A63L8336E-2.6

A63L8336 256K X 36 Bit Synchronous High Speed SRAM with Burst Counter and Pipelined Data Output Preliminary Document Title 256K X 36 Bit Synchronous High Speed SRAM with Burst Counter and Pipelined Data Output Revision History Rev. No. 0.0 History Initial issue Issue Date July 11, 2005 Remark Preliminary PRELIMINARY (July, 2005, Version 0.0) AMIC Technology, Corp. A63L8336 256K X 36 Bit Synchronous High Speed SRAM with Burst Counter and Pipelined Data Output Preliminary Features Fast access times: 2.6/2.8/3.2/3.5/3.8/4.2 ns (250/227/200/166/150/133 MHZ) Single +3.3V+10% or +3.3V-5% power supply Synchronous burst function Individual Byte Write control and Global Write Registered output for pipelined applications Three separate chip enables allow wide range of options for CE control, address pipelining Selectable BURST mode SLEEP mode (ZZ pin) provided Available in 100-pin LQFP package General Description The A63L8336 is a high-speed SRAM containing 9M bits of bit synchronous memory, organized as 256K words by 36 bits. The A63L8336 combines advanced synchronous peripheral circuitry, 2-bit burst control, input registers, output registers and a 256KX36 SRAM core to provide a wide range of data RAM applications. The positive edge triggered single clock input (CLK) controls all synchronous inputs passing through the registers. Synchronous inputs include all addresses (A0 A17), all data inputs (I/O1 - I/O36), active LOW chip enable ( CE ), two additional chip enables (CE2, CE2 ), burst control inputs ( ADSC , ADSP , ADV ), byte write enables ( BWE , BW1 , BW2 , BW3 , BW4 ) and Global Write ( GW ). Asynchronous inputs include output enable ( OE ), clock (CLK), BURST mode (MODE) and SLEEP mode (ZZ). Burst operations can be initiated with either the address status processor ( ADSP ) or address status controller ( ADSC ) input pin. Subsequent burst sequence burst addresses can be internally generated by the A63L8336 and controlled by the burst advance ( ADV ) pin. Write cycles are internally self-timed and synchronous with the rising edge of the clock (CLK). This feature simplifies the write interface. Individual Byte enables allow individual bytes to be written. BW1 controls I/O1 - I/O9, BW2 controls I/O10 - I/O18, BW3 controls I/O19 - I/O27, and BW4 controls I/O28 - I/O36, all on the condition that BWE is LOW. GW LOW causes all bytes to be written. PRELIMINARY (July, 2005, Version 0.0) 1 AMIC Technology, Corp. A63L8336 Pin Configuration ADSC ADSP BWE BW4 BW3 BW2 BW1 GND VCC ADV CE2 CE2 CLK GW OE CE A6 A7 A8 82 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 I/O19 I/O20 I/O21 VCCQ GNDQ I/O22 I/O23 I/O24 I/O25 GNDQ VCCQ I/O26 I/O27 NC VCC NC GND I/O28 I/O29 VCCQ GNDQ I/O30 I/O31 I/O32 I/O33 GNDQ VCCQ I/O34 I/O35 I/O36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 100 81 A9 80 79 78 77 76 75 74 73 72 71 70 69 68 67 NC I/O17 I/O16 VCCQ GNDQ I/O15 I/O14 I/O13 I/O12 GNDQ VCCQ I/O11 I/O10 GND NC VCC ZZ I/O8 I/O7 VCCQ GNDQ I/O6 I/O5 I/O4 I/O3 GNDQ VCCQ I/O2 I/O1 I/O9 A63L8336E 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 A5 A4 A3 A2 A1 A0 A10 A11 A12 A13 A14 A15 MODE GND VCC A17 PRELIMINARY (July, 2005, Version 0.0) 2 A16 NC NC NC AMIC Technology, Corp. A63L8336 Block Diagram ZZ MODE MODE LOGIC ADV CLK CLK LOGIC ADSC ADSP BURST LOGIC ADDRESS COUNTER CLR A0-A17 ADDRESS REGISTERS 18 8 BYTE1 WRITE DRIVER 8 GW BWE BW1 BW2 BW3 BW4 BYTE WRITE ENABLE LOGIC 8 BYTE2 WRITE DRIVER BYTE3 WRITE DRIVER BYTE4 WRITE DRIVER 9 9 256KX9X4 36 MEMORY OUTPUT REGISTERS ARRAY 9 8 9 36 4 DATA-IN REGISTERS 4 CE CE2 CE2 CHIP ENABLE LOGIC PIPELINED ENABLE LOGIC OE I/O1 - I/O36 OUTPUT ENABLE LOGIC PRELIMINARY (July, 2005, Version 0.0) 3 AMIC Technology, Corp. A63L8336 Pin Description Pin No. Symbol Description 32 – 37, 43 - 50, 81, 82, 99, 100 89 87, 93 - 96 88 86 92, 97, 98 83 84 85 31 A0 - A17 Address Inputs CLK BWE , BW1 - BW4 GW OE CE2 ,CE2, CE ADV ADSP ADSC MODE Clock Byte Write Enables Global Write Output Enable Chip Enables Burst Address Advance Processor Address Status Controller Address Status Burst Mode: HIGH or NC (Interleaved burst) LOW (Linear burst) Asynchronous Power-Down (Snooze): HIGH (Sleep) LOW or NC (Wake up) Data Inputs/Outputs 64 ZZ 1,2, 3, 6 - 9, 12, 13, 18, 19, 22 - 25, 28, 29, 30,51,52, 53, 56 - 59, 62, 63, 68, 69, 72 - 75, 78, 79,80 15, 41, 65, 91 17, 40, 67, 90 4, 11, 20, 27, 54, 61, 70, 77 5, 10, 21, 26, 55, 60, 71, 76 I/O1- I/O36 VCC GND VCCQ Power Supply Ground Isolated Output Buffer Supply GNDQ Isolated Output Buffer Ground PRELIMINARY (July, 2005, Version 0.0) 4 AMIC Technology, Corp. A63L8336 Synchronous Truth Table (See Notes 1 Through 5) Operation Address Used NONE CE H L L L L L L L L L X X H H X H X X H H X H CE2 CE2 X L X L X H H H H H X X X X X X X X X X X X ADSP ADSC ADV X X X X X X X X X X L L L L L L H H H H H H WRITE OE X X X X X L H X L H L H L H X X L H L H X X CLK L-H L-H L-H L-H L-H L-H L-H L-H L-H L-H L-H L-H L-H L-H L-H L-H L-H L-H L-H L-H L-H L-H Deselected Cycle, Power-down Deselected Cycle, Power-down Deselected Cycle, Power-down Deselected Cycle, Power-down Deselected Cycle, Power-down READ Cycle, Begin Burst READ Cycle, Begin Burst WRITE Cycle, Begin Burst READ Cycle, Begin Burst READ Cycle, Begin Burst READ Cycle, Continue Burst READ Cycle, Continue Burst READ Cycle, Continue Burst READ Cycle, Continue Burst WRITE Cycle, Continue Burst WRITE Cycle, Continue Burst READ Cycle, Suspend Burst READ Cycle, Suspend Burst READ Cycle, Suspend Burst READ Cycle, Suspend Burst WRITE Cycle, Suspend Burst WRITE Cycle, Suspend Burst X X H X H L L L L L X X X X X X X X X X X X X L L H H L L H H H H H X X H X H H X X H X L X X L L X X L L L H H H H H H H H H H H H X X X X X X X L H H H H H H L L H H H H L L I/O Operation High-Z High-Z High-Z High-Z High-Z Dout High-Z Din Dout High-Z Dout High-Z Dout High-Z Din Din Dout High-Z Dout High-Z Din Din NONE NONE NONE NONE External External External External External Next Next Next Next Next Next Current Current Current Current Current Current PRELIMINARY (July, 2005, Version 0.0) 5 AMIC Technology, Corp. A63L8336 Notes: 1. X = "Disregard", H = Logic High, L = Logic Low. 2. W RITE = L means: 1) Any BWx ( BW1 , BW2 , BW3 , or BW4 ) and BWE are low or 2) GW is low. 3. All inputs except OE must be synchronized with setup and hold times around the rising edge (L-H) of CLK. 4. For write cycles that follow read cycles, OE must be HIGH before the input data request setup time and held HIGH throughout the input data hold time. 5. ADSP LOW always initiates an internal Read at the L-H edge of CLK. A Write is performed by setting one or more byte write enable signals and BWE LOW or GW LOW for the subsequent L-H edge of CLK. Refer to the Write timing diagram for clarification. Write Truth Table Operation READ READ WRITE Byte 1 WRITE all bytes WRITE all bytes GW H H H H L BWE H L L L X BW1 X H L L X BW2 X H H L X BW3 X H H L X BW4 X H H L X PRELIMINARY (July, 2005, Version 0.0) 6 AMIC Technology, Corp. A63L8336 Linear Burst Address Table (MODE = LOW) First Address (External) X . . . X00 X . . . X01 X . . . X10 X . . . X11 Second Address (Internal) X . . . X01 X . . . X10 X . . . X11 X . . . X00 Third Address (Internal) X . . . X10 X . . . X11 X . . . X00 X . . . X01 Fourth Address (Internal) X . . . X11 X . . . X00 X . . . X01 X . . . X10 Interleaved Burst Address Table (MODE = HIGH or NC) First Address (External) X . . . X00 X . . . X01 X . . . X10 X . . . X11 Second Address (Internal) X . . . X01 X . . . X00 X . . . X11 X . . . X10 Third Address (Internal) X . . . X10 X . . . X11 X . . . X00 X . . . X01 Fourth Address (Internal) X . . . X11 X . . . X10 X . . . X01 X . . . X00 Absolute Maximum Ratings* Power Supply Voltage (VCC) . . . . . . . . . . -0.5V to +4.6V Voltage Relative to GND for any Pin Except VCC (Vin, Vout) . . . . . . . . . . . . . . . . . . . . . . . . . -0.5V to VCC +0.5V Power Dissipation (PD) . . . . . . . . . . . . . . . . . . . . . . . . 2W Operating Temperature (Topr) . . . . . . . . . . . 0°C to 70°C Storage Temperature (Tbias) . . . . . . . . . . -10°C to 85 °C Storage Temperature (Tstg) . . . . . . . . . . . -55°C to 125°C *Comments Stresses above those listed under "Absolute Maximum Ratings" may cause permanent damage to this device. These are stress ratings only. Functional operation of this device at these or any other conditions above those indicated in the operational sections of this specification is not implied or intended. Exposure to the absolute maximum rating conditions for extended periods may affect device reliability. Recommended DC Operating Conditions (0°C ≤ TA ≤ 70°C, VCC, VCCQ = 3.3V+10% or 3.3V-5%, unless otherwise noted) Symbol VCC VCCQ GND VIH VIHQ VIL Parameter Supply Voltage (Operating Voltage Range) Isolated Input Buffer Supply Supply Voltage to GND Input High Voltage Input High Voltage (I/O Pins) Input Low Voltage Min. 3.1 3.1 0.0 2.0 2.0 -0.3 Typ. 3.3 3.3 Max. 3.6 VCC 0.0 VCC+0.3 VCC+0.3 0.8 Unit V V V V V V 1, 2 1, 2 Note PRELIMINARY (July, 2005, Version 0.0) 7 AMIC Technology, Corp. A63L8336 DC Electrical Characteristics (0°C ≤ TA ≤ 70°C, VCC, VCCQ = 3.3V+10% or 3.3V-5%, unless otherwise noted) Symbol ⏐ILI⏐ ⏐ILO⏐ Parameter Input Leakage Current Output Leakage Current Min. - Max. ±2.0 ±2.0 Unit µA µA Test Conditions All inputs VIN = GND to VCC OE = VIH, Vout = GND to VCC Device selected; VCC = max. Iout = 0mA, all inputs = VIH or VIL Cycle time = tKC min. Device deselected; VCC = max. All inputs are fixed. All inputs ≥ VCC - 0.2V or ≤ GND + 0.2V Cycle time = tKC min. ZZ ≥ VCC - 0.2V IOL = 8 mA IOH = -4 mA Note ICC1 Supply Current - 400 mA 3, 11 ISB1 Standby Current - 180 mA 11 ISB2 VOL VOH Output Low Voltage Output High Voltage 2.4 150 0.4 - mA V V Capacitance Symbol CIN CI/O Parameter Input Capacitance Input/Output Capacitance Typ. 3 4 Max. 4 5 Unit pF pF Conditions TA = 25 C; f = 1MHz VCC = 3.3V * These parameters are sampled and not 100% tested. PRELIMINARY (July, 2005, Version 0.0) 8 AMIC Technology, Corp. A63L8336 AC Characteristics (0°C ≤ TA ≤ 70°C, VCC = 3.3V+10% or 3.3V-5%) Symbol Parameter -2.6 Min Max -2.8 Min Max -3.2 Min Max -3.5 Min Max -3.8 Min Max -4.2 Min Max Unit Note tKC tKH tKL tKQ tKQX tKQLZ tKQHZ tOEQ tOELZ tOEHZ Clock Cycle Time Clock High Time Clock Low Time Clock to Output Valid Clock to Output Invalid Clock to Output in Low-Z Clock to Output in High-Z 4.0 1.7 1.7 1.5 1.5 1.5 0 - 2.6 2.6 2.6 2.6 4.4 2.0 2.0 1.5 1.5 1.5 0 - 2.8 2.8 2.8 2.8 5.0 2.0 2.0 1.5 1.5 1.5 0 - 3.2 3.0 3.2 3.2 6.0 2.2 2.2 1.5 1.5 1.5 0 - 3.5 3.0 3.5 3.5 6.7 2.5 2.5 1.5 1.5 1.5 0 - 3.8 3.0 3.8 3.8 7.5 3.0 3.0 1.5 1.5 1.5 0 - 4.2 3.5 4.2 4.2 ns ns ns ns ns ns ns ns ns ns 5, 6 5, 6 8 5, 6 5, 6 OE to Output Valid OE to Output in Low-Z OE to Output in High-Z Setup Times tAS tADSS Address Address Status ( ADSC , ADSP ) Address Advance ( ADV ) Write Signals ( BW1 , BW2 , BW3 , BW4 , BWE , GW ) Data-in Chip Enable ( CE , CE2, CE2 ) 1.2 1.2 1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.5 ns ns 7, 9 7, 9 tADVS 1.2 - 1.4 - 1.4 - 1.5 - 1.5 - 1.5 - ns 7, 9 tWS 1.2 - 1.4 - 1.4 - 1.5 - 1.5 - 1.5 - ns 7, 9 tDS tCES 1.2 1.2 - 1.4 1.4 - 1.4 1.4 - 1.5 1.5 - 1.5 1.5 - 1.5 1.5 - ns ns 7, 9 7, 9 PRELIMINARY (July, 2005, Version 0.0) 9 AMIC Technology, Corp. A63L8336 AC Characteristics (continued) Symbol Parameter -2.6 Min Max -2.8 Min Max -3.2 Min Max -3.5 Min Max -3.8 Min Max -4.2 Min Max Unit Note Hold Times tAH tADVH Address Address Status ( ADSC , ADSP ) Address Advance ( ADV ) Write Signal ( BW1 , BW2 , BW3 , BW4 , BWE , GW ) Data-in Chip Enable ( CE , CE2, CE2 ) 0.3 0.3 0.4 0.4 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ns ns 7, 9 7, 9 tAAH 0.3 - 0.4 - 0.5 - 0.5 - 0.5 - 0.5 - ns 7, 9 tWH 0.3 - 0.4 - 0.5 - 0.5 - 0.5 - 0.5 - ns 7, 9 tDH tCEH 0.3 0.3 - 0.4 0.4 - 0.5 0.5 - 0.5 0.5 - 0.5 0.5 - 0.5 0.5 - ns ns 7, 9 7, 9 Notes: 1. All voltages refer to GND. 2. Overshoot: VIH ≤ +4.6V for t ≤ tKC/2. Undershoot: VIH ≥ -0.7V for t ≤ tKC/2. Power-up: VIH ≤ +3.6 and VCC ≤ 3.1V for t ≤ 200ms 3. ICC is given with no output current. ICC increases with greater output loading and faster cycle times. 4. Test conditions assume the output loading shown in Figure 1, unless otherwise specified. 5. For output loading, CL = 5pF, as shown in Figure 2. Transition is measured ±150mV from steady state voltage. 6. At any given temperature and voltage condition, tKQHZ is less than tKQLZ and tOEHZ is less than tQELZ. 7. A WRITE cycle is defined by at least one Byte Write enable LOW and ADSP HIGH for the required setup and hold times. A READ cycle is defined by all byte write enables HIGH and ( ADSC or ADV LOW) or ADSP LOW for the required setup and hold times. 8. OE has no effect when a Byte Write enable is sampled LOW. 9. This is a synchronous device. All addresses must meet the specified setup and hold times for all rising edges of CLK when either ADSP or ADSC is LOW and the chip is enabled. All other synchronous inputs must meet the setup and hold times with stable logic levels for all rising edges of clock (CLK) when the chip is enabled. Chip enable must be valid at each rising edge of CLK when either ADSP or ADSC is LOW to remain enabled. 10. The load used for VOH, VOL testing is shown in Figure 2. AC load current is higher than the given DC values. AC I/O curves are available upon request. 11. "Device Deselected" means device is in POWER-DOWN mode, as defined in the truth table. "Device Selected" means device is active (not in POWER-DOWN mode). 12. MODE pin has an internal pulled-up, and ZZ pin has an internal pulled-down. All of then exhibit an input leakage current of 10µA. 13. Snooze (ZZ) input is recommended that users plan for four clock cycles to go into SLEEP mode and four clocks to emerge from SLEEP mode to ensure no data is lost. PRELIMINARY (July, 2005, Version 0.0) 10 AMIC Technology, Corp. A63L8336 Timing Waveforms tKC CLK tKH tADSS ADSP tADSS ADSC tAS ADDRESS A1 tWS GW,BWE BW1-BW4 tCES CE (NOTE *2) (NOTE *4) tADVS ADV ADV suspends burst OE (NOTE *3) tKQLZ DOUT High-Z tKQ Single READ tOEHZ Q(A1) tOEQ tOELZ Q(A2) (NOTE *1) BURST READ tKQ tKQX Q(A2+1) Q(A2+2) Q(A2+3) Q(A2) Q(A2+1) Q(A3) tKQHZ tADVH tCEH Delselected cycle tWH tAH A2 A3 Burst continued with new base address tADSH tADSH tKL Burst wraps around to its initial state Read Timing Notes: *1. Q(A2) refers to output from address A2. Q(A2+1) refers to output from the internal burst address immediately following A2. *2. Timing for CE2 and CE2 is identical to that for CE . As shown in this diagram, when CE is LOW, CE2 is LOW and CE2 is HIGH. When CE is HIGH, CE2 is HIGH and CE2 is LOW. *3. Timing shown assumes that the device was not enabled before entering this sequence. OE does not cause Q to be driven until after the rising edge of the following clock. PRELIMINARY (July, 2005, Version 0.0) 11 AMIC Technology, Corp. A63L8336 Timing Waveforms (continued) tKC CLK tKH tADSS ADSP tADSS ADSC tAS ADDRESS A1 tAH A2 BYTE W RITE signals are ignored for first cycle when ADSP initiates burst BW E,BW 1-BW 4 (NOTE *5) tWS GW tCES CE (NOTE *2) tADVS ADV (NOTE *4) ADV suspends burst tADVH tCEH tWH A3 tWS tWH tADSH ADSC extends burst tADSS tADSH tADSH tKL OE (NOTE *3) tDS tDH D(A1) tOEHZ D(A2) D(A2+1) (NOTE *1) D(A2+1) D(A2+2) D(A2+3) D(A3) D(A3+1) D(A3+2) DIN High-Z DOUT BURST READ Single W RITE Extended BURST W RITE Write Timing Notes: *1. D(A2) refers to output from address A2. D(A2+1) refers to output from the internal burst address immediately following A2. *2. Timing for CE2 and CE2 is identical to that for CE . As shown in the above diagram, when CE is LOW, CE2 is LOW and CE2 is HIGH. When CE is HIGH, CE2 is HIGH and CE2 is LOW. *3. OE must be HIGH before the input data setup, and held HIGH throughout the data hold period. This prevents input/output data contention for the period prior to the time Byte Write enable inputs are sampled. *4. ADV must be HIGH to permit a Write to the loaded address. *5. Byte Write enables are decided by means of a Write truth table. PRELIMINARY (July, 2005, Version 0.0) 12 AMIC Technology, Corp. A63L8336 Timing Waveforms (continued) tKC CLK tKH tADSS ADSP tADSH tKL ADSC tAS tAH ADDRESS A1 A2 A3 tWS GW,BWE, BW1-BW4 (NOTE *3) tCES CE (NOTE *2) tCEH tWH A4 A5 A6 ADV OE tDS tKQ DIN High-Z tKQLZ DOUT High-Z Q(A1) Back-to-Back READs tOEHZ Q(A2) Single WRITE D(A3) tKQ (NOTE *1) Q(A3) Pass-through READ (NOTE *4) Q(A4) Q(A4+1) Q(A4+2) Q(A4+3) Back-to-Back WRITEs tDH tOELZ D(A5) D(A6) BURST READ Read/Write Timing Notes: *1. Q(A4) refers to output from address A4. Q(A4+1) refers to output from the internal burst address immediately following A4. *2. Timing for CE2 and CE2 is identical to that for CE . As shown in this diagram, when CE is LOW, CE2 is LOW and CE2 is HIGH. When CE is HIGH, CE2 is HIGH and CE2 is LOW. *3. Byte Write enables are decided by means of a Write truth table. *4. Pass-through occurs when data is first written, then Read in sequence. PRELIMINARY (July, 2005, Version 0.0) 13 AMIC Technology, Corp. A63L8336 AC Test Conditions Input Pulse Levels Input Rise and Fall Times Input Timing Reference Levels Output Reference Levels Output Load GND to 3V 1.5ns 1.5V 1.5V See Figures 1 and 2 Q 350Ω 5pF Q ZO=50Ω RL=50Ω VT=1.5V Figure 1. Output Load Equivalent +3.3V 320Ω Figure 2. Output Load Equivalent PRELIMINARY (July, 2005, Version 0.0) 14 AMIC Technology, Corp. A63L8336 Ordering Information Part No. A63L8336E-2.6 A63L8336E-2.6F A63L8336E-2.8 A63L8336E-2.8F A63L8336E-3.2 A63L8336E-3.2F A63L8336E-3.5 A63L8336E-3.5F A63L8336E-3.8 A63L8336E-3.8F A63L8336E-4.2 A63L8336E-4.2F Access Times (ns) 2.6 2.6 2.8 2.8 3.2 3.2 3.5 3.5 3.8 3.8 4.2 4.2 Frequency (MHz) 250 250 225 225 200 200 166 166 150 150 133 133 Package 100L LQFP 100L Pb-Free LQFP 100L LQFP 100L Pb-Free LQFP 100L LQFP 100L Pb-Free LQFP 100L LQFP 100L Pb-Free LQFP 100L LQFP 100L Pb-Free LQFP 100L LQFP 100L Pb-Free LQFP PRELIMINARY (July, 2005, Version 0.0) 15 AMIC Technology, Corp. A63L8336 Package Information LQFP 100L Outline Dimensions unit: inches/mm HE E 80 51 A2 A1 y D 81 50 HD D 100 31 1 30 e b c θ Symbol A1 A2 b c HE E HD D e L L1 y θ Dimensions in inches Min. 0.002 0.053 0.011 0.005 0.860 0.783 0.624 0.547 Nom. 0.055 0.013 0.866 0.787 0.630 0.551 0.026 BSC 0.018 0.024 0.039 REF 0° 3.5° 0.004 7° 0.030 Max. 0.057 0.015 0.008 0.872 0.791 0.636 0.555 Dimensions in mm Min. 0.05 1.35 0.27 0.12 21.85 19.90 15.85 13.90 Nom. 1.40 0.32 22.00 20.00 16.00 14.00 0.65 BSC 0.45 0.60 1.00 REF 0° 3.5° 0.1 7° 0.75 Max. 1.45 0.37 0.20 22.15 20.10 16.15 14.10 Notes: 1. Dimensions D and E do not include mold protrusion. 2. Dimensions b does not include dambar protrusion. Total in excess of the b dimension at maximum material condition. Dambar cannot be located on the lower radius of the foot. L L1 PRELIMINARY (July, 2005, Version 0.0) 16 AMIC Technology, Corp.