Low Noise Amplifier Design for Ultra-WideBand Radio - PDF by ztb16782


									                      Low Noise Amplifier Design for Ultra-WideBand Radio
                                          Jongrit Lerdworatawee, Won Namgoong
                                              Department of Electrical Engineering
                                                University of Southern California
                                            lerdwora@usc.edu, namgoong@usc.edu

                                                                             Unlike the narrowband LNA, the signal bandwidth of an
                                                                        UWB radio is several orders of magnitude greater. Hence, the
                    ABSTRACT                                            underlying single tone signal assumption employed in narrow-
                                                                        band LNA design becomes invalid, making many of the existing
     A new theoretical approach for designing a low-noise ampli-        narrowband design techniques [4] based on this assumption also
fier (LNA) for the ultra-wideband (UWB) radio is presented.             unsuitable.
Unlike narrowband systems, the use of the noise figure (NF) per-
formance metric becomes problematic in UWB systems because                    The LNA is often designed to present an input impedence of
of the difficulty in defining the signal-to-noise ratio (SNR). By       50Ω to avoid reflections on the transmission line connecting the
defining the SNR as the matched filter bound (MFB), the NF mea-         off-chip antenna to the on-chip LNA. In this paper we consider a
sures the degree of degradation caused by the LNA in the achiev-        highly integrated UWB radio system. We assume that the antenna
able receiver performance after the digital decoding process. The       is placed in close proximity of the LNA, allowing us to ignore the
optimum matching network that minimizes the NF as defined               50Ω input impedence requirement.
above has been solved. Since realizing the optimum matching net-
                                                                              For the noise factor (NF, or noise figure in dB) of the LNA to
work is in general difficult, an approach for designing a practical
                                                                        be a meaningful metric in an UWB receiver, we define the SNR as
but suboptimum matching network is also presented. The NF per-
                                                                        the matched filter bound (MFB) [5], which represents an upper
formance of both the optimum and the suboptimum matching net-
                                                                        limit on the performance of data transmission systems. The MFB
works is studied as a function of the LNA gain.
                                                                        is obtained when a noise whitened matched filter is employed to
                                                                        receive a single transmitted pulse. By defining the SNR as the
                                                                        MFB, the NF measures the degree of degradation caused by the
                                                                        LNA in the achievable receiver performance after the eventual
                                                                        digital decoding process. In this paper, the optimum matching net-
     The ultra-wideband (UWB) radio is a relatively new technol-        work that minimizes the NF as defined above has been solved.
ogy that is being pursued for both commercial and military pur-         Since the optimal LNA matching network is generally difficult to
poses [1][2]. It operates by spreading the energy of the radio          realize in practice, we also present an approach for designing a
signal very thinly over a wide bandwidth (e.g. several gigahertz).      sub-optimal but practical matching network.
The rationale for deploying the UWB radio systems lies in the
                                                                             The paper is organized as follows. The circuit and system
benefits of exceptionally wide bandwidths, thereby achieving a
                                                                        model of the LNA-Antenna is presented in Section 2. In Section 3,
combination of very fine time/range resolution, ability to resolve
                                                                        the general solution to the optimal and suboptimal matching LNA
multipath components, and favorable propagation condition of
                                                                        are derived. Performance results are presented in Section 4. Con-
material penetration at low frequencies [3].
                                                                        clusions are drawn in Section 5.
      The goal of the receiver analog front-end is to condition the
received analog signal for digitiziation, so that the highest perfor-   2 CIRCUIT AND SYSTEM MODEL
mance can be achieved after decoding in the digital domain. The
first and probably the most critical component of the analog front-          Throughout this paper, capital letters are used to denote the
end is the low noise amplifier (LNA), whose purpose is to amplify       Fourier transforms (e.g. X(ω)) of (voltage or current) system
the received signal from the antenna with as little distortion and      responses in the time domain, which are written in the correspond-
additional noise as possible. This is achieved by designing an          ing lower case letters (e.g. x(t)). Sometimes the terms ω and t are
appropriate matching network placed between the antenna and the         omitted for notational brevity unless needed for clarity.
                                                                        2.1 Circuit model of LNA-Antenna
This work was supported in part by the Army Research Office                  The quasi-static MOS transistor model is employed in this
under contract number DAAD19-01-1-0477 and National Sci-                paper to account for the high-field effects in short-channel devices
ence Foundation under contract number ECS-0134629.                      [6]. Accordingly, the transconductance gm and the gate-source
capacitance Cgs can be represented in terms of the power dissipa-                                               where S i i ( ω ) is the PSD of the cross-correlation of ig(t) and
                                                                                                                         g d
tion Po (= IdVsupply) and the normalized gate overdrive ρ (= (Vgs-
                                                                                                                id(t). For a long channel device c = 0.395j. For lack of a more
                                                                                                                accurate value currently available, we assume that the long chan-
                                        2P o                 1+ρ⁄2                                              nel values for c, α, γ and δ are also valid in the short channel
                       g m = ------------------------------ --------------------                          (1)   model employed in this paper.
                             V supply Lεsat ρ ( 1 + ρ )

                                               Po                     1+ρ
                      C gs = -- -----------------------------------  ----------- 
                             2                                                                                  2.2 System model of LNA-Antenna
                              -                                   -             -                         (2)
                             3 V supply v sat ε sat  ρ 2 

where L is the gate length, Vgs is the gate-source bias voltage, Vth                                                                                 jXb
                                                                                                                 ig(t)    Rs+jXa                                                      gmZload      vo(t)
is the threshold voltage, vsat and εsat are the saturation velocity                                                                            Rs+j(Xa+Xb)
and electric field, respectively.                                                                                             vs(t)
                                    jXa(ω)                                                                       v(t)
                    Rs(ω) jXs(ω)           jX1(ω)
                                                                      ig(t)           gmVgs id(t) Zload                   Figure 2 : System block diagram of LNA.
              +                                                                +                          +
        +                                                                      Vgs                    vo(t)          Fig. 2 is the system model of the circuit model in Fig. 1. The
                      source                                                   _                          _
                    impedance                                                                                   objective is to design the causal matching network (i.e., Xa(ω)
                                             jX2(ω)          jωCgs                                              and Xb(ω)) so that the SNR at the output vo(t) is maximized. In
               network                                 jXb(ω)                                                   the presence of ig(t), there exists an optimum gain in the matching
                                                                                                                network that balances the combined effects of ig(t), id(t) and sig-
                          Figure 1 : Circuit model of LNA                                                       nal amplification.
      Fig. 1 shows a circuit model of the analog front-end, includ-                                                 Note that ig(t) can be decomposed into two orthogonal com-
ing the antenna, the matching network, the LNA and a load, with                                                 ponents, i.e.,
three noise sources: the thermal voltage noise from the antenna
resistance vs(t), the MOS gate current noise ig(t), and drain cur-                                                                                                      id( t )
                                                                                                                                   i g ( t ) = i gu ( t ) + y c ( t ) ⊗ ----------
                                                                                                                                                                                 -                         (7)
rent noise id(t). With no loss in generality, the antenna is modeled                                                                                                      gm
as a voltage source v(t) with an impedance Zs(ω) = Rs(ω)+jXs(ω)                                                 where ⊗ is the convolution operator, igu(t) is the uncorrelated
while the amplifier is assumed as a common-source MOS transis-                                                  component of ig(t) to id(t), and yc(t) is the equivalent correlation
tor. The matching network is assumed lossless, consisting of two
                                                                                                                admittance between ig(t) and id(t)/gm. From (4)-(7), the Fourier
reactances, X1(ω) and X2(ω), as illustrated by the solid-line block
                                                                                                                transform of yc(t) (i.e., Yc(ω)) can be obtained and given by
in Fig. 1. For ease of analysis, the source reactance Xs(ω) is
grouped with X1(ω) and referred to as Xa(ω), and the gate-source                                                                         Si i ( ω )                                      δ
capacitance Cgs is grouped with X2(ω) and referred to as Xb(ω).                                                          Y c ( ω ) = g m ------------------ = jωC gs ⋅  α c
                                                                                                                                              g d
                                                                                                                                                          -                              ----- 
                                                                                                                                           Si ( ω )                                     5γ               (8)

     The power spectral density (PSD) of the thermal noise from                                                                    = jX c ( ω )
the antenna, the drain and the gate noise are given by
                                                                                                                      Using the definition of the SNR described earlier, the SNR
                                S v ( ω ) = 4kTRs ( ω )                                                   (3)
                                    s                                                                           at the input of the LNA (i.e., the SNR of the received input signal)
                                                   γ                                                            is given by [5]
                                  S i ( ω ) = 4kT -- g m
                                                   -                                                      (4)
                                     d            α                                                                                                        2               2
                                                                                                                                                        A P( ω)
                                             ( ωCgs )
                                                                               2                                                      SNR in =        ∫ ------------------------ dω
                                                                                                                                                             Sv ( ω )
                                                                                                                                                                               -                           (9)
                           S i ( ω ) = 4kTδα -------------------
                                                               -                                          (5)                                                   s
                              g                   5g m                                                          where P(ω) is the normalized channel response to a single multi-
where k = 1.38 x 10 J/K is the Boltzmann constant, T is the                                                     path component (i.e., ||p||2=1) and A is the scaling factor of the
absolute temperature, α is the ratio of gm to the zero-bias drain                                               received signal. With no loss in generality, we assume that the
conductance, γ and δ are the coefficients of channel and induced                                                received signal is a 2nd derivative of a Gaussian pulse [2].
gate noise. Random noise process ig(t) is correlated to id(t) with a                                                 Similarly, the SNR at the output of the LNA is
correlation coefficient c as given by [7]
                                                                                                                                                           2               2
                                                                                                                                                         A P( ω)
                                              Si i ( ω )
                                                  g d
                             c = -------------------------------------------
                                                                           -                           (6)
                                                                                                                                    SNR out =         ∫ ------------------------ dω
                                                                                                                                                           Sn ( ω )
                                                                                                                                                                               -                       (10)
                                     Si ( ω ) ⋅ S i ( ω )
                                              g                   d
where S n ( ω ) represents the input-referred noise of all the noise                                                                             As will be shown in the following sections, a trade-off between
                                                                                                                                                 high Gopt and low NFopt exists by varying ρ for a given Po.
sources in the LNA, which is given by
                                                                                                                                                      Note that Xa,opt(ω) and Xb,opt(ω) given in (13) minimize the
                                                     2          2
        Sn          = S v + S i ( Rs + X a )                                                                                         (11)        degradation in SNRout caused by the additive noise at every fre-
             out               s           gu
                                                                                                                                                 quency, and hence they become independent of the received signal
                                        2                         2 Si
                     + R s  ----- -X c +  Xa  ----- -X c + 1 ------
                          2 1                       1                   d                                                                        pulse. In a realistic matching network with a fixed structure, how-
                                 -                    -
                            Xb             Xb                g2                                                                            ever, designing Xa(ω) and Xb(ω) with arbitrary reactances as
where the spectrum of igu(t) is                                                                                                                  assumed in the optimum matching network is in general not possi-
                                                                                                                                                 ble. The matching network then becomes a function of the transmit-
                                          ( ωC gs )                 2
                                                                                                                                                 ted signal pulse.
                        S i ( ω ) = 4kTδα ------------------- ( 1- c )
                                                            -                                                                       (12)
                           gu                  5g m
                                                                                                                                                 3.2 Suboptimal matching

3.1 Optimal matching
      Reactances Xa(ω) and Xb(ω) that maximizes SNRout are
obtained by differentiating (10) with respect to Xa(ω) and Xb(ω) and
setting the result to zero. Assuming the output noise power of igu(t)
                                                                                 2             2
is less than that of id(t) (i.e., S i ( ω )Rs ( ω )g m < S i ( ω ) ), which is
                                                                 gu                                       d

typically the case, the optimum Xa(ω) and Xb(ω) (denoted as
Xa,opt(ω) and Xb,opt(ω)) can be solved:

        Xa, opt ( ω ) = ± R s ( ω ) ( 1 ⁄ Γ ( ω ) -R s ( ω ) )
        Xb, opt ( ω ) = -------------------------------------------------------------------------------------                       (13)
                                        −        Γ( ω)
                        Xc ( ω ) + -------------- ( 1 ⁄ Γ ( ω ) -Rs ( ω ) )
                                               Rs ( ω )                                                                                              Figure 3 : suboptmal vs. optimal reactance in a signal region
                                                                                                                                                                     given gm=1mS and Cgs=1pF
where Γ(ω) is
                           Si ( ω )                δα
                                                                  2           2
                                                                                                                                                       Since realizing the optimum matching network is in general
             Γ ( ω ) = ------------------------- = -------- ( 1- c ) ( ωCgs )
                                               -          -                                                                         (14)         difficult, a heurisitc approach for determining a practical but subop-
                       Si ( ω ) ⁄ g m                5γ
                                                                                                                                                 timum matching network is presented. Based on Xa,opt(ω) and
Substituting (13) into (11), the optimum NF, denoted as NFopt, is                                                                                Xb,opt(ω), a structure for the suboptimum matching network that
                                                                                                                                                 best approximates the optimal response is first selected. The
                                                            ∫ P ( ω ) dω -
                                                                                                                                                 antenna impedance is assumed to be 50 Ω across the bandwidth of
                        NF opt            = -----------------------------------------------------------
                                                                                                                                    (15)         interest. As shown in Fig. 3, the optimal matching network can be
                                                                P(ω )
                                            ∫ ------------------------------------------------- dω
                                                          ω 4δγ                             2
                                                                                                                                                 approximated by a two element (Lm and Cm) L-matching network,
                                                                                                                                                 i.e., Xa(ω) = jωLa and Xb(ω) = 1/jωCb, where Cb = Cgs + Cm and La
                                               1 + ------ -------- ( 1- c ) -
                                                         ωT 5                                                                                    = Lm. The choice of La and Cb is determined by numerically solving
where ωT is the unity gain angular frequency:                                                                                                    the following constrained optimization problem:

                                                                                                                                                                                                   ∫ P ( ω ) dω -
                                  gm       3 ν sat ( 1 + ρ ⁄ 2 )ρ
                           ω T = ------- = -- -------- ---------------------------
                                       -    - -                                  -                                                  (16)                   minimize NF =             ---------------------------------------------------------   (18)
                                 Cgs       4 L (1 + ρ)2                                                                                                                                                               2
     Assuming a resistive load Zload (= Rload), the corresponding
                                                                                                                                                                                     ∫ ---------------------------------------------- dω
                                                                                                                                                                                       1 + F1( ω ) + F2( ω )

signal voltage power gain (in units of V2/V2) of the LNA, denoted                                                                                                  subject to L a ≥ 0,                    Cb ≥ C gs                              (19)
as Gopt, is given by
                                                                Xb( ω )                                                                                                  δα ( ωCgs )
          g m R load ∫ ---------------------------------------------------------------------------- P ( ω ) dω
             2 2                                                                                                                2
                                                                                                              -                                                                                          2           2
                                        2                                                                    2                                                F1 ( ω ) = --------------------------- [ R s + ( ωL a ) ]
                                                                                                                                                                                                   -                                             (20)
                                  R s + ( X a, opt ( ω ) + Xb, opt ( ω ) )                                                                                                     5g m R s
G opt                                                                                                                                   -
        = ------------------------------------------------------------------------------------------------------------------------------- (17)
                                                                P ( ω ) dω
                                                                                                                    dB, increasing Po by 20 mW from 10 mW to 30 mW improves G
                       γ  2 2                                                                δ         2
     F2 ( ω ) = ----------------  R s ω C b + C gs  α c                                    -----          (21)   by less than 1.5 dB; whereas increasing Po by only 6 mW from 4
                αg m R s                                                                   5γ
                                                                                                                    mW to 10 mW increases G by more than 11 dB. This diminishing
                                                                            δ                                       returns in G suggests that large signal amplification is most effi-
      + 1-ω L a Cb  C b + ωC gs  α c                                     ----- 
                                                                                         
                                                                           5γ            
                                                                                                                    ciently achieved in multiple stages.

The cost function (i.e., NF) in (18) is obtained by substituting
Xa(ω) and Xb(ω) of the L-matching network into (10) and (11).
                                                                                                                    5 CONCLUSIONS
Similar to (17), the corresponding signal voltage power gain (in                                                         A generalized approach for designing an UWB LNA that
units of V2/V2) is                                                                                                  minimizes the NF with the SNR defined using the MFB has been
                                                                                                                    developed. The matching network consists of two lossless reac-
                                                           P(ω )                                                    tances, which are connected in series and in parallel to the MOS
           g m R load ∫ --------------------------------------------------------------- dω
              2 2
                                                                  2                              2                  amplifier. The optimum matching network depends only on the
                                   ( 1-ω 2 L a C b ) + ( ωR s C b )
       G = -----------------------------------------------------------------------------------------------   (22)   LNA device noise while the suboptimum matching network
                                            ∫ P ( ω ) dω
                                                                                                                    depends also on the received signal and noise. This additional
                                                                                                                    dependency of the suboptimum matching network results because
4 PERFORMANCE RESULTS                                                                                               designing matching networks with arbitrary reactances as
                                                                                                                    assumed in the optimum matching network is in general not pos-
                                                                                                                         For a simple LC suboptimum matching network that we con-
                                                                                                                    sidered, there exists an optimum G that minimizes the NF for a
                                                                                                                    given power dissipation. Although the optimum G can be
                                                                                                                    increased by increasing power consumption, this approach suffers
                                                                                                                    from diminishing returns. Hence, a single stage amplification may
                                                                                                                    not be sufficient; more complex matching network or multiple
                                                                                                                    amplification stages with attendant complexity may be required.

                                                                                                                    [1] M. Z. Win and R. A. Scholtz, “Impulse radio: How it
                                                                                                                        works,” IEEE Commun. Lett., vol. 2, no. 2, pp.36-38, Feb.
                                                                                                                    [2] M. Z. Win and R. A. Scholtz, “Ultra-wide bandwidth time-
                                                                                                                        hopping spread-spectrum impulse radio for wireless multi-
                                                                                                                        access communications,” IEEE Trans. Commnu., vol. 48,
 Figure 4 : Contours of noise figure and signal gain relating ρ for                                                     no. 4, pp. 679-691, Apr. 2000.
             a specified Po (the number on the curves)                                                              [3] M. Z. Win and R. A. Scholtz, “On the roubustness of
                                                                                                                        ultrawide bandwidth signals in dense multipath
     In Fig. 4 the NF is plotted against the signal voltage gain G                                                      environments,” IEEE Commun. Lett., vol. 2, no. 2, pp. 51-
(in units of V2/V2) for both the optimum (in dash-line) and the                                                         53, Feb. 1998.
suboptimum matching networks (in solid-line) when Po is fixed.                                                      [4] D. K. Shaeffer, T. H. Lee, “A 1.5-V, 1.5-Hz CMOS low
                                                                                                                        noise amplifier,” IEEE J. Solid-State Circuits, vol. 32, pp.
In the optimum matching network, a trade-off between reducing
                                                                                                                        745-759, May. 1997.
NF and increasing G can be made by varying the normalized gate
                                                                                                                    [5] J. Cioffi, “EE379A Course Notes,” Stanford University.
overdrive ρ. For sufficiently high G, large increases in G causes
                                                                                                                    [6] K.-Y. Toh, P.-K. Ko, and R. G. Meyer, “An Engineering
only a small increase in NF. For example, increasing G from 10
                                                                                                                        model for short-channel mos devices,” IEEE J. Solid-Sate
dB to 20 dB when Po is 10 mW increases the NF by less than 1
                                                                                                                        Circuits, vol. 23, no. 4, pp. 950-958, Aug. 1988.
dB. In the suboptimum matching network, there is an optimum G
                                                                                                                    [7] D. P. Triantis, A. N. Birbas, and D. Kondis, “Thermal noise
that minimizes the NF. For example, when Po is 10 mW, the opti-
                                                                                                                        modeling for short-channel MOSFET’s,” IEEE Trans.
mum G is approximately 7 dB. If operating below the optimum G,                                                          Electron Devices, vol. 43, pp. 1950-1955, Nov. 1996.
the NF does not increase much. However, if G is increased
beyond the optimum point, the NF increases abruptly. For exam-
ple, an increase in G from 10 dB to 20 dB when Po is 10 mW
increases the NF by almost 10 dB. Hence, the LNA that dissipates
Po should not be designed to operate with a gain that is much
greater than the optimum G. Another important observation is that
for a fixed NF, increasing G by increasing Po suffers from dimin-
ishing returns. For example, given a target NF of approximately 3

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