## Analysis, Design, and Optimization of Spiral Inductors and Transformers for Si RF IC's (1998)

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Venue: | IEEE J. Solid-State Circuits |

Citations: | 65 - 3 self |

### BibTeX

@ARTICLE{Niknejad98analysis,design,,

author = {Ali M. Niknejad and Student Member and Robert G. Meyer},

title = {Analysis, Design, and Optimization of Spiral Inductors and Transformers for Si RF IC's},

journal = {IEEE J. Solid-State Circuits},

year = {1998},

volume = {33},

pages = {1470--1481}

}

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### Abstract

Silicon integrated circuit spiral inductors and transformers are analyzed using electromagnetic analysis. With appropriate approximations, the calculations are reduced to electrostatic and magnetostatic calculations. The important effects of substrate loss are included in the analysis. Classic circuit analysis and network analysis techniques are used to derive two-port parameters from the circuits. From two-port measurements, loworder, frequency-independent lumped circuits are used to model the physical behavior over a broad-frequency range. The analysis is applied to traditional square and polygon inductors and transformer structures as well as to multilayer metal structures and coupled inductors. A custom computer-aided-design tool called ASITIC is described, which is used for the analysis, design, and optimization of these structures. Measurements taken over a frequency range from 100 MHz to 5 GHz show good agreement with theory.

### Citations

99 | On-chip spiral inductors with patterned ground shields for Si-based
- Yue, Wong
- 1997
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Citation Context ...nce matrix of the device segments can be extracted and used in (6). Various effects can be included in the capacitance matrix calculation, such as the presence of substrate taps and substrate shields =-=[16]-=-. The important effect of substrate coupling between structures residing on the same substrate can also be included. For more details, refer to [11]. III. ASITIC: A COMPUTER-AIDED-DESIGN TOOL FOR INDU... |

54 |
Inductance Calculations
- Grover
- 1946
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Citation Context ...frequency, this matrix may be computed easily since the self- and mutual inductance of each segment can be approximated in closed form by using the geometric mean distance (GMD) approximation. Grover =-=[13]-=- provides formulas for such calculations for fairly arbitrary configurations. In [14], an explicit formula appears for the GMD between two finite thickness parallel rectangular cross sections. In a sq... |

46 |
The modeling, characterization, and design of monolithic inductors for silicon RF IC’s
- Long, Copeland
- 1997
(Show Context)
Citation Context ...gh frequency [5], and thick oxide or floating inductors to isolate the inductor from the lossy substrate [6]. Little, though, has been written on the analysis and optimization of these structures. In =-=[7]-=-, an analysis approach is presented where an equivalent circuit for each segment of the spiral is calculated and the inductor is considered as an interconnection of such segments. The approach is limi... |

40 |
Large suspended inductors on silicon and their use in a 2-µm CMOS RF amplifier
- Chang, Abidi, et al.
- 1993
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Citation Context ...the area of the inductors [3], [4], low-loss substrates to reduce losses in the substrate at high frequency [5], and thick oxide or floating inductors to isolate the inductor from the lossy substrate =-=[6]-=-. Little, though, has been written on the analysis and optimization of these structures. In [7], an analysis approach is presented where an equivalent circuit for each segment of the spiral is calcula... |

39 |
IC–compatible inductors and LC passive filters
- Nguyen, Meyer, et al.
- 1990
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Citation Context ...rs. Hence, there is a great incentive to design, optimize, and model spiral inductors fabricated on Si substrates. This topic is addressed in this paper. Since the introduction of Si spiral inductors =-=[1]-=-, many authors have reported higher performance inductors on Si substrates, primarily utilizing advances in processing technology. This has included higher conductivity metal layers to reduce Manuscri... |

38 |
A 1.8-GHz low-phase-noise CMOS VCO using optimized hollow spiral inductors," Solid-State Circuits
- Craninckx, Steyaert
- 1997
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Citation Context ... allow the circuit designer freedom to choose parameters such as inductance, resistance, capacitance, and . Alternatively, researchers have used commercial threedimensional electromagnetic simulators =-=[8]-=-, [9] to design and analyze inductors and transformers. While this approach is accurate, it can be computationally very expensive and time consuming. This prevents the designer from performing optimiz... |

32 |
A physical model for planar spiral inductors on silicon
- Yue, Ryu, et al.
- 1996
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Citation Context ... is not physical and contains the effects of the capacitive coupling, which tends to boost the inductance as a function of frequency, similar to a parallel tank. The extraction technique presented in =-=[17]-=- is superior in this regard. In this paper, we use the standard extraction procedure to compare our simulation results to measurements. However, for our final device models, we use frequency-independe... |

29 |
Numerically Stable Green Function for Modeling and Analysis of Substrate Coupling
- Niknejad, Gharpurey, et al.
- 1998
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Citation Context ...rm involving the free-space Green function with the appropriate Green functions over a multilayer substrate, the volume of integration reduces to metal segments containing the charge and currents. In =-=[11]-=-, we derive the electrostatic Green function over a multilayer conductive substrate that can be used in (2). 1 By expanding and in (1) using (2) and (3) and by considering the currents and charges in ... |

29 |
A.Singh, “Resistive and Inductive Skin Effect in Rectangular Conductors
- Weeks, McAllister
- 1979
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Citation Context ...f each segment can be approximated in closed form by using the geometric mean distance (GMD) approximation. Grover [13] provides formulas for such calculations for fairly arbitrary configurations. In =-=[14]-=-, an explicit formula appears for the GMD between two finite thickness parallel rectangular cross sections. In a square spiral, all segments are parallel and these formulas suffice. However, for polyg... |

28 |
High Q inductor for wireless applications in a complementary silicon bipolar process
- Ashby, Koullias, et al.
- 1996
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Citation Context ...ering and Computer Science, University of California, Berkeley, CA 94720-1772 USA. Publisher Item Identifier S 0018-9200(98)06998-4. 0018–9200/98$10.00 © 1998 IEEE the loss resistance of the induct=-=or [2]-=-, use of multimetal layers to increase the effective thickness of the spiral inductor and thereby reduce loss, the connection of multimetal layer spirals in series to reduce the area of the inductors ... |

27 |
Circuit Models for Three-Dimensional Geometries Including Dielectrics
- Ruehli, Heeb
- 1992
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Citation Context ...onductive substrate that can be used in (2). 1 By expanding and in (1) using (2) and (3) and by considering the currents and charges in each segment separately, we obtain a system of linear equations =-=[12]-=-. Each equation has terms representing the internal impedance of each segment, as well as the mutual magnetic and electrical coupling between each segment and every other segment, and finally terms re... |

19 |
Microwave inductors and capacitors in standard multilevel interconnect silicon technology
- Burghartz, Soyuer, et al.
- 1996
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Citation Context ..., use of multimetal layers to increase the effective thickness of the spiral inductor and thereby reduce loss, the connection of multimetal layer spirals in series to reduce the area of the inductors =-=[3]-=-, [4], low-loss substrates to reduce losses in the substrate at high frequency [5], and thick oxide or floating inductors to isolate the inductor from the lossy substrate [6]. Little, though, has been... |

11 |
Analog Integrated Circuits for Communication
- Pederson, Mayaram
- 1991
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Citation Context ...ling is again modeled with . While the circuit of Fig. 22 is physically based, one can also derive the equivalent circuit, which contains an ideal transformer at the core with parasitic elements [7], =-=[19]-=-. The model parameters from measurement and simulation appear in Table V. V. CONCLUSION In this paper, we presented techniques to analyze, model, and optimize spiral inductors and transformers on the ... |

8 |
Silicon MMIC inductor modeling for high volume, low cost applications Microwave J. August 60–71
- Lovelace, Camilleri, et al.
- 1994
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Citation Context ...w the circuit designer freedom to choose parameters such as inductance, resistance, capacitance, and . Alternatively, researchers have used commercial threedimensional electromagnetic simulators [8], =-=[9]-=- to design and analyze inductors and transformers. While this approach is accurate, it can be computationally very expensive and time consuming. This prevents the designer from performing optimization... |

7 |
Optimization of high Q integrated inductors for multi-level metal
- Merrill, Lee, et al.
- 1995
(Show Context)
Citation Context ... of multimetal layers to increase the effective thickness of the spiral inductor and thereby reduce loss, the connection of multimetal layer spirals in series to reduce the area of the inductors [3], =-=[4]-=-, low-loss substrates to reduce losses in the substrate at high frequency [5], and thick oxide or floating inductors to isolate the inductor from the lossy substrate [6]. Little, though, has been writ... |

2 |
Temperature dependence of in spiral inductors fabricated in a silicon-germanium/BiCMOS technology
- Groves, Stein, et al.
- 1996
(Show Context)
Citation Context ...uencies for the two definitions. In the following sections on measurement results, the data are measured at room temperature. It is important to calculate at the frequency and temperature of interest =-=[18]-=-. At low frequencies, the temperature coefficient (TC) will depend on the metal TC, whereas at high frequency, the will change due to the TC of the substrate resistance. C. Square Spiral Inductors Sin... |

1 |
High -factor inductors integrated on MCM Si substrates
- Zu, Lu, et al.
- 1996
(Show Context)
Citation Context ...tor and thereby reduce loss, the connection of multimetal layer spirals in series to reduce the area of the inductors [3], [4], low-loss substrates to reduce losses in the substrate at high frequency =-=[5]-=-, and thick oxide or floating inductors to isolate the inductor from the lossy substrate [6]. Little, though, has been written on the analysis and optimization of these structures. In [7], an analysis... |

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