TMC2330AG1C

www.fairchildsemi.com TMC2330A Coordinate Transformer 16 x 16 Bit, 40 MOPS Features • Rectangular-to-Polar or Polar-to-Rectangular conversion at guaranteed 40 MOPS pipelined throughput rate • Polar data: 16-bit magnitude, 32-bit input/16-bit output phase • 16-bit user selectable two’s complement or sign-andmagnitude rectangular data formats • Input register clock enables and asynchronous output enables simplify interfacing • User-configurable phase accumulator for waveform synthesis and amplitude, frequency, or phase modulation • Magnitude output data overflow flag (in Polar-toRectangular mode) • Low power consumption CMOS process • Single +5V power supply • Available in a 120-pin plastic pin grid array package (PPGA), 120-pin ceramic pin grid array package (CPGA), 120-pin MQFP to PPGA (MPGA) package, and 120-pin metric quad flatpack package (MQFP) Description The TMC2330A VLSI circuit converts bidirectionally between Cartesian (real and imaginary) and Polar (magnitude and phase) coordinates at up to 40 MOPS (Million Operations Per Second). In its Rectangular-to-Polar mode, the TMC2330A can extract phase and magnitude information or backward “map” from a rectangular raster display to a radial (e.g., range-and-azimuth) data set. The Polar-to-Rectangular mode executes direct digital waveform synthesis and modulation. The TMC2330A greatly simplifies real-time image-space conversion between the radially-generated image scan data found in radar, sonar, and medical imaging systems, and raster display formats. All input and output data ports are registered, and a new transformed data word pair is available at the output every clock cycle. The user-configurable phase accumulator structure, input clock enables, and asynchronous three-state output bus enables simplify interfacing. All signals are TTL compatible. Fabricated in a submicron CMOS process, the TMC2330A operates at up to the 40 MHz maximum clock rate over the full commercial (0 to 70°C) temperature and supply voltage ranges, and is available in 120-pin plastic pin grid array, 120-pin ceramic pin grid array, 120-pin metric quad flatpack to PPGA package, and 120-pin metric quad flatpack packages. Applications • • • • • Scan conversion (phased array to raster) Vector magnitude estimation Range and bearing derivation Spectral analysis Digital waveform synthesis, including quadrature functions • Digital modulation and demodulation Logic Symbol ENXR 16 XRIN15-0 DATA INPUTS ENYP1-0 32 YPIN31-0 OEPY 2 ACC1-0 CONFIGURATION CONTROLS TCXY RTP CLK OVF 16 PYOUT15-0 16 RXOUT15-0 DATA OUTPUTS OERX TMC2330A REV. 1.1.8 10/31/00 PRODUCT SPECIFICATION TMC2330A Block Diagram XRIN15-0 ENXR YPIN31-0 ENYP 1-0 ACC1 ACC0 16 32 32 2 1 2 M C 32 AM 32 32 32 PM 32 FM 16 16 32 2 3 3 16 16 TCXY RPT TRANSFORMATION PROCESS 4-21 16 4-21 16 22 16 22 22 16 OERX OVF RXOUT15-0 PYOUT15-0 OEPY Functional Description The TMC2330A converts between Rectangular (Cartesian) and Polar (Phase and Magnitude) coordinate data word pairs. The user selects the numeric format and transformation to be performed (Rectangular-To-Polar or Polar-To-Rectangular), and the operation is performed on the data presented to the inputs on the next clock. The transformed result is then available at the outputs 22 clock cycles later, with new output data available every 20ns with a 40 MHz clock. All input and output data ports are registered, with input clock enables and asynchronous high-impedance output enables to simplify connections to system buses. When executing a Rectangular-To-Polar conversion, the input ports accept 16-bit Rectangular coordinate words, and the output ports generate 16-bit magnitude and 16-bit phase data. The user selects either two’s complement or sign-and-magnitude Cartesian data format. Polar magnitude data are always in magnitude format only. Since the phase angle word is modulo 2π, it may be regarded as either unsigned or two’s complement format (Tables 1 and 2). In Polar-To-Rectangular mode, the input ports accept 16-bit Polar magnitude and 32-bit phase data, and the output ports produce 16-bit Rectangular data words. Again, the user selects between two’s complement or sign-and-magnitude Cartesian data format. 2 REV. 1.1.8 10/31/00 TMC2330A PRODUCT SPECIFICATION Table 1. Data Input/Output Formats—Integer Format Port XRIN XRIN XRIN YPIN YPIN YPIN RXOUT RXOUT RXOUT PYOUT PYOUT PYOUT RTP 0 1 1 0 1 1 0 0 1 0 0 1 TCXY X 0 1 X 0 1 0 1 X 0 1 X ±20 Bit # 31 30 29 … 16 15 215 14 214 214 214 2-17 … … … … … 0 20 20 20 2-31 Format U S T (xπ)T/U S T NS –215 2-1 214 214 2-2 213 213 NS –215 … … 2-15 20 20 2-16 NS –215 215 214 214 214 214 214 2-1 20 20 20 20 20 2-15 S T U S T (xπ)T/U NS –215 ±20 Table 2. Data Input/Output Formats—Fractional Format Port XRIN XRIN XRIN YPIN YPIN YPIN RXOUT RXOUT RXOUT PYOUT PYOUT PYOUT Bit # RTP 0 1 1 0 1 1 0 0 1 0 0 1 TCXY X 0 1 X 0 1 0 1 X 0 1 X ±20 31 30 29 … 16 15 20 14 2-1 2-1 2-1 2-17 … … … … … 0 2-15 2-15 2-15 2-31 Format U S T (xπ)T/U S T NS –20 2-1 2-1 2-1 2-2 2-2 2-2 NS -20 … … … 2-15 2-15 2-15 2-16 NS –20 20 2-1 2-1 2-1 2-1 2-1 2-1 … … … … … … 2-15 2-15 2-15 2-15 2-15 2-15 S T U S T (xπ)T/U NS –20 ±20 Notes: 1. -215 denotes two’s complement sign bit. 2. NS denotes negative sign, i.e., ‘1’ negates the number. 3. ±20 denotes two’s complement sign or highest magnitude bit – since phase angles are modulo 2π and phase accumulator is modulo 232, this bit may be regarded as +π or -π. 4. All phase angles are in terms of π radians, hence notation “xπ.” 5. If ACC = 00, YPIN(15-0) are “don’t cares.” 6. Formats: T = Two’s Complement S = Signed Magnitude U = Unsigned HEX FFFF … 8001 8000 7FFF … 0001 0000 U 65535 … 32769 32768 32767 … 1 0 T –1 … -32767 -32768 32767 … 1 0 S -32767 … -1 0 32767 … 1 0 REV. 1.1.8 10/31/00 3 PRODUCT SPECIFICATION TMC2330A Static Control Inputs The controls RTP and TCXY determine the transformation mode and the assumed numeric format of the Rectangular data. The user must exercise caution when changing either of these controls, as the new transformed results will not be seen at the outputs until the entire internal pipe (22 clocks) has been flushed. Thus, these controls are considered static. Pin Assignments 120-Pin MQFP Pin 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 Name VDD PYOUT4 PYOUT3 GND PYOUT2 PYOUT1 PYOUT0 VDD OEPY GND RTP CLK GND TCXY ENPY GND ENPY1 ACC0 ACC1 VDD YPIN0 YPIN1 YPIN2 YPIN3 YPIN4 YPIN5 YPIN6 GND YPIN7 YPIN8 Pin 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Name GND YPIN9 YPIN10 VDD YPIN11 YPIN12 YPIN13 YPIN14 YPIN15 YPIN16 YPIN17 VDD YPIN18 YPIN19 YPIN20 GND YPIN21 YPIN22 YPIN23 VDD YPIN24 YPIN25 YPIN26 YPIN27 YPIN28 YPIN29 YPIN30 YPIN31 ENXR XRIN0 Pin 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 Name VDD XRIN1 XRIN2 GND XRIN3 XRIN4 XRIN5 GND XRIN6 XRIN7 XRIN8 XRIN9 XRIN10 XRIN11 XRIN12 GND XRIN13 XRIN14 XRIN15 VDD OERX GND RXOUT15 VDD RXOUT14 RXOUT13 RXOUT12 GND RXOUT11 RXOUT10 Pin 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 Name VDD RXOUT9 RXOUT8 GND RXOUT7 RXOUT6 RXOUT5 GND RXOUT4 RXOUT3 RXOUT2 VDD RXOUT1 RXOUT0 OVF GND PYOUT15 PYOUT14 PYOUT13 VDD PYOUT12 PYOUT11 PYOUT10 GND PYOUT9 PYOUT8 PYOUT7 GND PYOUT6 PYOUT5 Pin 1 4 REV. 1.1.8 10/31/00 TMC2330A PRODUCT SPECIFICATION Pin Assignments (continued) 120-Pin PPGA, H5 Package and 120-Pin CPGA, G1 Package and 120-Pin Metric Quad Flatpack to 120-Pin Plastic Pin Array, H6 Package 1 A B C D E F G H J K L M N Top View Cavity Up KEY 2 3 4 5 6 7 8 9 10 11 12 13 Pin A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 C1 C2 C3 C4 Name PYOUT5 PYOUT7 PYOUT8 PYOUT10 PYOUT12 PYOUT14 PYOUT15 RXOUT0 RXOUT2 RXOUT4 RXOUT6 RXOUT8 RXOUT10 PYOUT3 PYOUT4 PYOUT6 PYOUT9 PYOUT11 PYOUT13 OVF RXOUT1 RXOUT3 RXOUT5 RXOUT7 RXOUT9 RXOUT12 PYOUT1 PYOUT2 VDD GND Pin C5 C6 C7 C8 C9 C10 C11 C12 C13 D1 D2 D3 D11 D12 D13 E1 E2 E3 E11 E12 E13 F1 F2 F3 F11 F12 F13 G1 G2 G3 Name GND VDD GND VDD GND GND VDD RXOUT11 RXOUT13 OEPY PYOUT0 GND GND RXOUT14 RXOUT15 RTP GND VDD VDD GND OERX TCKY GND CLK VDD RXIN15 RXIN14 ENPY1 ENPY0 GND Pin G11 G12 G13 H1 H2 H3 H11 H12 H13 J1 J2 J3 J11 J12 J13 K1 K2 K3 K11 K12 K13 L1 L2 L3 L4 L5 L6 L7 L8 L9 Name GND XRIN12 RXIN13 ACCO ACC1 VDD XRIN9 XRIN10 XRIN11 YPIN0 YPIN1 YPIN3 GND XRIN7 XRIN8 YPIN2 YPIN4 GND GND XRIN5 XRIN6 YPIN5 YPIN7 GND VDD YPIN14 VDD GND VDD YPIN27 Pin L10 L11 L12 L13 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 N11 N12 N13 Name YPIN31 VDD XRIN3 XRIN4 YPIN6 YPIN9 YPIN11 YPIN13 YPIN16 YPIN18 YPIN20 YPIN23 YPIN25 YPIN28 ENXR XRIN1 XRIN2 YPIN8 YPIN10 YPIN12 YPIN15 YPIN17 YPIN19 YPIN21 YPIN22 YPIN24 YPIN26 YPIN29 YPIN30 XRIN0 Pin Descriptions Pin Number Pin Name MQFP CPGA/PPGA/ MPGA Description Power, Ground and Clock VDD 1, 8, 20, 34, 42, C3, E3, H3, L4, L6, The TMC2330A operates from a single +5V supply. All 50, 61, 80, 84, 91, L8, L11, F11, E11, power and ground pins must be connected. 102, 110 C11, C8, C6 4, 10, 13, 16, 28, D3, E2, F2, G3, 31, 46, 64, 68, 76, K3, L3, L7, K11, 82, 88, 94, 98, J11, G11, E12, 106, 114, 118 D11, C10, C9, C7, C5, C4 Ground GND REV. 1.1.8 10/31/00 5 PRODUCT SPECIFICATION TMC2330A Pin Descriptions Pin Name CLK (continued) Pin Number MQFP 12 CPGA/PPGA/ MPGA F3 Description The TMC2330A operates from a single clock. All enabled registers are strobed on the rising edge of CLK, which is the reference for all timing specifications. XRIN15-0 is the registered Cartesian X-coordinate or Polar Magnitude (Radius) 16-bit input data port. XRIN15 is the MSB. Inputs/Outputs XRIN15-0 79, 78, 77, 75, 74, 73, 72, 71, 70, 69, 67, 66, 65, 63, 62, 60 F12, F13, G13, G12, H13, H12, H11, J13, J12, K13, K12, L13, L12, M13, M12, N13 YPIN31-0 58, 57, 56, 55, 54, L10, N12, N11, 53, 52, 51, 49, 48, M10, L9, N10, M9, 47, 45, 44, 43, 41, N9, M8, N8, N7, 40, 39, 38, 37, 36, M7, N6, M6, N5, 35, 33, 32, 30, 29, M5, N4, L5, M4, 27, 26, 25, 24, 23, N3, M3, N2, M2, 22, 21 N1, L2, M1, L1, K2, J3, K1, J2, J1 83, 85, 86, 87, 89, 90, 92, 93, 95, 96, 97, 99, 100, 101, 103, 104 107, 108, 109, 111, 112, 113, 115, 116, 117, 119, 120, 2, 3, 5, 6, 7 59 D13, D12, C13, B13, C12, A13, B12, A12, B11, A11, B10, A10, B9, A9, B8, A8 A7, A6, B6, A5, B5, A4, B4, A3, A2, B3, A1, B2, B1, C2, C1, D2 YPIN31-0 is the registered Cartesian Y-coordinate or Polar Phase angle 32-bit input data port. The input phase accumulators are fed through this port in conjunction with the input enable select ENYP1,0. When RTP is HIGH (Rectangular-To-Polar), the input accumulators are normally not used. The 16 MSBs of YPIN are the input port, and the lower 16 bits become “don’t cares” if ACC = 00. YPIN31 is the MSB. RXOUT15-0 is the registered Polar Magnitude (Radius) or X-coordinate 16-bit output data port. This output is forced into the high-impedance state when OERX=HIGH. RXOUT15 is the MSB. PYOUT15-0 is the registered Polar Phase angle or Cartesian Y-coordinate 16-bit output data port. This output is forced to the high-impedance state when OEPY=HIGH. PYOUT15 is the MSB. RXOUT15-0 PYOUT15-0 Controls ENXR M11 The value presented to the input port XRIN is latched into the input registers on the current clock when ENXR is HIGH. When ENXR is LOW, the value stored in the register remains unchanged. The value presented to the YPIN input port is latched into the phase accumulator input registers on the current clock, as determined by the control inputs ENYP1,0, as shown below: Register Operation ENYP1,0 M 00 hold 01 load 10 hold 11 clear ENYP1,0 17, 15 G1, G2 C hold hold load load where C is the Carrier register and M is the Modulation register, and 0=LOW, 1=HIGH. See the Functional Block Diagram. 6 REV. 1.1.8 10/31/00 TMC2330A PRODUCT SPECIFICATION Pin Descriptions Pin Name RTP (continued) Pin Number MQFP 11 CPGA/PPGA/ MPGA E1 Description This registered input selects the current transformation mode of the device. When RTP is HIGH, the TMC2330A executes a Rectangular-To-Polar conversion. When RTP is LOW, a Polar-To-Rectangular conversion will be performed. The input and output ports are then configured to handle data in the appropriate coordinate system. This is a static input. See the Timing Diagram. In applications utilizing the TMC2330A to perform waveform synthesis and modulation in the Polar-To-Rectangular mode (RTP=LOW), the user determines the internal phase Accumulator structure implemented on the next clock by setting the accumulator control word ACC1,0, as shown below: ACC1,0 00 01 10 11 Configuration No accumulation performed (normal operation) PM accumulator path enabled FM accumulator path enabled (Nonsensical) logical OR of PM and FM ACC1,0 19, 18 H2, H1 where 0 = L0W, 1 = HIGH. See the Functional Block Diagram. The accumulator will roll over correctly when full-scale is exceeded, allowing the user to perform continuous phase accumulation through 2π radians or 360 degrees. Note that the accumulators will also function when RTP=HIGH (Rectangular-To-Polar), which is useful when performing backward mapping from Cartesian to polar coordinates. However, most applications will require that ACC1,0 be set to 00 to avoid accumulating the Cartesian Y input data. TCXY 14 F1 The format select control sets the numeric format of the Rectangular data, whether input (RTP=HIGH) or output (RTP=LOW). This control indicates two’s complement format when TCXY=HIGH and sign-and-magnitude when LOW. This is a static input. See the Timing Diagram. When RTP=LOW (Polar-To-Rectangular), the Overflow Flag will go HIGH on the clock that the magnitude of either of the current Cartesian coordinate outputs exceeds the maximum range. It will return LOW on the clock that the Cartesian out-put value(s) return to full-scale or less. See the Applications Discussion section. Overflow is not possible in Rectangular-To-Polar mode (RTP = HIGH). Data in the output registers are available at the outputs of the device when the respective asynchronous Output Enables are LOW. When OERX or OEPY is HIGH, the respective output port(s) is in the high impedance state. OVF 105 B7 OERX, OEPY 81, 9 E13, D1 REV. 1.1.8 10/31/00 7 PRODUCT SPECIFICATION TMC2330A Absolute Maximum Ratings (beyond which the device may be damaged)1 Parameter Supply Voltage Input Voltage Output Applied Voltage Short-Circuit Duration Operating Temperature Ambient Temperature Storage Temperature Junction Temperature Lead Soldering 10 seconds 2 3,4 Conditions Min -0.5 -0.5 -0.5 -3.0 Typ Max 7.0 VDD + 0.5 VDD + 0.5 6.0 1 Units V V V V sec °C °C °C °C °C Externally Forced Current Single output in HIGH state to ground -20 -20 -65 140 110 110 150 300 Notes: 1. Functional operation under any of these conditions is NOT implied. Performance and reliability are guaranteed only if Operating Conditions are not exceeded. 2. Applied voltage must be current limited to specified range. 3. Forcing voltage must be limited to specified range. 4. Current is specified as conventional current flowing into the device. Operating Conditions Parameter Min 4.75 TMC2330A TMC2330A-1 7 6 6 1 2.0 0.8 -2.0 4.0 0 70 Nom 5.0 Max 5.25 20 40 Units V MHz MHz ns ns ns ns V V mA mA °C VDD fCLK tPWH tPWL tS Power Supply Voltage Clock frequency Clock Pulse Width, HIGH Clock Pulse Width, LOW Input Data Setup Time Input Data Hold Time Input Voltage, Logic HIGH Input Voltage, Logic LOW Output Current, Logic HIGH Output Current, Logic LOW Ambient Temperature, Still Air tH VlH VIL IOH lOL TA 8 REV. 1.1.8 10/31/00 TMC2330A PRODUCT SPECIFICATION Electrical Characteristics Parameter IDD Power Supply Current TMC2330A TMC2330A-1 Conditions VDD = Max, CLOAD = 25pF, fCLK = Max 140 240 mA mA Min Nom Max Units IDDU Power Supply Current, Unloaded VDD = Max, OERX, OEPY = HIGH, fCLK = Max TMC2330A TMC2330A-1 95 175 5 5 mA mA mA pF ±10 ±10 ±10 ±10 -20 -80 0.5 µA µA µA µA mA V V IDDQ CPIN IIH IIL IOZH IOZL IOS VOH VOL Power Supply Current, Quiescent I/O Pin Capacitance Input Current, HIGH Input Current, LOW Hi-Z Output Leakage Current, Output HIGH Hi-Z Output Leakage Current, Output LOW Short-Circuit Current Output Voltage, HIGH Output Voltage, LOW VDD = Max, CLK = LOW VDD = Max,VIN = VDD VDD = Max,VIN = 0 V VDD = Max,VIN = VDD VDD = Max,VIN = 0 V S15-0, IOH = Max S15-0, IOL = Max 2.4 Switching Characteristics Parameter tDO Output Delay Time Output Hold Time Three-State Output Enable Delay Three-State Output Disable Delay Conditions1 CLOAD = 25 pF CLOAD = 25 pF CLOAD = 0 pF CLOAD = 0 pF 3 13 13 Min Nom Max 16 Units ns ns ns ns tHO tENA tDIS Note: 1. All transitions are measured at a 1.5V level except for tENA and tDIS. REV. 1.1.8 10/31/00 9 PRODUCT SPECIFICATION TMC2330A Timing Diagrams No Accumulation tS tH CLK 0 1 2 tPWH tPWL 3 … 22 23 RTP, TCXY ACC[1:0] ENXR, ENYP[1:0] XRIN[15:0], YPIN[31:0] RXOUT[15:0], PYOUT[15:0] 00 EN A 00 EN B 00 EN C … … … … tD … f(A) tHO f(B) Note: OERX = OEPY = LOW Phase Modulation CLK RTP, TCXY ACC[1:0] ENXR XRIN[15:0] ENYP[1:0] YPIN[31:0] RXOUT[15:0] PYOUT[15:0] R 10 C 01 I 01 J 01 K 01 L 00 01 01 01 01 … … … … … C+I 2C + J 3C + K 4C + L 0 1 2 3 … 22 23 24 25 Notes: 1. OERX = OEPY = LOW 2. Carrier C and amplitude R loaded on CLK0. 3. Modulation Values I, J, K, L… Loaded on CLK1, CLK2, etc. 4. Output corresponding to modulation loaded at CLKi emerged tDO after CLKi + 21. 5. To modulate amplitude, vary XRIN with ENXR = 1. Applications Discussion Numeric Overflow Because the TMC2330A accommodates 16-bit unsigned radii and 16-bit signed Cartesian coordinates, Polar-ToRectangular conversions can overflow for incoming radii greater than 32767= 7FFFh and will overflow for all incoming radii greater than 46341=B505h. (ln signed magnitude mode, a radius of 46340 = B504h will also overflow at all angles.) The regions of overflow and of correct conversion are illustrated in Figure 1. In signed magnitude mode, overflows are circularly symmetrical—if a given radius overflows at an angle P, it will also overflow at the angles π-P, π+P, and -P. This is because -X will overflow if and only if X overflows, and -Y will overflow if and only if Y overflows. In two’s complement mode, the number system’s asymmetry complicates the overflow conditions slightly. An input vector with an X component of -32768=8000h will not overflow, whereas one with an X component of +32768 will. Table 3 summarizes several simple cases of overflow and near-overflow. REV. 1.1.8 10/31/00 10 TMC2330A PRODUCT SPECIFICATION Table 3a. X-Dimensional Marginal Overflows TC 0 0 1 1 YPIN 0000 = 0 8000 = π 0000 = 0 8000 = π OV 1 1 1 0 RXOUT 0000 = +0 8000 = -0 8000 = -32768 8000 = -32768 CORRECT X +32768 -32768 +32768 -32768 Performing Scan Conversion with the TMC2330A Medical Imaging Systems such as Ultrasound, MRI, and PET, and phased array Radar and Sonar systems generate radial-format coordinates (range or distance, and bearing) which must be converted into raster-scan format for further processing and display. Utilizing the TMC2302A Image Resampling Sequencer, a minimum chipcount Scan Converter can be implemented which utilizes the trigonometric translation performed by the TMC2330A to backwards-map from a Cartesian coordinate set into the Polar source image buffer address space. As shown in Figure 2, the TMC2330A transforms the Cartesian source image addresses from the TMC2302A directly to vector distance and angle coordinates, while the TMC2302A writes the resulting resampled pixel values into the target memory in raster fashion. Note that the ability to perform this spatial transformation in either direction gives the user the freedom to process images in either coordinate space, with little restriction. Image manipulation such as zooms or tilts can easily be included in the transformation by programming the desired image manipulation into the TMC2302A’s transformation parameter registers. In all cases, RTP=0 (Polar-To-Rectangular mode) and XRIN=8000 (incoming radius=32768). Table 3b. Maximal Overflow (Radius In=65535) TC 0 0 1 1 YPIN 0000 = 0 8000 = π 0000 = 0 8000 = π OV 1 1 1 1 RXOUT 7FFF = +32767 FFFF = -32767 FFFF = -1 0001 = +1 CORRECT X +65535 -65535 +65535 -65535 In all cases, RTP=0 (Polar-To-Rectangular mode) and XRIN=7FFF (incoming radius=65535, which will always overflow). Numeric Underflow In RTP=1 (Rectangular-To-Polar) mode, if XRIN=YPIN=0, the angle is undefined. Under these conditions, the TMC2330A will output the expected radius of 0 (RXOUT= 0000) and an angle of 1.744 radians (PYOUT=4707). This angle is an artifact of the CORDIC algorithm and is not flagged as an error, since the angle of any 0 length vector is arbitrary. π/2 65535 X = R (Cos θ) Y = R (Sin θ) and R= X2 + Y2 θ = Tan-1 (Y/X) If R ≤ 32767, overflow will not occur (Region A). If R > 32767, overflow will not occur (Region B) if |X| ≤ 32767 and |Y| ≤ 32767. If R > 32767, overflow will occur (Region C) if |X| ≥ 32768 or |Y| ≥ 32768. C 32767 B A R Y θ X 32767 65535 Figure 1. First Quadrant Coordinate Relationships REV. 1.1.8 10/31/00 11 PRODUCT SPECIFICATION TMC2330A SADR SADR X Y TMC2330A COORDINATE TRANSFORMER R θ θ R SOURCE IMAGE BUFFER DATA OUT (2) TMC2302A IMAGE RESAMPLING SEQUENCERS U TADR TADR U V (4) TMC2011A DELAY REGISTER V Σ TMC2246A PIXEL INTERPOLATOR DATA IN TARGET IMAGE BUFFER TWR Figure 1. Figure 1. First Quadrant Coordinate Relationships Figure 2. Block Diagram of Scan Converter Circuit Utilizing TMC2330A and TMC2302A Image Resampling Sequencer Arithmetic Error for Two’s Complement Rectangular to Polar Conversion A random set of 5000 input vector coordinate pairs (X,Y), uniformly spread over a circle of radius 32767 was converted to polar coordinates. Radius Error Range Mean Radius Error Mean Absolute Radius Error Phase Error Range Mean Phase Error Mean Absolute Phase Error –0.609 to 0.746 LSB 0.019 LSB 0.252 LSB –1.373 to 1.469 LSB 0.058 LSB 0.428 LSB The results of the 10,000-vector study were as follows: Mean Error (X) Mean Error (Y) Mean Absolute Error (X) Mean Absolute Error (Y) Root Mean Square Error (X) Root Mean Square Error (Y) Max Error (X) Max Error (Y) +0.0052 LSB 0.0031 LSB 0.662 LSB 0.664 LSB 1.025 LSB 1.020 LSB +4/ -5 LSB +5 -4 LSB Statistical Evaluation of Double Conversion In this empirical test, 10,000 random Cartesian vectors were converted to and from polar format by the TMC2330A. The resulting Cartesian pairs were then compared against the original ones. The un-restricted database represents uniform sampling over a square bounded by -32769