Estimation of Attenuation and Phase Delay in Driving Voltage Waveform of an Ultra-High-Speed Image Sensor by Dimensional Analysis
We present an explicit expression to estimate driving voltage attenuation through RC networks representation of an ultrahigh- speed image sensor. Elmore delay metric for a fundamental RC chain is employed as the first-order approximation. By application of dimensional analysis to SPICE simulation data, we found a simple expression that significantly improves the accuracy of the approximation. Estimation error of the resultant expression for uniform RC networks is less than 2%. Similarly, another simple closed-form model to estimate 50 % delay through fundamental RC networks is also derived with sufficient accuracy. The framework of this analysis can be extended to address delay or attenuation issues of other VLSI structures.
[1] T. G. Etoh, D. Poggermann, A. Ruckelshausen, A. J. P. Theuwissen, G.
Kreider, H. O. Folkerts, H. Mutoh, Y. Kondo, H. Maruno, K. Takubo, H.
Soya, K. Takehara, T. Okinaka, Y. Takano, T. Reisinger, and C. Lohman,
"A CCD image sensor of 1Mframes/s for continuous image capturing of
103 frames", Digest of Technical Papers, IEEE Int. Solid-State Circuits
Conf., San Francisco, CA, pp. 46-47, 2002.
[2] T. G. Etoh, D. Poggermann, G. Kreider, H. Mutoh, A. J. P. Theuwissen, A.
Ruckelshausen, Y. Kondo, H. Maruno, K. Takubo, H. Soya, K. Takehara,
T. Okinaka, and Y. Takano, "An image sensor which captures 100
consecutive frames at 1,000,000 frame/s", IEEE Trans.Electron Dev., vol.
50, no. 1, Jan. 2003, pp. 144-151.
[3] T. G. Etoh, C. Vo Le, Y. Hashishin, N. Otsuka, K. Takehara, H. Ohtake,
T. Hayashida, and H. Maruyama, "Evolution of ultra-high-speed CCD
imagers", Plasma and Fusion Research, 2, S1021, 2007.
[4] P. Karimov, , C. Vo Le, K. Takehara, S. Yokoi, and T. G. Etoh, "Phototriggering
system for an ultra high speed video microscopy", Review of
scientific instruments, vol.78, 113702, Nov. 2007.
[5] W.C. Elmore, "The transient response of damped linear networks with
particular regard to wide-band amplifiers," J. Appl. Phys., vol. 19, no. 1,
Jan. 1948, pp. 55-63.
6
[6] S. Y. Kim and S. S. Wong, "Closed-form RC and RLC delay models
considering input rise time," IEEE Trans.Circuits Syst.-I, Regular Papers,
vol. 54, no. 9, Sep. 2007, pp. 2001-2010.
[7] L.T. Pillage and R.A. Rohrer, "Asymptotic waveform evaluation for
timing analysis," IEEE Trans. Comput-Aided Des.Integr.Circuits Syst.,
vol. 9, no. 4, Apr. 1990, pp. 352-366.
[8] C. L. Ratzlaff, N. Gopal, and L. T. Pillage, "RICE: Rapid interconnect
circuit evaluator," in Proc. IEEE/ACM Design Automation Conf., 1991,
pp. 555-560.
[9] Y. I. Ismail and C. Amin, "Computation of Signal Threshold Crossing
Times Directly from Higher Order Moments", IEEE Trans. Comput-
Aided Des.Integr. Circuits Syst.,vol. 23, no. 8, Aug. 2004, pp. 1264-1276.
[10] D. E. Khalil, Y. Ismail, M. Khellah, T. Karnik, and V. De, "Analytical
Model for the Propagation Delay of Through Silicon Vias", in Proc. 9th
Int. Symp. Quality Electronic Design, 2008, pp. 553-556.
[11] J. Vlach, J. A. Barby, A. Vannelli, T. Talkhan, and C. J. Shi, "Group
delay as an estimate of delay in logic," IEEE Trans. Comput.-Aided Des.
Integr. Circuits Syst., vol.10, no. 7, July 1991, pp. 949-953.
[12] M. Celik and L. T. Pillegi., "Metrics and bound for phase delay and
signal attenuation in RC(L) clock trees," IEEE Trans.Comput.-Aided Des.
Integr. Circuits Syst., vol.18, no. 3, Mar. 1999, pp. 293-300.
[1] T. G. Etoh, D. Poggermann, A. Ruckelshausen, A. J. P. Theuwissen, G.
Kreider, H. O. Folkerts, H. Mutoh, Y. Kondo, H. Maruno, K. Takubo, H.
Soya, K. Takehara, T. Okinaka, Y. Takano, T. Reisinger, and C. Lohman,
"A CCD image sensor of 1Mframes/s for continuous image capturing of
103 frames", Digest of Technical Papers, IEEE Int. Solid-State Circuits
Conf., San Francisco, CA, pp. 46-47, 2002.
[2] T. G. Etoh, D. Poggermann, G. Kreider, H. Mutoh, A. J. P. Theuwissen, A.
Ruckelshausen, Y. Kondo, H. Maruno, K. Takubo, H. Soya, K. Takehara,
T. Okinaka, and Y. Takano, "An image sensor which captures 100
consecutive frames at 1,000,000 frame/s", IEEE Trans.Electron Dev., vol.
50, no. 1, Jan. 2003, pp. 144-151.
[3] T. G. Etoh, C. Vo Le, Y. Hashishin, N. Otsuka, K. Takehara, H. Ohtake,
T. Hayashida, and H. Maruyama, "Evolution of ultra-high-speed CCD
imagers", Plasma and Fusion Research, 2, S1021, 2007.
[4] P. Karimov, , C. Vo Le, K. Takehara, S. Yokoi, and T. G. Etoh, "Phototriggering
system for an ultra high speed video microscopy", Review of
scientific instruments, vol.78, 113702, Nov. 2007.
[5] W.C. Elmore, "The transient response of damped linear networks with
particular regard to wide-band amplifiers," J. Appl. Phys., vol. 19, no. 1,
Jan. 1948, pp. 55-63.
6
[6] S. Y. Kim and S. S. Wong, "Closed-form RC and RLC delay models
considering input rise time," IEEE Trans.Circuits Syst.-I, Regular Papers,
vol. 54, no. 9, Sep. 2007, pp. 2001-2010.
[7] L.T. Pillage and R.A. Rohrer, "Asymptotic waveform evaluation for
timing analysis," IEEE Trans. Comput-Aided Des.Integr.Circuits Syst.,
vol. 9, no. 4, Apr. 1990, pp. 352-366.
[8] C. L. Ratzlaff, N. Gopal, and L. T. Pillage, "RICE: Rapid interconnect
circuit evaluator," in Proc. IEEE/ACM Design Automation Conf., 1991,
pp. 555-560.
[9] Y. I. Ismail and C. Amin, "Computation of Signal Threshold Crossing
Times Directly from Higher Order Moments", IEEE Trans. Comput-
Aided Des.Integr. Circuits Syst.,vol. 23, no. 8, Aug. 2004, pp. 1264-1276.
[10] D. E. Khalil, Y. Ismail, M. Khellah, T. Karnik, and V. De, "Analytical
Model for the Propagation Delay of Through Silicon Vias", in Proc. 9th
Int. Symp. Quality Electronic Design, 2008, pp. 553-556.
[11] J. Vlach, J. A. Barby, A. Vannelli, T. Talkhan, and C. J. Shi, "Group
delay as an estimate of delay in logic," IEEE Trans. Comput.-Aided Des.
Integr. Circuits Syst., vol.10, no. 7, July 1991, pp. 949-953.
[12] M. Celik and L. T. Pillegi., "Metrics and bound for phase delay and
signal attenuation in RC(L) clock trees," IEEE Trans.Comput.-Aided Des.
Integr. Circuits Syst., vol.18, no. 3, Mar. 1999, pp. 293-300.
@article{"International Journal of Electrical, Electronic and Communication Sciences:58956", author = "V. T. S. Dao and T. G. Etoh and C. Vo Le and H. D. Nguyen and K. Takehara and T. Akino and K. Nishi", title = "Estimation of Attenuation and Phase Delay in Driving Voltage Waveform of an Ultra-High-Speed Image Sensor by Dimensional Analysis", abstract = "We present an explicit expression to estimate driving voltage attenuation through RC networks representation of an ultrahigh- speed image sensor. Elmore delay metric for a fundamental RC chain is employed as the first-order approximation. By application of dimensional analysis to SPICE simulation data, we found a simple expression that significantly improves the accuracy of the approximation. Estimation error of the resultant expression for uniform RC networks is less than 2%. Similarly, another simple closed-form model to estimate 50 % delay through fundamental RC networks is also derived with sufficient accuracy. The framework of this analysis can be extended to address delay or attenuation issues of other VLSI structures.
", keywords = "Dimensional Analysis, Elmore model, RC network, Signal Attenuation, Ultra-High-Speed Image Sensor.", volume = "2", number = "10", pages = "2305-6", }