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Envelope Detector Sensitivity and Blocking Characteristics In: 2011 20Th European Conference on Circuit Theory and Design (ECCTD), 6043845 (Pp

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Envelope Detector Sensitivity and Blocking Characteristics In: 2011 20Th European Conference on Circuit Theory and Design (ECCTD), 6043845 (Pp http://www.diva-portal.org Postprint This is the accepted version of a paper presented at 20th European Conference on Circuit Theory and Design (ECCTD 2011), Linköping, Sweden, August 29-31, 2011. Citation for the original published paper: Nilsson, E., Svensson, C. (2011) Envelope Detector Sensitivity and Blocking Characteristics In: 2011 20th European Conference on Circuit Theory and Design (ECCTD), 6043845 (pp. 773-776). Piscataway, NJ: IEEE Press https://doi.org/10.1109/ECCTD.2011.6043845 N.B. When citing this work, cite the original published paper. Permanent link to this version: http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-16342 2011 20th European Conference on Circuit Theory and Design (ECCTD) Envelope Detector Sensitivity and Blocking Characteristics Emil Nilsson Christer Svensson CERES and MPE-lab ISY Halmstad University Linkoping¨ University Halmstad, SE-301 18, Sweden Linkoping,¨ SE-581 83, Sweden Email: [email protected] Email: [email protected] Abstract—This paper presents analytical expressions for the sensitivity of a low power envelope detector driven by a weak RF signal in the presence of a blocking signal. The envelope detector has been proposed for low power Wake-Up radios in applications such as RFID and wireless sensor systems. The theoretical results are verified with simulations of a modern short channel MOS transistor in a commonly used circuit topology. A discussion around a tutorial example of a radio frontend, consisting of an LNA and a detector, is presented. It is shown that the sensitivity of a low power envelope detector can reach -62 dBm with a low power LNA and in presence of a CW blocker. I. INTRODUCTION For a long time development of radio technology has focused on complicated high performance modulation schemes like QAM rather than simple OOK (on-off keying). However, Fig. 1. Envelope detector schematic. recent developments in ultra low power radio, with applica- tions such as RFID and wireless sensor systems have showed the need for simple wake up radios [1][2][3]. A wake up channel MOS transistor in a commonly used circuit topology. radio is intended to be in constant operation, listening on Further the use of the derived expressions is exemplified by the air interface for a wake up signal. Once receiving this analysis of a hypothetical detector in combination with an signal the wake up radio may start more power demanding LNA. The circuit in Fig. 1 is a common implementation of and sophisticated functional blocks. The requirements for the an envelope detector [4], transformed from a bipolar to a wake up radio thus are, ultra low power consumption, robust CMOS circuit. M1 is biased in subthreshold, where it displays and reliable functionality, and a reasonable sensitivity. OOK a maximum nonlinear transfer function. Transistor M2 acts modulation is a simple and robust non-coherent modulation, as a constant bias current source, keeping M1 gate bias not requiring an always running local oscillator. voltage Vgs0 constant. The detector output voltage is found The input voltage amplitude for the wake up radio detector over capacitor Cs which is charged by the output current io. is far below the traditional levels of a few hundred millivolts This capacitor also provides the RF signal grounding path. (kT=q) normally preferred to drive nonlinear components The detection of the RF-signal is performed by the nonlinear efficiently. The reason for these low levels is the wish to transfer function from voltage to current in M1. Detector effi- minimize RF amplification since this normally is a power ciency depends on how abrupt the nonlinear transfer function consuming part of the radio. Internal noise in the detector is. MOS transistors in subthreshold region of operation display together with noise from the preceding RF stages sets the an exponential nonlinearity at room temperature. lower limit of the detectable amplitude level. In addition to The paper is organized as follows; II) Theory for the this noise, external interfering sources may swamp the wake up envelope detector. III) Verification of theory with simulations. signal, causing interference and increased noise due to noise IV) Discussion. V) Conclusion. folding. A theory is needed for the performance of the system in II. THEORY FOR THE ENVELOPE DETECTOR these conditions. In this paper we develop such a theory together with analytical expressions for detector sensitivity. Assume that we use an NMOS transistor in subthreshold All expressions are based on the exponential transfer function for detection. Then the Id −Vgs characteristic is of the subthreshold biased transistor. The validity of this Vgs=V0 simplified model is verified by simulations of a modern short Id = Id0e ; (1) 978-1-4577-0616-5/11/$26.00 ©2011 IEEE 802 where V0 =nkT=q with 1<n<2. The gate to source voltage A. The detector sensitivity in presence of a blocking signal may be expanded to, The third noise component is RF noise being down con- verted to baseband. This RF noise is converted to baseband Vgs = Vg + Vgs0; (2) by mixing with the carrier or with an in band blocker. We where Vg is the small signal voltage, represented by VRF in will limit our analysis to first order, i.e. mixing with the first Fig. 1, and Vgs0 is the bias voltage. For small amplitudes of harmonic of the blocker signal only. Vg (meaning small deviations from Vgs0) we may, assuming In the noise calculation we do not consider the effects of any DC bias being included in Id0, expand (1) as signal driven cyclic variation of the transconductance, since the 2 2 transconductance is kept constant by the constant bias current dId d Id Vg Id = Id0 + Vg + 2 : (3) source. If we add a blocker of amplitude Vb, we will have dVg dVg 2 to modify the input signal component to Vg = Vs cos(!t) + Where the second derivative is Vb cos(!bt). However, the blocker is not necessarily small, so 2 d Id Id0 we may rewrite (1) as = 2 : (4) 2 Vs Vb dVg V0 cos !t cos !bt Id = Id0e V0 e V0 = 2 With an applied unmodulated RF signal we get Vg=Vs cos(!t) Vb Vs Vs 2 cos !bt 2 V0 and the quadratic term above can be expanded as cos (!t) = Id0 1 + cos !t + 2 cos !t e (9) V0 2V (1+cos 2!t)=2. We may now calculate the wanted incremental 0 The second exponent can be expanded as a Fourier series [4]: component in the output signal current io that is dependent on amplitude V as: Vb s cos !bt Vb Vb e V0 = I + 2I cos ! t + ··· (10) 2 0 V 1 V b Vs 0 0 is = Id0 2 (5) 4V0 Where I0 and I1 are modified Bessel functions of the first The output noise current contributors may be divided into kind. This means that the term we are interested in, the 2 three parts. Noise from the channel of the detector transistor, incremental current term proportional to Vs , can be written: baseband noise being transferred without any frequency con- 2 Vb Vs version, and noise at radio frequencies converted to baseband. is = Id0 I0 2 (11) V0 4V All these contributors have spectral components in the base- 0 band making them worth study. Noise self mixing components From (10) it is clear that a large blocking signal will have will also have spectral components in baseband, but the level an influence on the biasing conditions of the transistor. As from this contribution will be so low that it is negligible. a matter of fact an increased current due to a blocker will The channel noise will not vary with the input signal levels increase the detector sensitivity, but also risking the transistor since it is a function of the bias current being kept constant in to be pulled out of the subthreshold region. In our actual our circuit. The output noise current from the NMOS transistor circuit, see Fig. 1, the DC-current is kept constant through can be expressed as [5]: the bias current generator to Ibias. Therefore we have i2 = 4γkT g B Vb n m (6) Id0 I0 = Ibias; (12) V0 where gm = dId=dVg = Id0=V0, γ ≈ 1, and B is the noise bandwidth. From this we can estimate SNR to so we can expect the sensitivity (5), and the internal transistor channel noise current (6), to be unaffected by the blocker i2 g V 4 s m s power. However, the output DC voltage from the circuit will SNR = 2 = 2 : (7) in 64kT V0 B change with blocker power. We have here defined SNR from an incremental current is, In the presence of a blocker signal, the blocker will act as a assuming that our main interest is OOK modulation. We can local oscillator and convert some of the RF noise to baseband. then estimate the minimum Vs for a particular SNR giving us Strictly speaking also the signal may act as local oscillator, the envelope detector sensitivity, but by assuming the signal to be weak we can neglect this s contribution. Replacing Vs in (9) with input noise amplitude 2 4 64kT V0 B Vni at frequency !n gives, Vsmin = SNR: (8) gm Vb Vni cos !bt inb = Id0 1 + cos !nt e V0 ; (13) For a reasonably low power consumption (< 1 µA), we V0 may have g =10 µA/V. Further assuming B=100 kHz and m where we use only the first order noise term. Again utilizing SNR=10, we arrive to a sensitivity of 2.2 mV (peak, corre- the Fourier expansion of the exponential function, the resulting sponding to -43 dBm at 50 Ω).
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