feedforward to the matching stage such that the noise from the matching device cancels at the output, while adding signal contributions. In this way, one can minimize the LNA noise figure, at the price of power dissipation in the auxiliary amplifier. By using this technique in an LNA, low noise figures over a wide range of frequencies can be achieved, without the instability issues that are typically associated with wideband negative feedback amplifiers. Other attractive assets of the technique are: • Simultaneous cancellation of noise and distortion terms due to the matching device. • Robustness to variations in device parameters and the external source resistance RS. • Simultaneous noise and power matching. • Orthogonality of design parameters for input impedance and gain, allowing easier implementation of variable gain at constant input match. • Applicability in other IC technologies and amplifier topologies. REFERENCES
[1] J. Janssens, M. Steyaert and H. Miyakawa, “A 2.7Volt CMOS Broad band Low Noise Amplifier”, Dig. of Tech. paper, Symposyum of VLSI Circuits, pp. 8788, June 1997. [2] F. Bruccoleri, E.A.M. Klumperink and B. Nauta, “Noise Cancelling in Wideband CMOS LNAs”, Proceedings of the IEEE ISSCC, Vol. 45, Section 24.6, pp. 406407, San Francisco, CA, USA, February 2002. [3] F. Bruccoleri, “Wideband CMOS LowNoise Amplifiers” Ph.D. Thesis, University of Twente, Enschede, The Netherlands, to be published in 2003. [4] F. Bruccoleri, E.A.M. Klumperink, B. Nauta, "WideBand CMOS LowNoise Amplifier Exploiting ThermalNoise Canceling", IEEE Journal of SolidState Circuits, Vol. 39, No. 2, pp. 275 282, February 2004. [5] E.A.M. Klumperink, “Transconductance based CMOS Circuits: Generation, Classification and Analysis”, PhD. Thesis, University of Twente, Enschede, The Netherlands, 1997. [6] F. Bruccoleri, E. A. M. Klumperink and B. Nauta, “Generating All 2MOS Transistors Amplifiers Leads to New WideBand LNAs”, IEEE Journal SolidState Circuits, vol. 36, pp. 10321040, July 2001. [7] E. A. M. Klumperink F. Bruccoleri and B. Nauta, "Finding All Elementary Circuit Exploiting Transconductance", IEEE Transactions on Circuits and SystemsII, Vol. 48, No. 11, pp. 10391053, Nov. 2001. OUT
B IA S IN Fig. 6. LNA of fig. 3b implemented with bipolar transistors.
Gain (S21) @20MHz 3 dB Frequency rolloff S11 @20MHz Noise Figure @20MHz Output IP3 (100,100.1MHz) Output IP2 (100, 200MHz) Current consumption Chip size 20 dB 324 MHz 30 dB 1.53 dB +16 dBm +47 dBm 16mA 478umx500um Table. 1. Performance summary of the Bipolar LNA in fig. 6. D. Wideband Variable Gain LNA Even partial noise cancellation can result in advantages, as exemplified by the “Amp1” topology shown in the low part of fig.7.
Amp3
IN Mb Amp4
0
Mb 1 2
Ma Amp2
OUT 0
0 2
Ma 0
IN Mb 1 1 2
Ma OUT IN 0 0
Mb 2 0
Ma OUT 1 IN 2dB @12dB
1+NEF Amp1 Fig. 7. Noise figure as a function of gain al all systematically generated 2NMOStransistor LNAs [5,6,7]. Compared to three other wideband LNAs, which are systematically generated [5,6,7], its noise performance is remarkable. Even though the minimum noise figure is not below 3dB, it is relatively small compared to the other 374 12th GAAS Symposium  Amsterdam, 2004 ...
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