LOGIC L2330QC25, L2330QC20 Datasheet

DEVICES INCORPORATED

L2330

Coordinate Transformer

L2330

DEVICES INCORPORATED

FEATURES DESCRIPTION

❑❑

❑ Rectangular-to-Polar or Polar-to-

❑❑

Rectangular at 50 MHz

❑❑

❑ Performs Direct Digital Synthesis

❑❑

(DDS) functions along with PM and
FM Modulation

❑❑

❑ 24-Bit Polar Phase Angle Accuracy

❑❑
❑❑

❑ Replaces Fairchild TMC2330A

❑❑
❑❑

❑ 120-pin PQFP

❑❑

The L2330 is a coordinate transformer
that converts bidirectionally between
Rectangular and Polar coordinates.

When in Rectangular-to-Polar mode,
the L2330 is able to retrieve phase and
magnitude information or backward
map from a rectangular raster display
to a radial data set.

When in Polar-to-Rectangular mode,
the 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 converts bidirectionally
between Rectangular (Cartesian) and
Polar (Phase and Magnitude) coordi­nates. The user selects the numeric
format. A valid transformed result is

Coordinate T ransformer

seen at the output after 22 clock cycles
and will continue upon every clock
cycle thereafter.

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 2π so it may be
regarded as either unsigned or two’s
complement format.

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 BLOCK DIAGRAM

ENXR

XRIN

ENYP

YPIN

ACC

TCXY

RTP

CLK

15-0

1-0

31-0

1-0

16

32

OERX

2

2

POLAR

RECTANGULAR

16

16

RXOUT

OEPY

PYOUT

OVF

15-0

15-0

Special Arithmetic Functions

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09/27/2001–LDS.2330-E

DEVICES INCORPORATED

L2330

Coordinate T ransf ormer

L2330 FUNCTIONAL BLOCK DIAGRAM

15-0

XRIN

16

16

16

TCXY

RTP

16

16

OERX

ENXR ENYP

AM

TRANSFORM

*

PROCESSOR

YPIN

32

MC

31-0

Outputs

RXOUT15-0 — x-coordinate/Magnitude

1-0

ACC

1

32

2

ACC

0

Data Output

RXOUT15-0 is the 16-bit Cartesian
x-coordinate/Polar Magnitude Data
output port. When OERX is HIGH,
RXOUT15-0 is forced into the high­impedance state.

32

PM

32

PYOUT15-0 — y-coordinate/Phase Angle

Data Output

PYOUT15-0 is the 16-bit Cartesian
y-coordinate/Polar Phase Angle Data

FM

**

n

**

n

32

output port. When OEPY is HIGH,
PYOUT15-0 is forced into the high­impedance state.

Controls

ENXR — x-coordinate/Magnitude Data

Input Enable

16

When ENXR is HIGH, XRIN is latched
into the input register on the rising

16

edge of clock. When ENXR is LOW,
the value stored in the register is

OEPY

unchanged.

RXOUT

15-0

REQUIRES 18 CYCLES TO COMPLETE AND IS FULLY PIPELINED*
WHEN RTP IS HIGH ’n’ IS 16-BITS, WHEN RTP IS LOW ’n’ IS 24-BITS**

OVF

SIGNAL DEFINITIONS

Power

VCC and GND

+5V power supply. All pins must be
connected.

Clock

CLK — Master Clock

The rising edge of CLK strobes all
enabled registers.

PYOUT

15-0

Inputs

XRIN15-0 — x-coordinate/Magnitude

Data Input

XRIN15-0 is the 16-bit Cartesian
x-coordinate/Polar Magnitude Data
input port. XRIN15-0 is latched on the
rising edge of CLK.

YPIN31-0 — y-coordinate/Phase Angle

Data Input

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 is latched
on the rising edge of CLK.

ENYP1-0 — y-coordinate/Phase Angle

Data Input Control

ENYP1-0 is the 2-bit y-coordinate/
Phase Angle Data Input Control that
determines four modes as shown in

TABLE 1. REGISTER OPERATION

ENYP1-0 MC

0 0 Hold Hold
0 1 Load Hold
1 0 Hold Load
1 1 Clear Load

TABLE 2. ACCUMULATOR CONTROL

ACC1-0 Configuration

0 0 No accumulation (normal operation)
0 1 PM accumulator path enabled
1 0 FM accumulator path enabled
1 1 Logical OR of PM and FM (Nonsensical)

Special Arithmetic Functions

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09/27/2001–LDS.2330-E

DEVICES INCORPORATED

L2330

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.INPUT FORMATS

XRIN YPIN

15 14 13 2 1 0
2152142

15 14 13 2 1 0

NS 2142

13

13

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

(RTP = 0)

Fract. Unsigned Mag./Two's Comp.Integer Unsigned Magnitude

22212

0

Integer Signed Magnitude (RTP = 1, TCXY = 0)

22212

0

31 30 29 2 1 0

*±202–12

–2

31 30 29 18 17 16

NS 2142

13

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.

–292–302–31

2

22212

0

Integer Two's Complement (RTP = 1, TCXY = 1)

15 14 13 2 1 0

–2152142

13

22212

0

31 30 29 18 17 16

–2152142

13

22212

(RTP = 0)

Fractional Unsigned Magnitude

15 14 13 2 1 0

202–12

–2

–132–142–15

2

Fract. Unsigned Mag./Two's Comp.

31 30 29 2 1 0

*±202–12

–2

–292–302–31

2

Fractional Signed Magnitude (RTP = 1, TCXY = 0)

15 14 13 2 1 0

NS 2–12

–2

–132–142–15

2

31 30 29 18 17 16

NS 2–12

–2

–132–142–15

2

Fractional Two's Complement (RTP = 1, TCXY = 1)

15 14 13 2 1 0

–202–12

*±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.
NS denotes negative sign. (i.e. '1' negates the number)

–2

–132–142–15

2

31 30 29 18 17 16

–202–12

–2

–132–142–15

2

0

Special Arithmetic Functions

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DEVICES INCORPORATED

L2330

Coordinate T ransf ormer

OVF — Overflow Flag

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.OUTPUT FORMATS

RXOUT PYOUT

15 14 13 2 1 0

NS 2142

15 14 13 2 1 0

–2152142

13

13

OERX — x-coordinate/Magnitude Data

Output Enable

When OERX is LOW, RXOUT15-0 is
enabled for output. When OERX is
HIGH, RXOUT15-0 is placed in a
high-impedance state.

Integer Signed Magnitude (RTP = 0, TCXY = 0)

22212

0

Integer Two's Complement (RTP = 0, TCXY = 1)

22212

0

15 14 13 2 1 0

NS 2142

13

15 14 13 2 1 0

–2152142

13

OEPY — y-coordinate/Phase Angle Data

Output Enable

When OEPY is LOW, PYOUT15-0 is
enabled for output. When OEPY is
HIGH, PYOUT15-0 is placed in a
high-impedance state.

22212

22212

0

0

(RTP = 1)

Fract. Unsigned Mag./Two's Comp.Integer Unsigned Magnitude

15 14 13 2 1 0
2152142

13

22212

0

15 14 13 2 1 0

*±202–12

–2

–132–142–15

2

Fractional Signed Magnitude (RTP = 0, TCXY = 0)

15 14 13 2 1 0

NS 2–12

–2

–132–142–15

2

15 14 13 2 1 0

NS 2–12

–2

–132–142–15

2

Fractional Two's Complement (RTP = 0, TCXY = 1)

15 14 13 2 1 0

–202–12

–2

–132–142–15

2

15 14 13 2 1 0

–202–12

–2

–132–142–15

2

(RTP = 1)

Fract. Unsigned Mag./Two's Comp.Fractional Unsigned Magnitude

15 14 13 2 1 0

202–12

*±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
NS denotes negative sign. (i.e. '1' negates the number)

–2

–132–142–15

2

15 14 13 2 1 0

*±202–12

–2

–132–142–15

2

.

Special Arithmetic Functions

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DEVICES INCORPORATED

L2330

Coordinate Transformer

Conversion Ranges

The 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). Note that in signed
magnitude mode r = 46340 (B504H)
will also cause an overflow. For 32767 ≤
r ≤ 46340, overflow may occur depend­ing on the exact values of r and θ.
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.

complement number system is not
symmetric about zero. For example, if
the X or Y component of the input is
–32768 (8000H), no overflow occurs.
But if the X or Y component of the
input is +32768, overflow does occur.

FIGURE 2. CONVERSION RANGES

π/2

65535

32767

When converting from Rectangular-to­Polar, if both inputs are zero the radius
is zero but the angle is not defined.
The L2330 will output 4707H in this
case. Since the angle is not defined for a
zero length vector, this is not an error.

C

B

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 θ cause
an overflow, the same r will cause an
overflow for the angles -θ, π+θ , π-θ.

However, when in two’s complement
mode, the overflows aren’t quite the
same. This occurs because the two’s

A

y

r

θ

x

32767

65535

Special Arithmetic Functions

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