Theoretical Upper and Lower Limits for Normalized Bandwidth of Digital Phase-Locked Loop in GNSS Receivers
Determining the loop noise bandwidth and the coherent integration time is essential and important for the design of a reliable digital phase-locked loop (DPLL) in global navigation satellite system (GNSS) receivers. In general, designers set such parameters approximately by utilizing the well-known...
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MDPI AG
2023-06-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/23/13/5887 |
| _version_ | 1827734469130321920 |
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| author | Young-Jin Song Thomas Pany Jong-Hoon Won |
| author_facet | Young-Jin Song Thomas Pany Jong-Hoon Won |
| author_sort | Young-Jin Song |
| collection | DOAJ |
| description | Determining the loop noise bandwidth and the coherent integration time is essential and important for the design of a reliable digital phase-locked loop (DPLL) in global navigation satellite system (GNSS) receivers. In general, designers set such parameters approximately by utilizing the well-known fact that the DPLL is stable if the normalized bandwidth, which is the product of the integration time and the noise bandwidth, is much less than one. However, actual limit points are not fixed at exactly one, and they vary with the loop filter order and implementation method. Furthermore, a lower limit on the normalized bandwidth may exist. This paper presents theoretical upper and lower limits for the normalized bandwidth of DPLL in GNSS receivers. The upper limit was obtained by examining the stability of DPLL with a special emphasis on the digital integration methods. The stability was investigated in terms of <i>z</i>-plane root loci with and without the consideration of the computational delay, which is a delay induced by the calculation of the discriminator and the loop filter. The lower limit was analyzed using the DPLL measurement error composed of the thermal noise, oscillator phase noise, and dynamic stress error. By utilizing the carrier-to-noise density ratio threshold which indicates the crossing point between the measurement error and the corresponding threshold, the lower limit of the normalized bandwidth is obtained. |
| first_indexed | 2024-03-11T01:29:31Z |
| format | Article |
| id | doaj.art-91cb1b90c028481591384f5f647a7b4e |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-11T01:29:31Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
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| series | Sensors |
| spelling | doaj.art-91cb1b90c028481591384f5f647a7b4e2023-11-18T17:28:15ZengMDPI AGSensors1424-82202023-06-012313588710.3390/s23135887Theoretical Upper and Lower Limits for Normalized Bandwidth of Digital Phase-Locked Loop in GNSS ReceiversYoung-Jin Song0Thomas Pany1Jong-Hoon Won2Autonomous Navigation Laboratory, Department of Electrical and Computer Engineering, Inha University, Incheon 22212, Republic of KoreaInstitute of Space Technology and Space Applications, University of Federal Armed Forces Munich, 85577 Neubiberg, GermanyDepartment of Electrical Engineering, Inha University, Incheon 22212, Republic of KoreaDetermining the loop noise bandwidth and the coherent integration time is essential and important for the design of a reliable digital phase-locked loop (DPLL) in global navigation satellite system (GNSS) receivers. In general, designers set such parameters approximately by utilizing the well-known fact that the DPLL is stable if the normalized bandwidth, which is the product of the integration time and the noise bandwidth, is much less than one. However, actual limit points are not fixed at exactly one, and they vary with the loop filter order and implementation method. Furthermore, a lower limit on the normalized bandwidth may exist. This paper presents theoretical upper and lower limits for the normalized bandwidth of DPLL in GNSS receivers. The upper limit was obtained by examining the stability of DPLL with a special emphasis on the digital integration methods. The stability was investigated in terms of <i>z</i>-plane root loci with and without the consideration of the computational delay, which is a delay induced by the calculation of the discriminator and the loop filter. The lower limit was analyzed using the DPLL measurement error composed of the thermal noise, oscillator phase noise, and dynamic stress error. By utilizing the carrier-to-noise density ratio threshold which indicates the crossing point between the measurement error and the corresponding threshold, the lower limit of the normalized bandwidth is obtained.https://www.mdpi.com/1424-8220/23/13/5887coherent integration timeglobal navigation satellite system (GNSS) receiverloop noise bandwidthnormalized bandwidthphase-locked loop (PLL)signal tracking loop |
| spellingShingle | Young-Jin Song Thomas Pany Jong-Hoon Won Theoretical Upper and Lower Limits for Normalized Bandwidth of Digital Phase-Locked Loop in GNSS Receivers Sensors coherent integration time global navigation satellite system (GNSS) receiver loop noise bandwidth normalized bandwidth phase-locked loop (PLL) signal tracking loop |
| title | Theoretical Upper and Lower Limits for Normalized Bandwidth of Digital Phase-Locked Loop in GNSS Receivers |
| title_full | Theoretical Upper and Lower Limits for Normalized Bandwidth of Digital Phase-Locked Loop in GNSS Receivers |
| title_fullStr | Theoretical Upper and Lower Limits for Normalized Bandwidth of Digital Phase-Locked Loop in GNSS Receivers |
| title_full_unstemmed | Theoretical Upper and Lower Limits for Normalized Bandwidth of Digital Phase-Locked Loop in GNSS Receivers |
| title_short | Theoretical Upper and Lower Limits for Normalized Bandwidth of Digital Phase-Locked Loop in GNSS Receivers |
| title_sort | theoretical upper and lower limits for normalized bandwidth of digital phase locked loop in gnss receivers |
| topic | coherent integration time global navigation satellite system (GNSS) receiver loop noise bandwidth normalized bandwidth phase-locked loop (PLL) signal tracking loop |
| url | https://www.mdpi.com/1424-8220/23/13/5887 |
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