L2330 TMC2330A 2330-D XRIN15-0 YPIN31-0 RXOUT15-0 PYOUT15-0 16-BITS 24-BITS - Datasheet Archive

 

L2330 DEVICES INCORPORATED Coordinate Transformer Coordinate Transformer DEVICES INCORPORATED FEATURES DESCRIPTION u

 

L2330 L2330 L2330 L2330 DEVICES INCORPORATED Coordinate Transformer Coordinate Transformer DEVICES INCORPORATED FEATURES DESCRIPTION u Rectangular-to-Polar or Polar-toRectangular at 50 MHz u 24-Bit Polar Phase Angle Accuracy u Replaces Fairchild TMC2330A TMC2330A u 120-pin PQFP The L2330 L2330 is a coordinate transformer that converts bidirectionally between Rectangular and Polar coordinates. seen at the output after 22 clock cycles and will continue upon every clock cycle thereafter. When in Rectangular-to-Polar mode, the L2330 L2330 is able to retrieve phase and magnitude information or backward map from a rectangular raster display to a radial data set. When in Rectangular-to-Polar mode, the user inputs a 16-bit Rectangular coordinate and the output generates a Polar transformation with 16-bit magnitude and 16-bit phase. The user may select the data format to be either two's complement or sign-andmagnitude Cartesian data format. Polar Magnitude data is always in magnitude format only. Polar Phase Angle data is modulo 2 so it may be regarded as either unsigned or two's complement format. When in Polar-to-Rectangular mode, the L2330 L2330 is able to execute direct digital waveform synthesis and modulation. Real-time image-space conversions are achieved from radially-generated images, such as RADAR, SONAR, and ultrasound to raster display formats. Functional Description The L2330 L2330 converts bidirectionally between Rectangular (Cartesian) and Polar (Phase and Magnitude) coordinates. The user selects the numeric format. A valid transformed result is When in Polar-to-Rectangular mode, the user inputs 16-bit Polar Magnitude and 32-bit Phase data and the output generates a 16-bit Rectangular coordinate. The use may select the data format to be either two's complement or sign-and-magnitude Cartesian data format. L2330 L2330 BLOCK DIAGRAM OERX ENXR XRIN 15-0 ENYP 1-0 YPIN 31-0 16 2 POLAR 16 RXOUT 15-0 32 OEPY ACC 1-0 2 RECTANGULAR 16 PYOUT 15-0 TCXY RTP OVF CLK Special Arithmetic Functions 1 08/16/2000­LDS.2330-D 2330-D L2330 L2330 DEVICES INCORPORATED Coordinate Transformer Outputs L2330 L2330 FUNCTIONAL BLOCK DIAGRAM XRIN15-0 XRIN15-0 ENXR 16 ENYP1-0 YPIN31-0 YPIN31-0 32 RXOUT15-0 RXOUT15-0 - x-coordinate/Magnitude Data Output ACC0 RXOUT15-0 RXOUT15-0 is the 16-bit Cartesian x-coordinate/Polar Magnitude Data output port. When OERX is HIGH, RXOUT15-0 RXOUT15-0 is forced into the highimpedance state. 2 32 M ACC1 C AM 32 PM FM PYOUT15-0 PYOUT15-0 - y-coordinate/Phase Angle Data Output 32 PYOUT15-0 PYOUT15-0 is the 16-bit Cartesian y-coordinate/Polar Phase Angle Data output port. When OEPY is HIGH, PYOUT15-0 PYOUT15-0 is forced into the highimpedance state. 32 *n 16 16 TCXY RTP Controls *n ENXR - x-coordinate/Magnitude Data Input Enable * TRANSFORM PROCESSOR 16 16 16 16 OERX When ENXR is HIGH, XRIN is latched into the input register on the rising edge of clock. When ENXR is LOW, the value stored in the register is unchanged. OEPY RXOUT15-0 RXOUT15-0 OVF ENYP1-0 - y-coordinate/Phase Angle Data Input Control PYOUT15-0 PYOUT15-0 * REQUIRES 18 CYCLES TO COMPLETE AND IS FULLY PIPELINED * WHEN RTP IS HIGH 'n' IS 16-BITS 16-BITS, WHEN RTP IS LOW 'n' IS 24-BITS 24-BITS ENYP1-0 is the 2-bit y-coordinate/ Phase Angle Data Input Control that determines four modes as shown in SIGNAL DEFINITIONS Inputs Power XRIN15-0 XRIN15-0 - x-coordinate/Magnitude Data Input VCC and GND +5V power supply. All pins must be connected. Clock CLK - Master Clock The rising edge of CLK strobes all enabled registers. TABLE 1. REGISTER OPERATION XRIN15-0 XRIN15-0 is the 16-bit Cartesian x-coordinate/Polar Magnitude Data input port. XRIN15-0 XRIN15-0 is latched on the rising edge of CLK. ENYP1-0 M C 00 Hold Hold 01 Load Hold 10 Hold Load 11 Clear Load YPIN31-0 YPIN31-0 - y-coordinate/Phase Angle Data Input YPIN31-0 YPIN31-0 is the 32-bit Cartesian y-coordinate/Polar Phase Angle Data input port. When RTP is HIGH, the input accumulators should not be used. When ACC is LOW, the upper 16 bits of YPIN are the input port and the lower 16 bits become "don't cares". YPIN31-0 YPIN31-0 is latched on the rising edge of CLK. TABLE 2. ACCUMULATOR CONTROL ACC1-0 Configuration 00 No accumulation (normal operation) 01 PM accumulator path enabled 10 FM accumulator path enabled 11 Logical OR of PM and FM (Nonsensical) Special Arithmetic Functions 2 08/16/2000­LDS.2330-D 2330-D L2330 L2330 DEVICES INCORPORATED Coordinate Transformer Table 1. `M' is the Modulation Register and `C' is the Carrier Register as shown in the Functional Block Diagram. RTP - Rectangular-to-Polar When RTP is HIGH, Rectangular-toPolar conversion mode is selected. When RTP is LOW, Polar-to-Rectangular conversion mode is selected. FIGURE 1A. ACC1-0 - Accumulator Control ACC1-0 is the 2-bit accumulator control that determines four modes as shown in Table 2. Changing of the internal phase Accumulator structure is very useful when RTP is LOW allowing for waveform synthesis and modulation. ACC1-0 set to `00' is most commonly used when RTP is HIGH unless performing backward mapping from Cartesian to Polar coordinates. TCXY - Data Input/Output Format Select When TCXY is HIGH, two's complement format is selected. When TCXY is LOW, sign-and-magnitude format is selected. INPUT FORMATS XRIN YPIN Integer Unsigned Magnitude 15 14 13 215 214 213 (RTP = 0) Fract. Unsigned Mag./Two's Comp. 2 1 0 22 21 20 31 30 29 *±20 2­1 2­2 2 1 0 2­29 2­30 2­31 Integer Signed Magnitude (RTP = 1, TCXY = 0) 15 14 13 NS 214 213 2 1 0 22 21 20 31 30 29 NS 214 213 18 17 16 22 21 20 Integer Two's Complement (RTP = 1, TCXY = 1) 15 14 13 ­215 214 213 2 1 0 22 21 20 31 30 29 ­215 214 213 18 17 16 22 21 20 (RTP = 0) Fractional Unsigned Magnitude Fract. Unsigned Mag./Two's Comp. 15 14 13 20 2­1 2­2 2 1 0 2­13 2­14 2­15 31 30 29 *±20 2­1 2­2 2 1 0 2­29 2­30 2­31 Fractional Signed Magnitude (RTP = 1, TCXY = 0) 15 14 13 NS 2­1 2­2 2 1 0 2­13 2­14 2­15 31 30 29 NS 2­1 2­2 18 17 16 2­13 2­14 2­15 Fractional Two's Complement (RTP = 1, TCXY = 1) 15 14 13 ­20 2­1 2­2 2 1 0 2­13 2­14 2­15 31 30 29 ­20 2­1 2­2 18 17 16 2­13 2­14 2­15 *±20 denotes two's complement sign or highest magnitude bit. Since phase angles are modulo 2 and phase accumulator is modulo 232, this bit may be regarded as ±. NS denotes negative sign. (i.e. '1' negates the number) Special Arithmetic Functions 3 08/16/2000­LDS.2330-D 2330-D L2330 L2330 DEVICES INCORPORATED Coordinate Transformer OVF - Overflow Flag OERX - x-coordinate/Magnitude Data Output Enable When OERX is LOW, RXOUT15-0 RXOUT15-0 is enabled for output. When OERX is HIGH, RXOUT15-0 RXOUT15-0 is placed in a high-impedance state. OVF will go HIGH on the clock the magnitude of either of the current Cartesian coordinate outputs exceed the maximum range. OVF will return LOW on the clock that the Cartesian output value(s) return within range. An overflow condition can only occur when RTP is LOW. FIGURE 1B. OEPY - y-coordinate/Phase Angle Data Output Enable When OEPY is LOW, PYOUT15-0 PYOUT15-0 is enabled for output. When OEPY is HIGH, PYOUT15-0 PYOUT15-0 is placed in a high-impedance state. OUTPUT FORMATS RXOUT PYOUT Integer Signed Magnitude (RTP = 0, TCXY = 0) 15 14 13 NS 214 213 2 1 0 22 21 20 15 14 13 NS 214 213 2 1 0 22 21 20 Integer Two's Complement (RTP = 0, TCXY = 1) 15 14 13 ­215 214 213 2 1 0 22 21 20 15 14 13 ­215 214 213 Integer Unsigned Magnitude 15 14 13 215 214 213 2 1 0 22 21 20 (RTP = 1) Fract. Unsigned Mag./Two's Comp. 2 1 0 22 21 20 15 14 13 *±20 2­1 2­2 2 1 0 2­13 2­14 2­15 Fractional Signed Magnitude (RTP = 0, TCXY = 0) 15 14 13 NS 2­1 2­2 2 1 0 2­13 2­14 2­15 15 14 13 NS 2­1 2­2 2 1 0 2­13 2­14 2­15 Fractional Two's Complement (RTP = 0, TCXY = 1) 15 14 13 ­20 2­1 2­2 2 1 0 2­13 2­14 2­15 15 14 13 ­20 2­1 2­2 2 1 0 2­13 2­14 2­15 (RTP = 1) Fractional Unsigned Magnitude Fract. Unsigned Mag./Two's Comp. 15 14 13 20 2­1 2­2 2 1 0 2­13 2­14 2­15 15 14 13 *±20 2­1 2­2 2 1 0 2­13 2­14 2­15 *±20 denotes two's complement sign or highest magnitude bit. Since phase angles are modulo 2 32 and phase accumulator is modulo 2 , this bit may be regarded as ±. NS denotes negative sign. (i.e. '1' negates the number) Special Arithmetic Functions 4 08/16/2000­LDS.2330-D 2330-D L2330 L2330 DEVICES INCORPORATED Conversion Ranges The L2330 L2330 supports 16-bit unsigned radii and 16-bit signed Cartesian coordinates. Since the 16-bit rectangular coordinate space does not completely cover the polar space defined by 16-bit radii, certain values of "r" will not map correctly. This condition is indicated by the overflow (OVF) flag. In Polar-to-Rectangular conversions, no overflow occurs for r 32767 (7FFFH). Overflow will always occur when r > 46341 (B505H B505H). Note that in signed magnitude mode r = 46340 (B504H B504H) will also cause an overflow. For 32767 r 46340, overflow may occur depending on the exact values of r and . Figure 2 shows, for the first quadrant, these three regions: A = no overflow (correct conversion), B = possible overflow, C = overflow. The other quadrants are mapped in a similar manner. When in signed magnitude mode, the overflows on the other three quadrants are the same as in the first. This occurs because the signed magnitude number system is symmetric about zero. For example, if a given r and angle cause an overflow, the same r will cause an overflow for the angles -, + , -. Coordinate Transformer complement number system is not symmetric about zero. For example, if the X or Y component of the input is ­32768 (8000H 8000H), no overflow occurs. But if the X or Y component of the input is +32768, overflow does occur. FIGURE 2. 65535 When converting from Rectangular-toPolar, if both inputs are zero the radius is zero but the angle is not defined. The L2330 L2330 will output 4707H 4707H in this case. Since the angle is not defined for a zero length vector, this is not an error. CONVERSION RANGES /2 C 32767 B A y r However, when in two's complement mode, the overflows aren't quite the same. This occurs because the two's x 32767 65535 Special Arithmetic Functions 5 08/16/2000­LDS.2330-D 2330-D L2330 L2330 DEVICES INCORPORATED Internal Precision When performing a coordinate transformation, inaccuracies are introduced by a combination of quantization and approximation errors. The accuracy of a coordinate transformer is dependent on the word length used for the input variables, the word length used for internal calculations, as well as the number of iterations or steps performed. Truncation errors are due to the finite word length, and approximation errors are due to the finite number of iterations. For example, in the case of performing a polar-to-rectangular transformation, the accuracy of the rotation will be determined by how closely the input rotation angle was approximated by the summation of sub-rotation angles. In this study, we examine the effectiveness of 16-bit internal precision versus 24-bit internal precision. 10,000 random Rectangular coordinates were converted to Polar and back to Rectangular. The resulting Rectangular coordinates from this double conversion were then compared to the original Coordinate Transformer Rectangular coordinates input to the device. These vectors, with maximum word width of 16-bits, were sent through a 16-bit internal processor versus a 24-bit internal processor. The Rectangular coordinates were limited to the following conditions: ­32769