Differential RCS - Revision history

Nico at 10:49, 26 June 2022

2022-06-26T10:49:41Z

← Older revision		Revision as of 10:49, 26 June 2022
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	For a short-circuited half-wavelength dipole at 915 MHz, rotating at a distance of <math>r=12.5</math> cm, delta RCS is equal to -10 dBsm (920 cm<math>^2</math>) which outperforms any UHF tag.		For a short-circuited half-wavelength dipole at 915 MHz, rotating at a distance of <math>r=12.5</math> cm, delta RCS is equal to -10 dBsm (920 cm<math>^2</math>) which outperforms any UHF tag.

	* For a scatterer characterized by a polarization scattering matrix equal to <math> \begin{bmatrix} S_{vv} & S_{vh}\\ S_{hv} & S_{hh} \end{bmatrix} </math> rotating in a plan which is normal to propagation vector and impinged by a vertical plane wave, the delta RCS of this rotating dipole can simply be expressed as:		* For a scatterer characterized by a polarization scattering matrix equal to <math> \begin{bmatrix} S_{vv} & S_{vh}\\ S_{hv} & S_{hh} \end{bmatrix} </math> rotating in a plan which is normal to propagation vector and impinged by a vertical plane wave, the delta RCS of this rotating dipole can simply be expressed as <ref>N. Barbot, [https://nicolas-barbot.ovh/wiki/pool/deltapol.pdf "Delta RCS Expression of Linear Time-Variant Transponders based on Polarization Modulation,"] in 2022 IEEE RFID Technology and Applications Conference (RFID-TA), Cagliari, Italy, Sep. 2022, pp. 1–4.</ref>:

	<math>		<math>
	\sigma_{d\,vv} = 4 \pi \frac{\|S_{vv}-S_{hh}\|^2+4\|S_{vh}\|^2}{8} = \sigma_{d\,hh} = \sigma_{d\,vh}		\sigma_{d\,vv} = 4 \pi \frac{\|S_{vv}-S_{hh}\|^2+4\|S_{vh}\|^2}{8} = \sigma_{d\,hh} = \sigma_{d\,vh}
	</math>		</math>

	Note that the delta RCS is the same whatever the polarization of the reader antenna.		Note that the delta RCS is the same whatever the polarization of the reader antenna.

Nico at 10:40, 26 June 2022

2022-06-26T10:40:46Z

← Older revision		Revision as of 10:40, 26 June 2022
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	For a short-circuited half-wavelength dipole at 915 MHz, rotating at a distance of <math>r=12.5</math> cm, delta RCS is equal to -10 dBsm (920 cm<math>^2</math>) which outperforms any UHF tag.		For a short-circuited half-wavelength dipole at 915 MHz, rotating at a distance of <math>r=12.5</math> cm, delta RCS is equal to -10 dBsm (920 cm<math>^2</math>) which outperforms any UHF tag.

	* For a scatterer characterized by a polarization scattering matrix equal to		* For a scatterer characterized by a polarization scattering matrix equal to <math> \begin{bmatrix} S_{vv} & S_{vh}\\ S_{hv} & S_{hh} \end{bmatrix} </math> rotating in a plan which is normal to propagation vector and impinged by a vertical plane wave, the delta RCS of this rotating dipole can simply be expressed as:
	<math>
	\begin{bmatrix}
	S_{vv} & S_{vh}\\
	S_{hv} & S_{hh}
	\end{bmatrix}
	</math>
	rotating in a plan which is normal to propagation vector and impinged by a vertical plane wave, the delta RCS of this rotating dipole can simply be expressed as:
	<math>		<math>
	\sigma_{d\,vv} = 4 \pi \frac{\|S_{vv}-S_{hh}\|^2+4\|S_{vh}\|^2}{8} = \sigma_{d\,hh} = \sigma_{d\,vh}		\sigma_{d\,vv} = 4 \pi \frac{\|S_{vv}-S_{hh}\|^2+4\|S_{vh}\|^2}{8} = \sigma_{d\,hh} = \sigma_{d\,vh}

Nico at 10:39, 26 June 2022

2022-06-26T10:39:40Z

← Older revision		Revision as of 10:39, 26 June 2022
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	This quantity is generally sightly lower than the previous case but allows one to increase the data rate and/or the spectral efficiency.		This quantity is generally sightly lower than the previous case but allows one to increase the data rate and/or the spectral efficiency.

	* For a vertical dipole oriented along <math>z</math> rotating at a frequency <math>f_r</math> located at a distance <math>r</math> of its axis and impinged by a vertical plane, the delta RCS of this rotating dipole can simply be expressed as:		* For a vertical dipole oriented along <math>z</math> rotating at a frequency <math>f_r</math> located at a distance <math>r</math> of its axis and impinged by a vertical plane wave, the delta RCS of this rotating dipole can simply be expressed as:

	<math>		<math>
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	For a short-circuited half-wavelength dipole at 915 MHz, rotating at a distance of <math>r=12.5</math> cm, delta RCS is equal to -10 dBsm (920 cm<math>^2</math>) which outperforms any UHF tag.		For a short-circuited half-wavelength dipole at 915 MHz, rotating at a distance of <math>r=12.5</math> cm, delta RCS is equal to -10 dBsm (920 cm<math>^2</math>) which outperforms any UHF tag.

			* For a scatterer characterized by a polarization scattering matrix equal to
			<math>
			\begin{bmatrix}
			S_{vv} & S_{vh}\\
			S_{hv} & S_{hh}
			\end{bmatrix}
			</math>
			rotating in a plan which is normal to propagation vector and impinged by a vertical plane wave, the delta RCS of this rotating dipole can simply be expressed as:
			<math>
			\sigma_{d\,vv} = 4 \pi \frac{\|S_{vv}-S_{hh}\|^2+4\|S_{vh}\|^2}{8} = \sigma_{d\,hh} = \sigma_{d\,vh}
			</math>
			Note that the delta RCS is the same whatever the polarization of the reader antenna.

			For a short-circuited half-wavelength dipole at 915 MHz, rotating in the previously described configuration, delta RCS is equal to -19.4 dBsm (115 cm<math>^2</math>).

	==Measurement==		==Measurement==

Nico at 20:02, 18 April 2022

2022-04-18T20:02:35Z

← Older revision		Revision as of 20:02, 18 April 2022
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	of -22 dBsm (63 cm<math>^2</math>) and -16 dBsm (230 cm<math>^2</math>) respectively.		of -22 dBsm (63 cm<math>^2</math>) and -16 dBsm (230 cm<math>^2</math>) respectively.

	* For a multi-state transponder (i.e. a transponder which can switch its internal impedance between <math>N</math> different values), its differential RCS can be expressed as <ref>A. Voisin, A. Dumas, N. Barbot and S. Tedjini, “Differential RCS of Multi-State Transponder,” 2022 IEEE Wireless Power Week Conference (WPW 2022), Bordeaux, France, Jul. 2022, pp. 1–4.</ref>:		* For a multi-state transponder (i.e. a transponder which can switch its internal impedance between <math>N</math> different values), its differential RCS can be expressed as <ref>A. Voisin, A. Dumas, N. Barbot and S. Tedjini, [https://nicolas-barbot.ovh/wiki/pool/nstate2.pdf “Differential RCS of Multi-State Transponder,”] 2022 IEEE Wireless Power Week Conference (WPW 2022), Bordeaux, France, Jul. 2022, pp. 1–4.</ref>:

	<math>		<math>

Nico at 19:19, 18 April 2022

2022-04-18T19:19:58Z

← Older revision		Revision as of 19:19, 18 April 2022
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	</math>		</math>

			This quantity is generally sightly lower than the previous case but allows one to increase the data rate and/or the spectral efficiency.

	* For a vertical dipole oriented along <math>z</math> rotating at a frequency <math>f_r</math> located at a distance <math>r</math> of its axis and impinged by a vertical plane, the delta RCS of this rotating dipole can simply be expressed as:		* For a vertical dipole oriented along <math>z</math> rotating at a frequency <math>f_r</math> located at a distance <math>r</math> of its axis and impinged by a vertical plane, the delta RCS of this rotating dipole can simply be expressed as:

Nico at 19:15, 18 April 2022

2022-04-18T19:15:28Z

← Older revision		Revision as of 19:15, 18 April 2022
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	of -22 dBsm (63 cm<math>^2</math>) and -16 dBsm (230 cm<math>^2</math>) respectively.		of -22 dBsm (63 cm<math>^2</math>) and -16 dBsm (230 cm<math>^2</math>) respectively.

	* For a multi-state transponder (i.e. a transponder which can switch its internal impedance between <math>N</math> different values), its differential RCS can be expressed as		* For a multi-state transponder (i.e. a transponder which can switch its internal impedance between <math>N</math> different values), its differential RCS can be expressed as <ref>A. Voisin, A. Dumas, N. Barbot and S. Tedjini, “Differential RCS of Multi-State Transponder,” 2022 IEEE Wireless Power Week Conference (WPW 2022), Bordeaux, France, Jul. 2022, pp. 1–4.</ref>:
	<ref>A. Voisin, A. Dumas, N. Barbot and S. Tedjini, “Differential RCS of Multi-State Transponder,” 2022 IEEE Wireless Power Week Conference (WPW 2022), Bordeaux, France, Jul. 2022, pp. 1–4.</ref>:

	<math>		<math>
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	where <math>2b</math> is the span of the instrument and <math>\epsilon</math> a constant allowing to remove the static contribution generated by the tag (and the environment).		where <math>2b</math> is the span of the instrument and <math>\epsilon</math> a constant allowing to remove the static contribution generated by the tag (and the environment).

			==References==

	<references />		<references />

Nico at 19:14, 18 April 2022

2022-04-18T19:14:40Z

← Older revision		Revision as of 19:14, 18 April 2022
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	At 915 MHz, this equation predicts a maximal delta RCS for passive (i.e., <math>\{\Gamma_1 = 0; \Gamma_2=-1\})</math> and semi-passive (i.e., <math>\{\Gamma_1 = +1; \Gamma_2=-1\})</math> UHF tags		At 915 MHz, this equation predicts a maximal delta RCS for passive (i.e., <math>\{\Gamma_1 = 0; \Gamma_2=-1\})</math> and semi-passive (i.e., <math>\{\Gamma_1 = +1; \Gamma_2=-1\})</math> UHF tags
	of -22 dBsm (63 cm<math>^2</math>) and -16 dBsm (230 cm<math>^2</math>) respectively.		of -22 dBsm (63 cm<math>^2</math>) and -16 dBsm (230 cm<math>^2</math>) respectively.

			* For a multi-state transponder (i.e. a transponder which can switch its internal impedance between <math>N</math> different values), its differential RCS can be expressed as
			<ref>A. Voisin, A. Dumas, N. Barbot and S. Tedjini, “Differential RCS of Multi-State Transponder,” 2022 IEEE Wireless Power Week Conference (WPW 2022), Bordeaux, France, Jul. 2022, pp. 1–4.</ref>:

			<math>
			\sigma_d = \frac{\lambda^2 G^2}{4\pi}\left[ \sum_i p_i \|\Gamma_i-\Gamma_s\|^2\right].
			</math>


	* For a vertical dipole oriented along <math>z</math> rotating at a frequency <math>f_r</math> located at a distance <math>r</math> of its axis and impinged by a vertical plane, the delta RCS of this rotating dipole can simply be expressed as:		* For a vertical dipole oriented along <math>z</math> rotating at a frequency <math>f_r</math> located at a distance <math>r</math> of its axis and impinged by a vertical plane, the delta RCS of this rotating dipole can simply be expressed as:

Nico at 19:37, 14 October 2021

2021-10-14T19:37:19Z

← Older revision		Revision as of 19:37, 14 October 2021
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	[[File:Delta.png\|thumb\|right\|Fig. 1: Power spectral density of the signal backscattered by a modulating tag in the frequency domain.]]		[[File:Delta.png\|thumb\|right\|Fig. 1: Power spectral density of the signal backscattered by a modulating tag in the frequency domain.]]

	Details have been presented in <ref>N. Barbot, O. Rance, and E. Perret, [https://nicolas-barbot.ovh/wiki/pool/~~delta~~.pdf "Differential RCS of modulated tag,"] IEEE Transactions on Antennas and Propagation, pp. 1–1, 2021, early access. doi: 10.1109/TAP.2021.3060943.</ref> and can be seen as a complementary definition compared to the time definition. The basic idea relies on the decomposition of the RCS <math>\sigma</math> into a static RCS <math>\sigma_s</math> and a dynamic RCS <math>\sigma_d</math> and to pass into the frequency domain. Fig. 1 presents the main result where the (total) backscattered signal by the modulating UHF tag can be decomposed into 2 parts. Component located at <math>f_0</math> can be linked to <math>\sigma_s</math> whereas component located around <math>f_0</math> can be linked to <math>\sigma_d</math>.		Details have been presented in <ref>N. Barbot, O. Rance, and E. Perret, [https://nicolas-barbot.ovh/wiki/pool/rcs.pdf "Differential RCS of modulated tag,"] IEEE Transactions on Antennas and Propagation, pp. 1–1, 2021, early access. doi: 10.1109/TAP.2021.3060943.</ref> and can be seen as a complementary definition compared to the time definition. The basic idea relies on the decomposition of the RCS <math>\sigma</math> into a static RCS <math>\sigma_s</math> and a dynamic RCS <math>\sigma_d</math> and to pass into the frequency domain. Fig. 1 presents the main result where the (total) backscattered signal by the modulating UHF tag can be decomposed into 2 parts. Component located at <math>f_0</math> can be linked to <math>\sigma_s</math> whereas component located around <math>f_0</math> can be linked to <math>\sigma_d</math>.

	Also, this frequency definition (as the original definition) is not limited to RFID tags and can be applied to any linear time-varying system such as rotating tags, moving tag and (surprisingly) barcodes.		Also, this frequency definition (as the original definition) is not limited to RFID tags and can be applied to any linear time-varying system such as rotating tags, moving tag and (surprisingly) barcodes.
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	<math>		<math>
	\sigma_d = (1 - J_0(\beta)) \sigma		\sigma_d = [1 - J_0(\beta)] \sigma
	</math>		</math>

Nico at 12:27, 16 August 2021

2021-08-16T12:27:34Z

← Older revision		Revision as of 12:27, 16 August 2021
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	Differential RCS characterizes the aptitude of a tag to modulate the backscattered power. This parameter is has been introduced by P. Nikitin for UHF tags <ref>P. V. Nikitin, K. V. S. Rao, and R. D. Martinez, “Differential RCS of RFID tag,” Electronics Letters, vol. 43, no. 8, pp. 431–432, Apr. 2007.</ref> and is classically estimated based on the variation of the IQ channels of the two states of the chip in the time domain. This quantity can however be generalized for any modulating tag in the frequency domain. The frequency definition remains compatible to the time definition. Finally, this new definition allows to estimate the delta RCS of any tag accurately using a simple spectrum analyzer.		Differential RCS (or delta RCS) characterizes the aptitude of a tag to modulate the backscattered power. This parameter is has been introduced by P. Nikitin for UHF tags <ref>P. V. Nikitin, K. V. S. Rao, and R. D. Martinez, “Differential RCS of RFID tag,” Electronics Letters, vol. 43, no. 8, pp. 431–432, Apr. 2007.</ref> and is classically estimated based on the variation of the IQ channels of the two states of the chip in the time domain. This quantity can however be generalized for any modulating tag in the frequency domain. The frequency definition remains compatible to the time definition. Finally, this new definition allows to estimate the delta RCS of any tag accurately using a simple spectrum analyzer.

	__TOC__		__TOC__
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	Another consequence is that linear time-invariant systems, are characterized by a delta RCS of 0.		Another consequence is that linear time-invariant systems, are characterized by a delta RCS of 0.

	==Known ~~Differential~~ RCS==		==Known Delta RCS==

	* For a UHF tag, assuming that the chip can switch with a equal probability in-between 2 states characterized with <math>\Gamma_1</math> and <math>\Gamma_2</math>, and is connected to a half-wavelength antenna, the delta RCS <math>\sigma_d</math> can be expressed as:		* For a UHF tag, assuming that the chip can switch with a equal probability in-between 2 states characterized with <math>\Gamma_1</math> and <math>\Gamma_2</math>, and is connected to a half-wavelength antenna, the delta RCS <math>\sigma_d</math> can be expressed as:

Nico at 09:49, 16 August 2021

2021-08-16T09:49:14Z

← Older revision		Revision as of 09:49, 16 August 2021
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	Differential RCS characterizes the aptitude of a tag to modulate the backscattered power. This parameter is has been introduced by P. Nikitin for UHF tags <ref>P. V. Nikitin, K. V. S. Rao, and R. D. Martinez, “Differential RCS of RFID tag,” Electronics Letters, vol. 43, no. 8, pp. 431–432, Apr. 2007.</ref> and is classically estimated based on the variation of the IQ channels of the two states of the chip in the time domain. This quantity can however be generalized for any modulating tag in the frequency domain. The frequency definition remains ~~(almost)~~ compatible to the time definition. Finally, this new definition allows to estimate the delta RCS of any tag accurately using a simple spectrum analyzer.		Differential RCS characterizes the aptitude of a tag to modulate the backscattered power. This parameter is has been introduced by P. Nikitin for UHF tags <ref>P. V. Nikitin, K. V. S. Rao, and R. D. Martinez, “Differential RCS of RFID tag,” Electronics Letters, vol. 43, no. 8, pp. 431–432, Apr. 2007.</ref> and is classically estimated based on the variation of the IQ channels of the two states of the chip in the time domain. This quantity can however be generalized for any modulating tag in the frequency domain. The frequency definition remains compatible to the time definition. Finally, this new definition allows to estimate the delta RCS of any tag accurately using a simple spectrum analyzer.

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