ECE 497 JS Lecture - 13 Projects

Transcription

1 ECE 497 JS Lecture - 13 Projects Spring 2004 Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois jose@emlab.uiuc.edu 1

2 ECE 497 JS - Projects All projects should be accompanied with a short paper (3-5 pages) Paper surveys should be about pages. P1. Write a program that simulates transients on a uniform lossless line. P2. Write a moment method code to calculate the capacitance per unit length of a single microstrip line. P3. Write a program that predicts the TDR response of a device from the measured s parameters. P4. Write an FDTD program to calculate the frequency dependence of a microstrip line P5. Develop an IBIS model for a CMOS differential amplifier P6. Write a single TL program that will accept IBIS models at its terminations P7. TBD on power distribution P8. On signaling techniques P9. Paper survey on related subjects 2

3 P1 - Procedure for Multiconductor Solution 1) Get L and C matrices and calculate LC product 2) Get square root of eigenvalues and eigenvectors of LC matrix Λ m 3) Arrange eigenvectors into the voltage eigenvector matrix E 4) Get square root of eigenvalues and eigenvectors of CL matrix Λ m 5) Arrange eigenvectors into the current eigenvector matrix H 6) Invert matrices E, H, Λ m. 7) Calculate the line impedance matrix Z c Z c = E -1 Λ -1 m EL 3

4 P1 - Procedure for Multiconductor Solution 8) Construct source and load impedance matrices Z s (t) and Z L (t) 9) Construct source and load reflection coefficient matrices Γ 1 (t) and Γ 2 (t). 10) Construct source and load transmission coefficient matrices T 1 (t), T 2 (t) 11) Calculate modal voltage sources g 1 (t) and g 2 (t) 12) Calculate modal voltage waves: a 1 (t) = T 1 (t)g 1 (t) + Γ 1 (t)a 2 (t - τm) a 2 (t) = T 2 (t)g 2 (t) + Γ 2 (t)a 1 (t - τm) b 1 (t) = a 2 (t - τ m ) b 2 (t) = a 1 (t - τ m ) 4

5 ai ai a i( t τ m ) = ai mode 1 mode mode n ( t τ 2( t τ ( t τ τ mi is the delay associated with mode i. τ mi = length/velocity of mode i. The modal volage wave vectors a 1 (t) and a 2 (t) need to be stored since they contain the history of the system. 13) Calculate total modal voltage vectors: V m1 (t) = a 1 (t) + b 1 (t) V m2 (t) = a 2 (t) + b 2 (t) 14) Calculate line voltage vectors: V 1 (t) = E -1 V m1 (t) V 2 (t) = E -1 V m2 (t) P1 - Wave-Shifting Solution m1 m2 mn ) ) ) 5

6 P1 Example: 7-Line Microstrip ALS04 Drive Line 1 ALS240 ALS04 Drive Line 2 ALS240 ALS04 Drive Line 3 ALS240 Sense Line 4 ALS04 Drive Line 5 ALS240 ALS04 Drive Line 6 ALS240 ALS04 Drive Line 7 ALS240 z=0 z=l L s = 312 nh/m; C s = 100 pf/m; L m = 85 nh/m; C m = 12 pf/m. 6

7 P1 - References J. E. Schutt-Aine and R. Mittra, "Transient analysis of coupled lossy transmission lines with nonlinear terminations," IEEE Trans. Circuit Syst., vol. CAS-36, pp , July J. E. Schutt-Aine and D. B. Kuznetsov, "Efficient transient simulation of distributed interconnects," Int. Journ. Computation Math. Electr. Eng. (COMPEL), vol. 13, no. 4, pp , Dec D. B. Kuznetsov and J. E. Schutt-Ainé, "The optimal transient simulation of transmission lines," IEEE Trans. Circuits Syst.-I., vol. cas-43, pp , February W. T. Beyene and J. E. Schutt-Ainé, "Efficient Transient Simulation of High-Speed Interconnects Characterized by Sampled Data," IEEE Trans. Comp., Hybrids, Manufacturing Tech. vol. 21, pp , February

8 P2 Static Field Solver Methods Acronyms PEEC: partial element equivalent circuit MOM: method of moments MOL: method of lines FEM: finite element method CGM: conjugate gradient method Geometry Physical Model Static Analysis Maxwell's Equations: (d/dt =0) Integral Form Differential Form Integral Equation Methods Domain Methods Green's Function - Spectral domain - Closed-form PEEC No retardation FEM Static MOL Static Solvers - MOM - CGM - Fast Multipole Matrix Solver - Sparse matrix techniques - Full matrix techniques Output - Charge distribution Output - Potential distribution Circuit models R, L, G, C 8

9 P2 - Capacitance Calculation φ = grr (, ') σ (') r dr' φ = potential ( known) g( r, r ') = Green' s function (known) σ ( r ') = charg e distribution ( unknown) Once the charge distribution is known, the total charge Q can be determined. If the potential φ=v, we have Q=CV To determine the charge distribution, use the moment method 9

10 P2 - METHOD OF MOMENTS Operator equation L(f) = g L = integral or differential operator f = unknown function g = known function Expand unknown function f f = n α n f n 10

11 P2 - METHOD OF MOMENTS in terms of basis functions f n, with unknown coefficients α n to get Matrix equation n α n L(f n ) = g Finally, take the scalar or inner product with testing of weighting functions w m : α n w m, Lf n = w m,g n [ l mn ][ α n ]=[ g m ] 11

12 P2 - METHOD OF MOMENTS [ l mn ]= w 1, Lf 1 w 1, Lf 2... w 2, Lf 1 w 2, Lf [ α n ]= α 1 α 2 Solution for weight coefficients. 1 [ α n ]= l nm [ g m ]= [ ] [ ] g m w 1,g w 2,g. 12

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14 P3 - Using Frequency Domain Data for Time-Domain Simulation a 1 (ω) b 1 (ω) One-Port Approach Scattering parameter of one-port network can be measured over a wide frequency range. Since incident and reflected voltage waves are related through the measured scattering parameters, the total voltage can be determined as a function of frequency. 14

15 P3 - One-Port S-Parameter Measurements Z o x=0 V f Zo Unknown and Junction Discontinuities V b V s (ω) Reference Line Vs ( ω) Vf ( x= 0, ω) = 2 Vs ( ω) Vb ( x= 0, ω) = S11( ω) 2 Vs ( ) V( x= 0, ω) = ω [ 1 + S11( ω) ] = Vo ( ω) 2 15

16 P3 - Frequency-to-Time Analysis S 11 (ω) is measured experimentally. Assume v s (t) to be an arbitrary time-domain signal (unit step, pulse, impulse). V s (ω) is its transform j2π ft Vs( ω) vs( t) e dt = Since the system is linear, its response in the time domain is the superposition of the responses due to all frequencies + j2 [ ω ] π ft v () t V ( ω)1 S ( ) e dt o = s

17 P3 - Transformation Steps Measure S 11 (f) Calculate V s (ω) analytically Evaluate V o (ω)= [1+S 11 (ω)]. Feed V o (ω) into inverse Fourier transform to get v o (t) 17

18 P3 - Problems and Issues Discretization: (not a continuous spectrum) Truncation: frequency range is band limited F: frequency range N: number of points f = F/N: frequency step t = time step 18

19 P3 - Addressing Frequency and Time Limitations 1. For negative frequencies use conjugate relation V(-ω)= V*(ω) 2. DC value: use lower frequency measurement 3. Rise time is determined by frequency range or bandwidth 4. Time step is determined by frequency range 5. Duration of simulation is determined by frequency step 19

20 P3 - Addressing Frequency and Time Limitations Problems & Limitations (in frequency domain) Discretization Consequences (in time domain) Time-domain response will repeat itself periodically (Fourier series) Aliasing effects Solution Take small frequency steps. Minimum sampling rate must be the Nyquist rate Truncation in Frequency Time-domain response will have finite time resolution (Gibbs effect) Take maximum frequency as high as possible No negative frequency values Time-domain response will be complex Define negative-frequency values and use V(-f)=V*(f) which forces v(t) to be real No DC value Offset in time-domain response, ringing in base line Use measurement at the lowest frequency as the DC value 20

21 P3 Example: Microstrip Line TDR Simulation 1.5 Simulated Step Response 1.0 Reflection Coefficient Time (ns) 21

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23 P4 - Study of Microstrip Structures By Using FDTD and PML -The finite difference time domain (FDTD) method discretizes Maxwell s equations in both space and time using second-order accurate central difference formulas. - Arbitrary geometries are described on a uniform rectangular mesh, and the electric and magnetic fields are determined at discrete locations within the mesh as a function of the time - The electric field values are located on the edges of the rectangular FDTD cells, and the magnetic field values are located at the centers of the faces of the cells. - The dimensions of each cell are x by y by z, and time step is t. 23

24 P4 - Yee Algorithm ( ) n E x (i, j,k) = n 1 1 t Ex (i, j,k) + ε y H z n 1/2 n 1/2 (i, j,k) H z (i, j 1,k ) ( ) 1 t ε z H y n 1/2 n 1/2 (i, j,k) H y (i, j,k 1) n+1/2 H x (i, j,k) = n 1/2 1 t Hx (i, j,k) µ y E z n n (i, j + 1, k) E z (i, j,k) ( ) 1 t µ z E y n n (i, j,k + 1) E y (i, j,k) ( ) 24

25 P4-3D Yee Cell E y H z E x E x E y E z H x E z Hy H y z E y y E z E x H x H z E z Ex x (i,j,k) E y 25

26 P4 Full-Wave Field Solver Methods Geometry Physical Model Dynamic Analysis Acronyms FDTD: finite difference time domain TLM: transmission line method Maxwell's Equations: (d/dt 0) Frequency Domain Full-Wave Techniques Spectral methods Time Domain Time-Domain Techniques - FDTD - TLM Output E(f), H(f) Fourier Output E(t), H(t) Visualization - Matlab - Hoops Dynamic circuit models R(f), L(f), G(f), C(f) 26

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28 P5 IBIS Diagram Power Clamp Input Package Enable Package GND Clamp Power Clamp Threshold & Enable Logic Pullup Ramp Pulldown Ramp Pullup V/I Pulldown V/I Power Clamp GND Clamp Output Package GND Clamp 28

29 P5 IBIS Input Topology Vcc R_pkg L_pkg Power_Clamp C_pkg GND_Clamp C_comp GND GND

30 P5 IBIS Output Topology V cc V cc R_pkg C_omp L_pkg C_pkg Pullup Pulldown Ramp Power_Clamp GND_Clamp GND GND 30

31 P4 IBIS Model Generation Create an IBIS model from either simulation or empirical data Model from Empirical data? No Get SPICE I/O info Yes Collect Data Data in IBIS text file Run SPICE to IBIS Translator Run IBIS Parser No Parser Pass Yes Run model on Simulator No Model validated? Yes Adopt model 31

32 P4 IBIS References Visit 32