FULLY INTEGRATED CURRENT-MODE SUBAPERTURE CENTROID CIRCUITS AND PHASE RECONSTRUCTOR Alushulla J. Ambundo 1 and Paul M. Furth 2

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1 FULLY NTEGRATED CURRENT-MODE SUBAPERTURE CENTROD CRCUTS AND PHASE RECONSTRUCTOR Alushulla J. Ambundo 1 and Paul M. Furth 1 Mixed-Signal-Wireless (MSW), Texas nstruments, Dallas, TX aambundo@ti.com Dept. of Electrical & Computer Engineering, New Mexico State Univ., Las Cruces, NM pfurth@nmsu.edu Abstract This work describes a single-chip solution to the problem of phase reconstruction of an aberrated plane wave. n this solution we amplify a current generated by a CMOS imager, compute the second derivative and inject it directly into a resistive grid in one chip. Four large photodiodes, arranged as a quad cell, generate continuous photocurrents in the picoampere range. We use the translinear characteristics of MOS transistors operating in the subthreshold region to linearly amplify each photocurrent and normalize them by the sum of the photocurrents in the quad cell. Thus, our centroid computation is independent of the absolute light intensity. The finite difference computation is achieved through current summation at the nodes on the resistive grid. This work describes the design, analysis and characterization to solve the problem of computing the phase of an incoming wavefront. ntroduction Compared to digital signal processing, analog signal processing is proving to be the way forward in large-scale neural computation. Analog processing has higher possible bandwidth and, given that the Metal Oxide Semiconductor (MOS) devices operate in the subthreshold region, power consumption is extremely low. Sensory data is in the analog domain and thus compatibility to higher-level analog signal processing blocks is guaranteed. There is no need for costly analog-to-digital (A/D) conversions. Further, current-mode operation provides circuit simplicity, higher operating speed, low power dissipation and wide dynamic range. Finally, low power circuits implemented in subthreshold occupy small silicon area, thus leading to higher yield.

2 The motivation behind this work is to come up with a single chip solution that will reconstruct the phase of an aberrated plane wave incident upon a surface. t is based on research previously published by Furth and Clark [1] in which centroid computations and wave reconstruction are not integrated on one chip. Lenslets focus the slope of the phase onto a spot, which represents the first derivative of the phase. The purpose of our centroid circuit is to determine the position of the focused spot. Signals from the centroid circuit are then processed and injected into a resistive grid, which does phase reconstruction [] by solving Poisson s equation. n this work we are able to integrate the centroid computation, the second derivative and phase reconstruction on one chip. Figure 1 depicts a brief summary of the project implementation. Further hardware testing was carried out on a previously fabricated chip to verify the translinear principle. Aberrated wavefront Lenslets Finite difference R + - inj V node R + - inj V node R + - 1st derivative of phase inj V node R recontructed phase Focused spot location Resistive grid Figure 1 One-dimensional diagram of fully integrated current-mode subaperture centroid circuits and phase reconstructor.

3 The second derivative can be computed by taking the difference between the centroid currents at neighboring quad cells. Equation (1) shows the unnormalized second derivative along the x-axis while equation () shows the same along the y-axis. The resistive grid then yields the solution to the Poisson's equation, i.e. reconstructs the phase of the wavefront. u x u x ( ) ( ) out11 out1 out3 out4 out13 out14 out1 out ( ) ( ) out11 out13 out3 out34 out1 out14 out31 out33 (1) () [1,1] [1,3] out 1,1 out1,3 out,3 out,1 [,1] [,3] V x [1,] [1,4] out1,4 out 1, out, out,4 [,] [,4] V y Figure Current injection into a x resistive grid along the x-axis. x Figure shows how currents are injected into the resistive grid. Consider node V. Currents out1, 1, out1,, out, 3 and out, 4 are amplified photocurrents generated by sensor s [1,1],[1,],[,3] and [,4] respectively. Using PMOS low voltage current mirrors these currents are sourced into node V. Next, currents out1, 3, out1, 4, x out,1 and out, are amplified photocurrents generated by sensor s [1,3] [1,4], [,1] and [,] respectively. Using NMOS low voltage current mirrors these currents are sunk out of node V x. Further we need to keep the centroid computation insensitive to light intensity. According to [3] we can determine the x and y tilt of the wavefront averaged over the subaperture defined by the lenslet using a difference between neighbors divided by the sum of all the photocurrents in a centroid. The normalized second derivative along the x-

4 axis is now given by (4) while the normalized second derivative along the y-axis is given by (5). x y u u ( photo11 photo1 photo3 photo4 ) ( ) photo11 photo1 photo13 photo14 ( photo11 photo13 photo3 photo34 ) ( ) photo11 photo13 photo1 photo14 ( photo13 photo14 photo1 photo ) ( ) photo1 photo photo3 photo4 ( photo1 photo14 photo31 photo33 ) ( ) photo31 photo3 photo34 photo33 ( 4) ( 5) n designing a current we make use of the translinear loop principle [4]. This principle should hold as long as the source to bulk voltage is made equal to zero or constant [6]. Using the translinear principle on the current and looking at the loop -A- B-C- of Figure 3 we are able to generate the following relation: V CW CCW V + V V 0 (3) Assuming κ 1 κ κ3 κ 4 that the gate-to-source voltages are approximately given by V GS VT κ ln S D o it follows that V T κ 1 ln S 0 ln S o 3 ln S o 4 ln S o 0 (4) 1 34 ln ln (5) So S o f the device dimensions are similar then or out

5 V DD V DD M1 V 1 B V 3 M3 4 out 1 A M C 3 V 4 M4 V photodiode V SS Figure 3 Simple Current [4 and 5] As equations (4) and (5) suggest the normalizing current is the sum of the currents going into each of the sense s, we generate a copy of the photocurrent going into the sense so that we can feed it back to the summing node (Figure 4). Using low-voltage cascode current mirrors [7] a modified current is shown in Figure 4. M4 M5 M14 VD D M15 M16 M17 M18 M6 ph 1 photodiode M1 M7 A V M19 B Mcasc1 D M M9 4 i 1 V3 ph1 M3 M10 M0 M1 M M3 scaler outp outp outn outn M11 M1 M13 V1 M5 M6 V4 M4 M7 M8 VSS Figure 4 Modified current that computes the centroid by dividing by the sum of the four photocurrents in the quad cell.

6 Simulations generated from hooking up a two by two resistive grid (Figure 5) are shown in Figure 6. NMOS and PMOS devices connected as a transmission gate and operated in subthreshold make pseudo resistors that replace all resistors in the resistive grid. [1,1] [1,3] [,1] [,3] V top [1,] [1,4] [,] [,4] V left V right V node [3,1] [3,3] [4,1] [4,3] [3,] [3,4] V bott [4,] [4,4] Figure 5 Two by two resistive grid. For a change along the y-axis, photocurrents going into sensor s [1,1] [1,3] [,1] [,3] [3,] [3,4] [4,] and [4,4] are varied from 0.1pA to 9.9pA while photocurrents going into sensor s [1,] [1,4] [,] [,4] [3,1] [3,3] [4,1] and [4,3] are varied from 9.9pA to 0.1pA. Here we expect V right and V left to have a higher voltage than Vtop and V bott. We also increase the total intensity of the incoming currents to see what effect it will have on the overall behavior of the circuit. This is a test for normalization; an increase in photocurrent should have no effect on the node voltage.

7 Figure 6 shows thatv right and V left have higher voltages than V top and V bott since there is little activity along the x-axis. Figure 6 Simulated node voltages for y-axis variation of a two by two phase reconstructor using pseudo-resistors. The three curves on the left correspond to a total photocurrent of 10pA, whereas the three curves on the right correspond to a total photocurrent of 0pA. Note that the voltage response is virtually independent of the absolute light intensity, or total photocurrent.

8 Figure 7 Simulated voltages for the three by three pseudo resistive grid in response to the y-axis variations in the input photocurrents. Simulations were also done on a three by three-resistive grid and the results are shown in Figure 7. To show that normalization has been achieved we have increased the current to 19.8 pa for comparison. From Figure 7 we may also note that node voltages do not change with an increase in photocurrent. Further V1 and V voltages have been offset by.5mv for clarity. We then went into the laboratory to verify that the cell is going to work. Using a transistor array that we designed and tested using the 0.5-µm AM n-well process, we verified the operation of the basic translinear. Results in Figure 8 show that the actual measured data may be split into two regions. Region A is a high gain region. This region is characterized by a steep slope. n this region leakage currents are on the order of the photocurrents that we are injecting into the. Region B has reduced gain, very close to the ideal value. This implies that working in this region will give results that are concurrent with the translinear principle. This is true because as we increase the photocurrents, κ could be changing as a function of V SB.

9 Figure 8 Plots of output current versus input photo current. shown below. Further we make a layout for the cell and the quad cell. The proposed layout is Figure 9 Proposed chip layout.

10 Summary This work has dealt with phase reconstruction based on centroid location. The motivation behind this project was to come up with a single chip solution that will reconstruct the phase of a plane wave incident upon a surface. We need to keep the centroid computation independent to light intensity. This is achieved using normalization. According to [3] we can determine the x and y phase of the wavefront averaged over the subaperture defined by the lenslet using a difference between neighbors divided by the sum of all the photocurrents in a centroid. n the current solution lenslets focus the phasal orientation onto a spot and our centroid circuit should be able to determine the position of the focused spot. Signals from the centroid circuit are then injected into a resistive grid, which does phase reconstruction by giving a solution to Poisson s equation. Further, simulations are done to verify operation at the cell level. Based on the work by Meitzler and Andreou [8] we expect the circuit simulator not to converge for large dimensional systems. We therefore performed simulations for a two by two-resistive grid and hooked up the whole system, predicting that the system is going to conform to theory. We also did a simulation for a three by three-resistive grid. We should note that in this case we are simulating a total of approximately 1400 devices. This work will only be complete once we are able to read out the voltages at the nodes from the resistive grid. With this in mind, we need to be able to define the boundary conditions. deally integrating the photo detector, Poisson equation solver and voltage to phase conversion in one chip will make the system very compact. References [1] P. M Furth and N. Clark, Analog VLS Subaperture Centroid Circuits, Proc. 7 th NASA Symp. VLS Design, Albuquerque, NM, Oct [] Ramirez Angulo, J. Treece, K Deyoung M., Real time Solution of Laplace Equation Using Analog VLS Circuits, EEE nternational Symposium on Circuits and Systems, London, England, May 1994.

11 [3] David H. Pollock, Countermeasure Systems: The nfrared and Electro- Optical Systems Handbook. Volume 7,the society of Photo-Optical nstrumentation Engineers, Page56. [4] A. G. Andreou and K. A. Boahen, Current Mode Subthreshold MOS circuit for analog VLS neural systems. EEE transactions neural networks, Vol No., [5] A. G. Andreou and K. A. Boahen, Translinear Circuits in subthreshold CMOS. J. Analog nteg. Circ.Sig. Proc, [6] Teresa Serrano-Gotarredona, Bernabé Linares-Barranco and Andreas G Andreou, A general Translinear principle for subthreshold MOS transistors, EEE transactions on circuits and systems. Fundamental theory and applications,vol 46 No.5,1999. [7] R. Jacob Baker, Harry W. Li, David E. Boyce, CMOS Circuit Design, Layout and Simulation. EEE. nc pages 118, 446 [8] Meitzler, R.C.; Andreou, A.G., On the simulation of analog VLS systems operating in the subthreshold and transition regions." University/Government/ndustry Microelectronics Symposium, Proceedings of the Tenth Biennial, Page(s): , 1993.