Note: Descriptions are shown in the official language in which they were submitted.
' WO 93/00737 . PCI`/AU92/00305
21~ 2252
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ARBITRARY WAVEFORM GENERATOR ARCHITECTURE
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;~' BACKGROUND OF THE INVENTION
This invention relates to a method of digitally generating linear frequency
modulated continuous wave (FMCW) waveforms at high frequency for use in
5 such applications as high-freq~ency radar systems.
In its most general sense the invention can be applied to any system requiring
virtually any waveform. In this discussion its application in HF radar systems
will be used as an example.
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;j Signal sources used in HF radar systems require very high dynamic range,
10 low phase noise and amplitude accuracy over a wide frequency band. In
many applications they also require fast frequency switching and known
~, phase characteristics. Typical signal sources use one of two methods to
generate these signals - phase~ locked loop synthesis or direct digital
~; synthesis.
15 Phase locked loop methods, in their most simple form, suffer from poor phase
noise andlor poor~ frequency resolution~ a relative large step between
permissible frequenciss). Frequency sw~itchîng time can also be rather poor
(long).~ Direct ~digital~synthesis methods are usually based on phase
accumulator techniques or memory look-up techniques. These techniques
20 allow for both low phase~noise and~narrow 1requency resolution. However,
. , ~ ~ ~
the phase accu~mulator design is optimised for the generation of a fixed
frequenc~ tone~an~d~the memory; lookup technique suffers from large
~3 ~ computational overheads as~all data points must be calculated in advance.
This invention combines and ~extends thé phase accumulator technique to
25 provide a device~which can gerlerate arbitrary or pseudo-arbitrary waveforms.This is particularly important~in a real-time~system. The invention described
here~ may~be used as a pseudo-arbitrary wavetorm generator with high
capability and low com~putational overhead. ~
A common waveform used in HF radar systems is the linear frequency
30 modulated continuous wave ;~FMCW) waveform, where the frequency is swept
linearly up or down~ over a programmable frequency span in a programmable
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sources it is necessary to approximate the desired waveform by a series o~
short fixed-frequency steps. This invention can produce true linear FMCW
waveforms. The technique may be further extended to produce more complex
5 waveforms of higher order, or these waveforms may be approximated by a
piecewise linear approximation. This approximation, being a second order
approximation, is inherently more accurate than the first order approximation
of conventional phase accumulator techniques.
The continuous time equation for a single cycle of a sawtooth waveform
10 (linear FMCW ramp) is given by:
f(~) = 511~1[t {~I)o I 2T t}]
where T = the period of the waveform
= 2~fo the starting;frequency of the ramp
~1 = 2~1fj the ending frequency of the ramp.
15 Converting this equation to an ~equivalent discrete time equation with
sampling period ts ~and adding the constraint that there are an integer number
~N) of samples in a ramp period, reveals that it can be written more simply as:
~ :
f(n) = SlN[n(a + bn)l
:
where ~ a =
20 ~ ~ ~ ` b -~ 2~N ~
This~analysis leads to the~discovery that a discrete digital synthesis ramp
generator: may be implemented with~two levels of accumulation and a
;; sinusoidal look-up ROM if the~two phase registers are loaded with the initial values a + b and 2b~ r*spectiv~ly. ~ ~ ~
25 The technique of cascading accumulators can be extended to allow the
- generation of hlgherorder~waveforms. In fact anywaveform s(t) = SlN(~t))
where
~(t) = ao+a1t + a2tZ + ...~+antn
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P~/AU / 9 2 / O 0 3 0 5
R CEI\/E~ 0 8 JAI'~ lg93
~1122~2
can be generated with n cascaded accumulators. By including a cosine
lookup ROM as well as a sine lookup ROM any waveform s(t) = eJ~(t) can be
generated. Note also that the lookup ROM is not constrained to sinusoidal
waveforms, but can be used to map any periodic function. In practice
5 implementing further stages of accumulation becomes difficult due to a need
for greater arithmetic precision in the early stages of accumulation, and to
account for propagation delays through the accumulator chain. The design
presented here àpproximates higher order waveforms by a piecewise linear
approximation.
1 0 SUMMARY OF THE INVENTION
According to perhaps one form of this invention there is proposed an arbitrary
waveform generator comprising:
a plurality of accumulators each adapted to produce an output vatue from one
or more input values;
1 5 one or more memory~means adapted to map the output of one or more
accumulators to an ampl~tude value;
a converter means adapted to convert the amplitude value from digital form to
analogue form;~ and~
a control means adapted to synchronise the operation of the waveform
2 0 generator.
In prsferenGe ~the input va~lues are stored in a plurality of input registers.
In preference thè ~converter; means is a digital to analogue converter that
c onverts a digital ~signal from the digital section of the generator to an
analogue~sbnal.; ~
2 5 In preference the~ memory~means is an addressable solid state memory device
such as a rea~ only~memory device containing a look-up table for mapping a
linear variation in; phase to~ a sinusoidal variation in amplitude. Alternatively,
the merr~ory~means~couid be an EPROM, Beta card, DRAM or other similar
memory device.~The memory device look-up table may contain other periodic
3~ ~functions. ~ ~ ~
In preferencè the control~ means is a microprocessor incorporating a clock
means which is a~high purity oscillator. In order to interface to the very
cemplex waveiorm scheduling requirements of on operational OTHR radar
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' control system a high performance microprocessor is required.
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In preference there is provided a filter means which filters the output of the
digital to analogue converter. In praetice this is a low pass filter.
In a further form of this invention there is proposed a method of direet digital5 synthesis of linear frequ~ney modulated waveforms eomprising the steps of:
at a given regular time, adding a fixed frequeney increment word to a
frequency eontrol value stored in a first register to produce a linearly
inereasing frequeney eontrol word;
adding the frequeney eontrol word stored in the first register to a seeond
10 register to form a quadratieally inereasing phase word;
eonverting the quadratieally inereasing phase word to an amplitude value
;'i ~ using a look-up~table stored in a memory means to produee a linearly
inereaslng frequeney; and ~ ~ ~
periodieally resetting the frequeney eontrol word to produee a frequency
1 5 sawtooth. ~ ~ ~
In preferenee~the~ amptitude value is eonverted from a digital value to an
analogue value~using a digital to analogue eonverter.
;~ In preferenee there is provided a~ tiiter means after the digital to analogue
converter~and~in preference this is a low pass filter.
20 In preferenee there is provided a eloek means to provide the given regular
: timeandcontrolthe~periodlc~resening~
' '~ DESCRIPTION OF THE PREFERRED EMBODIMENT
For~a b~er understanding ~of;this' invention~a~ preferred embodiment will now
be described~with rèfèrenee to;the~attaehed drawing in whieh: -
'25- ~ ~ FIG~ is a~schematic of an~ arbitrary~waveforrn generator consisting of two
phase accu mulator stages.; ~
: ~
Ph~se accumulator signal synthesis is a digital technique whereby a fixed
phase increment~is added~to a value stored in a phase register, giving rise to alinearly varying phase. ~As the instantaneous frequency is defined to be the
~ ~ ~ 30 time derivative~ of the phase, the phase~ accumulator thus generates a fixed
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WO 93/00737 PCr/AU92/0030~S
5 2112252
frequenoy signat. This signal is mapped to an amplitude by a sinusoidal
lookup table, which may then be converted to an analogue form by a digital-
to-analogue converter.
Referring in detail to the figure, the inputs to the generator are a frequency
increment word 1, an initial frequency 2 and an initial phase 3. The frequency
register 4 is incremented in an adder 5 by the value of the increment word 1
on each reference clock pulse of a clock 6, giving a linear frequency
progression. The llnearly chan~ing frequency output trom the ~requency
register 4 is added in adder 7 to the phase register 8 on each clock pulse to
produce a quadratic phase progression which is mapped by the ROM 9 to
produce a linearly increasing frequency ramp. By resetting the control values
at regular intervals the output becomes a repetitive frequency sawtooth A
digital to analogue converter 10~ converts the digital signal 11 to analogue
form which is subsequently~passed through a low-pass filter 12 to produce the
desired output.
Each ramp can be completely defined by four parameters or control values:
initial phase, initial frequency, trequency increment word and duration of
ramp. Any of the first three parameters may be unused (taking the final value
of the previous r~amp),~ which allows for~reater flexibility in waveform
generation and reduces some computational overhead.
A logical extension;~ of this technique is to implement more stages of
` ~ accumulation to ~generate~ polynomials of higher order, allowing even more
complex waveforms to be~generated directly. However, current technology
imposes restrictions on the capabi!ity~of such higher-order polynomials, such
25 ~ ~ that it is presently more appropriate to generate these higher-order
polynomials in a~piècewise linear approximation using short linear FMCW
ramps. ~
~; ' The method of controlllng this dual phase accumulator allows independent
setting of the initia!~phase, initia! frequency, and frequency deviation rate It~; 30 also allows pseudo-arbitrary~waveforms to be generated relatively simply by
~means of piecewise~Onear approximation with short time intervals (possibly as
short as 10-20 microseconds). This is a very powerful method of generating
pseudo-arbitrary waveforms, as the length of the waveform sequence is
dependent only on the~ storage requirements for the waveform definition,
rather than on the storage requirements for the entire sequence (as in the
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WO 93/00737 ` PCI'/AU92/0030~ .
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211Z252
memory lookup method of arbitrary waveform synthesis). It also allows real-
time generation of data points, avoiding the long overheads of memory lookup
techniques.
The waveform generator may be configured to either repetitively generate the
5 same ramp or produce a series of independent ramps. Pseudo-arbitrary
waveforms can be generated by a piecewise linear approximation of ramps to
the desired waveform instead of using a muleiple accumulator architecture of
higher order. As each ramp segment is defined by four parameters only it is
possible to reduce the minimum ramp duration to the time required to transfer
10 these four parameters to the appropriate registers. With current high
performance microprocessors a minimum step size of 10 to 20 microseconds
is a physically achievable value that will provide a good approximation to
most desired waveforms. The pseudo-arbitrary waveform is implemented as a
series of short frequency ramps approximating the desired waveform. The
15 total number of ramp segments tha~ can be put in a sequence has yet to be
determined, but will number in the thousands and will be limited only by
~ ~ parameter storage~ requiremen~s. The speed of programming and
j ~ implementing these ramps as well as the maximum number of ramps is
determined only by the speed and~storage capabilities of the controlling
20 microprocessor.; ~This is a very~powerful method of producing pseudo-arbitrary
waveforms and allows very~complex waveforms of long duration to be
generated relative~ly simply~without recourse to multiple accumulator
architectures.~
The `invention~offers~a number of advantages. The output frequency can be
25 ~ ~ ~changed~ very~ rapidly w~thout~impacting on the quality ot the output signal.
The~ non-pipe!ined~ nature of the ~design~allows the output frequency to change
within ~a single~sampling cbck period.~ Furthermorc, any changes in frequency
are~contr~lled to~provide non-discontinuous changes in phase and frequency
$.~ ~ unless discontinuity is desired~, in whi¢h case the discontinuity is known and
30 can thus be contro~ lled; ~
In~the same manner as a singie phase accumulator is optimised for a fixed
frequency tone, the ~dual accumulator is optimised for quadratic phase
generation (i.e. Iinear FMCW). The addition of further stages of phase
$~ accumulation provide;a mèthod for optimised generation of higher order
~, 35 waveforms. Being all ~digital the phase and amplitude are controlled at all
times. This has~ particular importance in radar systems where a coherent
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detection process is implemented. Coherent detPction requires a known,
repeatable phase progression and phase errors translate directly to errors in
detection.
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