4th Order LC-Based Sigma Delta Modulators
Due to the characteristic of narrow band conversion around a central radio frequency, the Sigma Delta Modulator (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>Δ</mo>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/22/22/8915 |
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| author | Evelyn Cristina de Oliveira Lima Antonio Wallace Antunes Soares Diomadson Rodrigues Belfort |
| author_facet | Evelyn Cristina de Oliveira Lima Antonio Wallace Antunes Soares Diomadson Rodrigues Belfort |
| author_sort | Evelyn Cristina de Oliveira Lima |
| collection | DOAJ |
| description | Due to the characteristic of narrow band conversion around a central radio frequency, the Sigma Delta Modulator (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>Δ</mo></mrow></semantics></math></inline-formula>M) based on LC resonators is a suitable option for use in Software-Defined Radio (SDR). However, some aspects of the topologies described in the state-of-the-art, such as noise and nonlinear sources, affect the performance of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>Δ</mo></mrow></semantics></math></inline-formula>M. This paper presents the design methodology of three high-order LC-Based single-block Sigma Delta Modulators. The method is based on the equivalence between continuous time and discrete time loop gain using a Finite Impulse Response Digital-to-Analog Converter (FIRDAC) through a numerical approach to defining the coefficients. The continuous bandpass LC <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>Δ</mo></mrow></semantics></math></inline-formula>M simulations are performed at a center frequency of 432 MHz and a sampling frequency of 1.72 GHz. To the proposed modulators a maximum Signal-to-Noise Ratio (SNR) of 51.39 dB, 48.48 dB, and 46.50 dB in a 4 MHz bandwidth was achieved to respectively 4th Order Gm-LC <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>Δ</mo></mrow></semantics></math></inline-formula>M, 4th Order Magnetically Coupled <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>Δ</mo></mrow></semantics></math></inline-formula>M and 4th Order Capacitively Coupled <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>Δ</mo></mrow></semantics></math></inline-formula>M. |
| first_indexed | 2024-03-09T18:00:34Z |
| format | Article |
| id | doaj.art-ef277668220b48cf8f3c52244c21960e |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-09T18:00:34Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-ef277668220b48cf8f3c52244c21960e2023-11-24T09:57:52ZengMDPI AGSensors1424-82202022-11-012222891510.3390/s222289154th Order LC-Based Sigma Delta ModulatorsEvelyn Cristina de Oliveira Lima0Antonio Wallace Antunes Soares1Diomadson Rodrigues Belfort2Graduate Program in Electrical and Computer Engineering, Federal University of Rio Grande do Norte, Natal 59078-970, RN, BrazilDepartment of Electrical Engineering, Federal University of Rio Grande do Norte, Natal 59078-970, RN, BrazilDepartment of Electrical Engineering, Federal University of Rio Grande do Norte, Natal 59078-970, RN, BrazilDue to the characteristic of narrow band conversion around a central radio frequency, the Sigma Delta Modulator (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>Δ</mo></mrow></semantics></math></inline-formula>M) based on LC resonators is a suitable option for use in Software-Defined Radio (SDR). However, some aspects of the topologies described in the state-of-the-art, such as noise and nonlinear sources, affect the performance of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>Δ</mo></mrow></semantics></math></inline-formula>M. This paper presents the design methodology of three high-order LC-Based single-block Sigma Delta Modulators. The method is based on the equivalence between continuous time and discrete time loop gain using a Finite Impulse Response Digital-to-Analog Converter (FIRDAC) through a numerical approach to defining the coefficients. The continuous bandpass LC <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>Δ</mo></mrow></semantics></math></inline-formula>M simulations are performed at a center frequency of 432 MHz and a sampling frequency of 1.72 GHz. To the proposed modulators a maximum Signal-to-Noise Ratio (SNR) of 51.39 dB, 48.48 dB, and 46.50 dB in a 4 MHz bandwidth was achieved to respectively 4th Order Gm-LC <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>Δ</mo></mrow></semantics></math></inline-formula>M, 4th Order Magnetically Coupled <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>Δ</mo></mrow></semantics></math></inline-formula>M and 4th Order Capacitively Coupled <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>Δ</mo></mrow></semantics></math></inline-formula>M.https://www.mdpi.com/1424-8220/22/22/8915AD converterSigma Delta ModulatorLC filter |
| spellingShingle | Evelyn Cristina de Oliveira Lima Antonio Wallace Antunes Soares Diomadson Rodrigues Belfort 4th Order LC-Based Sigma Delta Modulators Sensors AD converter Sigma Delta Modulator LC filter |
| title | 4th Order LC-Based Sigma Delta Modulators |
| title_full | 4th Order LC-Based Sigma Delta Modulators |
| title_fullStr | 4th Order LC-Based Sigma Delta Modulators |
| title_full_unstemmed | 4th Order LC-Based Sigma Delta Modulators |
| title_short | 4th Order LC-Based Sigma Delta Modulators |
| title_sort | 4th order lc based sigma delta modulators |
| topic | AD converter Sigma Delta Modulator LC filter |
| url | https://www.mdpi.com/1424-8220/22/22/8915 |
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