臺灣博碩士論文加值系統

當電路的特徵尺度越來越小, 很多次要因素逐漸彰顯, 例如: 在電壓網格網路上, 動態電壓振蕩不能再被忽略. 在這篇論文中, 我們把焦點放在電壓網格網路上的暫態反應, 並且觀察此反應下的電壓波動效應 ( 此效應被稱為電阻壓降 ), 希望討論在何種樣本下會產生最大的壓降. 我們研究了兩種方法來解決或分析此電壓波動效應. 第一種是傳統模擬, 我們自行開發線性常微分方程解題工具, 並且由此工具來驗證我們的想法. 另一種是猜測法, 此種方法建立在對電路上的認知, 而且能避開模擬, 因為模擬很花時間. 除此之外, 我們觀察到電壓網格網路和傳輸線是同構, 所以我們嘗試利用信號在傳輸線上的延遲和衰退效果來作為猜測的基石. 尤有甚者, 目前工業界採用退耦電容 (Decoupling capacitance) 來降低電流變化率, 進而減低電感壓降效應. 但是退耦電容的研究皆著重在頻譜上阻抗的壓制, 此阻抗壓制效果並不能表示暫態反應的結果, 只能說共振頻率的避免是必要條件.

As feature size of a circuit decrease, many second order effects such as transient effect of power grid network cannot be ignored during design. In this thesis, we focus on transient effect of power grid network, this transient effects cause voltage fluctuation over power grid network, called IR drop. We survey two approaches to solve/analyze voltage fluctuation over power grid network. The first approach is prediction-based method different from simulated-based approach. We observe that power grid network is isomorphic to a transmission line and we try to predict voltage fluctuation by signal propagation and decay properties without simulating state equation like HSPICE. The other is effect of decoupling capacitance on power grid network, we connect decap effect with transmission line, but relationship between steady state response and transient problem is not clear.

Abstract …………………………………………………………………1

Contents …………………………………………………………………2

List of Figures …………………………………………………………..4

List of Tables ……………………………………………………………9

Chapter 1 Introduction ……………………………………………...10

Chapter 2 IR drop …………………………………………………...12

Chapter 3 Network topology ……………………………………….14
3.1 Power grid network ……………………….………………….14
3.2 (Step 1) Convert power grid network to RLC network ........15
3.3 (Step 2) Transform logic device to ideal current source ........15
3.3.1 Dimension of interconnect …………………………….…...19
3.3.2 Dimension of MOSFET ………………………………….....20
3.4 (Step 3) Build up circuit equation based on state analysis. ...22
3.5 Three approaches to solve /analyze IR drop. ……………....23
3.6 Relationship between power network and Transmission
line. .............................................................................................24

Chapter 4 Resistor-network ………………………………………...26

Chapter 5 Transmission line theory ………………………………..31
5.1 T model of transmission line ………………………………….31
5.2 decay property of transmission line ………………………….34
5.3 Propagation property of lumped circuit …………..…………34
5.4 Schematic diagram for wave propagation …………………...34

Chapter 6 Approximation Scheme …………………………………40
6.1 Approximation of RLC circuit by RC model ………………...40
6.2 Simple RC circuit ( approximated RLC circuit ) …………....41
6.3 Current direction and propagation of RC network, and RLC
network. ………………………………………………………..44
Chapter 7 Decoupling capacitance analysis ………………………47
7.1 Objectives of decap insertion ……………………………..47
7.2 How does decap work ? ……………………………………47
7.3 Harmonic analysis for decap effect ……………………….47
7.4 Classification of decap ……………………………………..48
7.5 Dimension between MOSFET device and MOS_decap ….49
7.6 Decap effect estimation …………………………….............50
7.7 Capacitive effect of simple RLC …………………………...51
7.8 Spectrum of circuit matrix in Transmission line …………52
7.9 high frequency modes in transmission line ……………….53

Chapter 8 Conclusions ………………………………………….….57

Reference ………………………………………………………….….58

Appendix A : State equation build-up ……………………………....59
1. Nodal analysis ………………………………………………....59
2. Loop analysis …………………………………………….……59
3. Cut-set analysis ……………………………………….….……60
4. State analysis ……………………………………………..……61

Appendix B Transmission line theory ………………………………63
B.1 Transmission line of distributed RLC …………………….63
B.2 Discrete Transmission line with lump circuit elements ….65

Appendix C Harmonic Analysis …………………………………........68
C.1 Fourier Transformation and uncertainty principle ……...68
C.2 Translation property ……………………………………….69

[1] HSPICE manual
[2] ROBERT E. COLLIN, foundations for microwave engineering, 2nd edition.
[3] McOwen, Partial differential Equations Methods and Applications, 2nd edition.
[4] Paul M. Chirlian, Basic Network Theory.
[5] Bharat Kinariwala, Franklin F. Kuo, Nai-kuan Tsao, Linear Circuits and Computation.
[6] Franklin F. Kuo, Computer Applications in Electrical Engineering Series.
[7] David Kincaid, Ward Cheney, Numerical Analysis.
[8] Uyemura, Introduction to VLSI circuits and Systems.
[9] Larry D. Smith, Raymond E. Anderson, Douglas W. Forehand, Thomas J. Pelc and Tanmoy Roy, Power Distribution System Design Methodology and Capacitor Selection for Modern CMOS Technology.
[10] Patrik Larssion, Parasitic Resistance in an MOS Transistor Used as On-Chip Decoupling Capacitance.