READING RANGE CONSIDERING THE TRANSMITTER LEAK- AGE AND A SIC TECHNIQUE

6.2 READING RANGE CONSIDERING THE TRANSMITTER LEAK-

(referred to the antenna), which, depending on its configuration, may be written as

α⁻_iso¹=







I_cc⁻¹+|Γa|⁻² , single-antenna w/ circulator;

Ccp/Icp+|Γa|⁻² , single-antenna w/ coupler;

I_a⁻¹ , two-antenna;

(6.8)

where Γ_a represents the voltage reflection coefficient of the reader antenna,C_cpis the coupling factor of the coupler andI_cc,I_cpandI_a represent the isolation factors of the circulator, coupler, and between antennas, respectively.

Alternatively, the noise leakage term can be expressed as N_i^l= Ptx

αisoF OMr

, (6.9)

where F OM_r =α_sicSN R_tx is a figure of merit related to the reader [119]. As a result, the maximum reading range calculated from the sensitivity expression obtained from the radar equation (assuming line- of-sight propagation) is equal to

d^tn_(max)= ⁴ s

PtxG²_aδpol

Sr

λ²RCS

(4π)³ , (6.10)

where G_a is the antenna gain, δ_pol is an attenuation factor due to polarization mismatch between the antenna and the tag. The superscript tnmakes reference to thetotal noise.

Similar to an analysis made for an RFID chipped system [119], provided a transmitter power level (Ptx), the sensitivity will be deter- mined either by the thermal noise or by the transmitter leakage noise.

When this power is low, the thermal noise is the dominant noise source, thus, the traditional equation from the radar equation can be used.³ However, when it is high, the leakage noise dominates. The transition be- tween both conditions depends onαiso,αsic, andSN Rtx. Moreover, the leakage noise is expected to be more severe in single-antenna monostatic readers, since the isolation factorαisois typically lower, and the reader sensitivity becomes more dependent on the SIC circuit performance (see (6.9)). Therefore, forN_i^th<< N_i^l, (6.10) is reduced to

d^ln_(max)≈ ⁴ s

F OMaF OMr

SN Ro

λ²RCS

(4π)³ , (6.11)

3Refer to (2.2) in Section 2.1.

where F OMa =αisoδpolG²_a is the antenna figure of merit. Here, the superscriptlnemphasizes that this equation considers only theleakage noise.

Equation (6.11) is in agreement with the expression obtained in [119]⁴. Nevertheless, in chipless RFID tag measurements, not only the transmitter thermal noise must be considered but also its phase noise, since it produces a residual noise after downconversion of the signal backscattered from the tag due to the so-calledrange correlation effect [124]. Then, the phase-noise should be taken into account by including it in the SN Rtx, i.e.,Ntx =N_tx^th+N_tx^ph. This component is equal to the total integrated phase noise within the band of interest

N_tx^ph=

Z fn+∆f fn

S_ph(f)α_ph(f)df, (6.12) which is dependent on the phase-noise power spectrum of the transmitter signal (S_ph(f)) and the range correlation factorα_ph(f) = 4 sin²(πf τ_rt), whereτ_rt is the round-trip delay time of the CW interrogating signal that impinges on the tag.

6.2.2 Leakage signal power analysis

Besides the impact of the transmitter leakage noise, its high-power leakage signal must be analyzed as well. For instance, it is necessary that the downconverted signal is digitized with enough accuracy at the input of the digital processing unit. We can express this requirement by relating the minimum resolvable step of the Analog-to-Digital Converter (ADC) at the end of the receiving chain and the minimum SNR at processing unit:

F SV

2^{EN OB} < GbVtag

pSN R_o(min). (6.13) The left term represents the least significant bit value given by the ratio of the full-scale voltage (F SV) and the effective number of bits (EN OB) of the ADC, and Gb is the baseband voltage gain of the receiver chain (baseband amplifier plus filter).

The maximum achievable value of the baseband gain without saturating the baseband reception chain is limited by the sum of ampli- tudes of the downconverted signals retrieved from the tag (V_tag) and

4For chipped tags,RCS=G²tagηM ODλ⁴/4π.

transmitter residual leakage signal (Vl) due to the SIC circuit. Typically, the portion due to the tag is very weak compared to the residual leakage signal, soV_l+V_tag≈V_l. Therefore,

G_b(max)≈ F SV

V_l . (6.14)

Furthermore, it can be stated that

V_l²/V_tag² =P_i^l/P_i^tag, (6.15) where P_i^l = Ptx/αisoαsic is the leakage power from the transmitter referred at the antenna, and P_i^tag is the input power due to the tag backscattering signal deduced from the radar equation. Finally, by substitutingG_bandV_tagin (6.13) using (6.14) and (6.15), the maximum reading range can be determined from

d^dr_(max)= ⁴ s

F OMaαsic4^{EN OB} SN R_o

λ²RCS

(4π)³ , (6.16) where the superscriptdrindicates its relation to thedynamic range.

We should notice that (6.16) is similar to (6.11), both being affected by the SIC attenuation factor. In the case of a reader where SN Rtx>4^{EN OB}, the reading distance would be restricted by the power of the transmitter leakage signal rather than its leakage noise.

At this point, it is important to remark that the downconverted leakage signal is typically not a relevant issue in traditional RFID chipped tags since this signal is downconverted at a different frequency, lower than the backscattering link frequency of the tag. Thus, it could be filtered out before reaching the ADC.