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Cordic

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  • 2014 Synopsys, Inc. All rights reserved. 1

    Digital Track: Project

    DTMF signal generator

  • 2014 Synopsys, Inc. All rights reserved. 2

    Agenda

    DTMF

    CORDIC

    Fixed point arithmetic

    Project

  • 2014 Synopsys, Inc. All rights reserved. 3

    DTMF

    Dual Tone Multiple Frequency

  • 2014 Synopsys, Inc. All rights reserved. 4

    Dual-tone multi-frequency signaling

    Used for telecommunication signaling over analog

    telephone lines

    Introduced by AT&T in 1963. Replaced the rotary dial.

    Standardized by ITU

  • 2014 Synopsys, Inc. All rights reserved. 5

    Example of DTMF signal

    DTMF output is the sum of a low and a high frequency

    sinusoidal waves

    697 Hz Sine Wave + 1209 Hz Sine Wave = DTMF Tone "1"

    + =

  • 2014 Synopsys, Inc. All rights reserved. 6

    DTMF Keypad: Frequencies

    1209 Hz 1336 Hz 1477 Hz 1633 Hz

    697 Hz 1 2 3 A

    770 Hz 4 5 6 B

    852 Hz 7 8 9 C

    941 Hz * 0 # D

    Upper band

    Lower

    band

    Keypad is a 4x4 matrix

    Rows represents low frequencies

    Columns represents high frequencies

  • 2014 Synopsys, Inc. All rights reserved. 7

    Mark and space

    The time which a Dtmf digit tone is actually producing

    signaling, is called the "Mark" time.

    The silence after a mark is called the "Space".

    Most Dtmf decoders and controllers will list a minimum

    Mark/Space speed, expressed in millisecond

  • 2014 Synopsys, Inc. All rights reserved. 8

    CORDIC

    COordinate Rotation DIgital Computer

  • 2014 Synopsys, Inc. All rights reserved. 9

    We need to create sine waves

    We only have logic gates and flip flops

    Several approaches could exists to calculate the

    trigonometric functions

    Most of them will require multipliers and dividers which are

    expensive in terms of performance and area

    We need an alternative to compute these functions

  • 2014 Synopsys, Inc. All rights reserved. 10

    COordinate Rotation DIgital Computer:

    CORDIC

    Also known as the digit-by-digit method and Volder's

    algorithm (1959)

    It is a simple and efficient algorithm to calculate

    hyperbolic and trigonometric functions.

    It is commonly used when no hardware multiplier is

    available (e.g., simple microcontrollers and FPGAs)

    It only requires: addition, subtraction, bit-shift and table

    lookup.

    It can lead to an area efficient hardware implementation

    For k bit precision, k iterations are required

  • 2014 Synopsys, Inc. All rights reserved. 11

    CORDIC bases

    It uses pseudo-rotations with fixed angles.

    it explodes mathematical properties of , and .

    fixed angles are selected to use division by 2 (binary

    shift)

    more info: http://en.wikibooks.org/wiki/Digital_Circuits/CORDIC and Google

    http://en.wikibooks.org/wiki/Digital_Circuits/CORDIChttp://en.wikibooks.org/wiki/Digital_Circuits/CORDIC

  • 2014 Synopsys, Inc. All rights reserved. 12

    Using the Cordic: rotation mode

    +1 = 2

    +1 = + 2

    +1 =

    = arctan 2 values are

    precomputed

    = ()

    if 0 =1

    and 0 = 0 then

    = cos 0

    = sin(0)

    = 1 + 21=0

  • 2014 Synopsys, Inc. All rights reserved. 13

    Fixed point arithmetic

  • 2014 Synopsys, Inc. All rights reserved. 14

    Fixed-point number representation (1/2)

    Value of a n-bit binary fixed point number with digits :

    = 2 21

    =0 = 21

    =0

    where:

    is a constant giving the position of the binary point (from left)

    resolution: = 2

    number of fractional bits: = .

    Signed numbers: use 2s complement. Notation: .

    0 1 0 . 1 1 1 0 0

    f p s

    8 bits

  • 2014 Synopsys, Inc. All rights reserved. 15

    Fixed-point number representation (2/2)

    Binary fixed-point to decimal: to convert to an integer and

    multiply by

    Decimal number to fixed-point binary number:

    (a) multiply by 2

    (b) round to nearest whole integer (max. error = r/2)

    (c) resulting decimal integer to binary integer

    0 1 0 . 1 1 1 0 0

    f p s

    8 bits

  • 2014 Synopsys, Inc. All rights reserved. 16

    example and operations

    E.g.:

    The four basic operations (+,-,*,/) on fixed-point binary

    numbers can be performed as if they were integers.

    Adding two . fixed-point numbers could give a result that is a ( + 1). fixed-point number.

    Format Number r Integer Value

    1.3 1.011 0.125 (2^-3) 11 1.375 (11/8)

    s1.3 01.011 0.125 (2^-3) 11 1.375 (11/8)

    s1.3 11.011 0.125 (2^-3) -5 -0.625 (-5/8)

    2.4 10.0111 0.0625 (2^-4) 39 2.4375 (39/16)

  • 2014 Synopsys, Inc. All rights reserved. 17

    Project

    DTMF Generator

  • 2014 Synopsys, Inc. All rights reserved. 18

    Objective

    To design and implement a simple DTMF generator

    No silences between key changes are required

    No digital to analog conversion

    To use CORDIC algorithm to calculate sine or cosine

    To use Fixed-point numbers for calculations.

  • 2014 Synopsys, Inc. All rights reserved. 19

    Specifications

    Output of 16 bits named out[15:0]

    Input of 5 bits for keypad named key[4:0]

    16 key stroke combinations + 1 no-stroke

    unused combinations must not produce signaling

    Asynchrony Reset called rst

    Pin Clock clk

    Clock frequency must be determined by you.

    mark=40ms; space=40ms

    Minimize Power and Area, but achieve accurate timing

    All paths must complete on a clock period

    Accurate output wave frequencies are required.

  • 2014 Synopsys, Inc. All rights reserved. 20

    Stamp the idea in paper

    DMFT Diagram

    sin(wt)

    CORDIC

    keypad

    Digital Input

    sin(wt)

    CORDIC

    Modulated

    Digital Tone

    DECODE

    Frequency

    Lookup

    Table

  • 2014 Synopsys, Inc. All rights reserved. 21

    Can we physically implement our

    designs?

  • 2014 Synopsys, Inc. All rights reserved. 22

    MOSIS (Metal Oxide Semiconductor

    Implementation Service)

    Is probably the oldest (1981) integrated circuit (IC)

    foundry service

    MOSIS is operated by the Information Sciences Institute

    at the University of Southern California (USC)

    MOSIS has prototyped more than 50,000 chip designs

    for private businesses, government agencies, research

    agencies and universities

  • 2014 Synopsys, Inc. All rights reserved. 23

    MOSIS Educational Program (MEP)

    Instructional Program

    The MOSIS Instructional program provides free fabrication of

    integrated circuits designed by students in organized classes

    associated with an accredited university.

    These runs are currently sponsored by MOSIS.

    Available technologies:

    ON Semiconductor 0.50 micron C5 (5 parts per design)

    IBM 0.18 micron 7RF (14 parts per design)

    Max die size: 1.5mmX1.5mm

    MOSIS will provide ceramic or OCP packaging

  • 2014 Synopsys, Inc. All rights reserved. 24

    DIP 28 package

  • 2014 Synopsys, Inc. All rights reserved. 25

    Thank You