1. Page | 1
Shanmugha Arts, Science, Technology & Research Academy
(SASTRA University)
Tirumalaisamudram, Thanjavur-613402.
Department of Electronics and Communication Engineering
BONAFIDE CERTIFICATE
Certified that the project work entitled “REFLECTION SOLITON OSCILLATOR”
submitted to Shanmugha Arts, Science, Technology & Research Academy (SASTRA
UNIVERSITY), Thanjavur by BADRI NARAYANAN.R (Reg No:011004039), CHETHAN RAM
NARAYAN.B (Reg No:011004047), VIGNESH K (Reg No:011004257) in partial fulfillment of
the award of the degree of Bachelor of Technology in Electronics and Communication
Engineering is the original and independent work carried out under my guidance during the
period Dec 2009 – April 2010.
Internal Guide
Dr. R. GANAPATHY
Assistant Professor(III), SEEE,
SASTRA
Professor In charge
Department of Electronics and Communication Engineering
External Examiner Internal Examiner
2. Page | 2
Shanmugha Arts, Science, Technology &ResearchAcademy
(SASTRA University)
Tirumalaisamudram, Thanjavur-613402.
Department of Electronics and Communication Engineering
DECLARATION
We submit this project work entitled “REFLECTION SOLITON OSCILLATOR” to Shanmugha
Arts, Science, Technology & Research Academy (SASTRA University), in partial fulfillment of
the requirements for the award of the degree of Bachelor of Technology and we declare
that it is our original and independent work carried out under the guidance of
Dr.R. GANAPATHY as Internal Guide Assistant Professor(III), SEEE, SASTRA.
BADRI NARAYANAN.R (Reg No: 011004039)
CHETHAN RAM NARAYAN.B (Reg No: 011004047)
VIGNESH K (Reg No011004257)
.Date: 15th April, 2010.
Place: Thanjavur.
3. Page | 3
ACKNOWLEDGEMENTS
We thank Prof.R.Sethuraman, theVice Chancellor of SASTRA University
for providing us the opportunity to work on this project, as a part of the B.Tech
degree program.
We wish to express our heartfelt regards and sincere thanks to our Registrar,
Prof.S.NSrivastava, for his patronage.
We are deeply indebted to Prof. M.Narayanan, Dean of Students Affairs,
SASTRA University for his continuous encouragement.
We express our gratitude to our internal guide Dr.R.GANAPATHY Assistant
professor(III),ECE, SEEE, SASTRA and Project co-ordinator Mr. R.Amirtharajan,
Assistantprofessor(III), ECE, SEEE, SASTRA University for his, for his excellent
guidance and support.
We thank Dr. John Bosco Balaguru, AssociateDean (Research) and Dr.
K.Thenmozhi, AssociateDean (SEEE), who helped us during this projectwork.
We thank all our teaching and technical Staff, who directly or indirectly helped
us during this project work.
5. Page | 5
We report on an electrical oscillator that
self-generates a periodic train of short-duration pulses. The oscillator consists
of a nonlinear transmission line (NLTL), one end of which is connected to a
one-port amplifier and the other end is open. In the steady state, a self-generated
short-duration pulse travels back and forth on the NLTL, reflected at both ends
of the NLTL due to impedance mismatches. The one-port amplifier produces a
negative output resistance for a voltage beyond a particular threshold and a
positive output resistance for a voltage below that threshold, and thus, the
reflection from the amplifier provides gain for the main upper portion of the
6. Page | 6
pulse to compensate loss, and attenuates small perturbations to ensure
oscillation stability. The NLTL substantially sharpens the pulse.
7. Page | 7
CONTENTS
List of Figures ................................................................................................................................
Synopsis.........................................................................................................................................
1.Introduction to soliton .........................................................................................................9
1.1 Problem statement........................................................................................................9
1.2 Brief history of solitons................................................................................................10
1.3 Solitons ........................................................................................................................12
2.Non Linear Transmission Line..............................................................................................13
2.1Toda Lattice.....................................................................................................................15
2.2Lossy NLTL .......................................................................................................................16
3.Soliton Oscillator ................................................................................................................18
3.1 Basic Topology ..............................................................................................................18
3.2 Instability Mechanisms.................................................................................................21
3.2.1 Voltage Limiting Amplifier.....................................................................................21
3.2.2 Linear Amplifier.....................................................................................................22
3.3 Identification Of 3 Instability Mechanisms...................................................................24
3.4 NLTL Soliton Oscillator – Working Model .....................................................................25
3.4.1 Operating Principle................................................................................................25
3.4.2 Bias Adjustment ....................................................................................................26
3.4.3 Amplifier Operation ..............................................................................................27
3.5 Stability Mechanisms - Solutions..................................................................................30
3.5.1 Distortion Reductions............................................................................................30
3.5.2 Perturbation Rejection.......................................................................................... 30
3.5.3 Single mode selection...........................................................................................31
4. Reflection Soliton Oscillator..............................................................................................33
4.1 Introduction ...............................................................................................................33
4.2 Cutler’s Oscillator.......................................................................................................33
4.3 Haus’s Oscillator.........................................................................................................34
8. Page | 8
5. Reflection Soliton Oscillator..............................................................................................39
5.1 Reflection at Amplifier End...........................................................................................40
5.2 Reflection at Open End.................................................................................................42
6. Reflection Soliton Oscillator – Amplifier Design..................................................................45
6.1 Need For Adaptive Bias...............................................................................................45
6.2 Open Port Reflection Amplifier with Adaptive Bias ...................................................46
6.3 Improved Network .....................................................................................................52
7. Multisim Circuits ..................................................................................................................54
7.1 Amplifier Circuits.........................................................................................................55
7.1.1 Amplifier Output ..................................................................................................56
7.2 Initial Design ...............................................................................................................58
7.2.1 Output ..................................................................................................................59
7.3 Refined Model ............................................................................................................61
7.3.1 Output ..................................................................................................................62
7.4 Final circuit.........................................................................................................................64
7.4.1 Output ..................................................................................................................65
7.4.2 Extended ..............................................................................................................66
8. Comparision with Circular Soliton Oscillator.......................................................................68
8.1 Energy Efficiency.........................................................................................................68
8.2 Pulse Width ................................................................................................................69
8.3 Circuit Size ..................................................................................................................69
Refrences..................................................................................................................................68
9. Page | 9
1
INTRODUCTION TO SOLITON
1.1 ) Problem Statement:
One Meaningful extension of past2-port
NLTL works would beto constructa 1-portself sustained soliton
oscillator by properly combining the NLTL with an Amplifier with positive
feedback .Such an oscillator would self-startby growing fromambient
noise to producea train of periodic Soliton pulses.In steady stateand
hence would make self contained soliton generator not requiring an
external high frequency input.
10. Page | 10
1.2) Brief History of Solitons:
1834-John ScottRussellnoticed noted that a wave maintained its
single pulse state while propagating for long distances .This is the first
noted observation of a Soliton ,which Russell named ”The Waveof
Translation”.
1895-Korteweg and DeVries wrotefamous paper on water
dynamics. In it they developed KDV equation for the evolution of
shallow water waves.This provided theanalytical solution for Russell’s
“Waveof Translation” based upon the physics of water waves.
1955-C.C.Cutler developed a new field known as mode locking. In this
work he developed the first regenerative pulsegenerator that produced
a periodic train of electrical pulses that is a Mode locked oscillator .In his
work He combined a linear transmission line that is non-soliton,with an
11. Page | 11
amplifier and a novel constructthat was able to sharpen linear electrical
pulses.This sharpening mechanismwas achieved through threshold
dependant gain attenuation mechanismplaced in the oscillator loop.This
mechanismis known today as Saturableabsorption and is used
extensively in optical mode locking.
1960-Rolf Landauer introduced an electrical structureknown as the
non linear transmission line for paremetric amplification.These
propogates solitons in the formof voltage waves, This is whatis used in
our work.
1988-Tan introduced a tapered NLTL wherethe dispersion of the line
is reduced along the line.This line was able to compress an input pulse
by 7x[27].
1990-Two students of D.Bloom,Mark Rodwelland Daniel Van der
Weide adapted Tan’s technique and integrated it on a monolithic
substratewith the state-of-artGaAS technologies to producefastest
electrical pulses ever generated froman All electrical system.
12. Page | 12
1.3) SOLITONS:
Solitons are a special class of pulse
shaped waves that propogates in non-linear dispersivemedia while
maintaining their spatial confinement.They are found through out the
nature wherethe proper balance between non linearity and dispersion
is achieved .Examples of Soliton phenomena include shallow water
waves vibrations in a non linear spring mass lattice acoustic waves in
plasma and optical pulses in fiber optic cable.
In electronics the non-linear
transmission line (NLTL) serves as a Non-Linear dispersivemedium that
propogates voltage solitons .Electrical Solitons in the NLTL have been
actively investigated over the pastyears particularly in the micro wave
domain for sharp pulsegeneration and for High speed RF and
Microwavesampling applications.In these past studies the NLTL has
been pre-dominantly used as a 2-portsystemwhere a high frequency
input is required to generate a sharp soliton output through a transient
process ,Butin our work weuse a 1-portself sustained system.
13. Page | 13
2
NON-LINEAR
TRANSMISSION LINE
The Non Linear Transmission line(NLTL)
can be constructed froman Linear Transmission LineSuch as a
Coplanar Strip line by periodically Loading it with Varactors such
as Reverse biased PN junction or MOS Capacitors.Varactorsor
Non linear Capacitors,whoseCapacitancechanges with the
applied Voltage. An NLTL can alternatively obtained by replacing
linear capacitors of an artificial LC transmission Linewith
Varactors. This Latter implementation is an exact Analog to Non
linear lattice wherethe masses arereplaced by Inductors,And the
Non linear Springs by Varactors.
The NLTL is a Non linear Dispersivesystem
which supports the formation and propogation of Electrical
15. Page | 15
2.1) Toda Lattice:
We can derive the Dynamics of the NLTL
by solving the Nodal equations for the voltages and currents shown in
fig[C].
16. Page | 16
This is an Importantresultas it says:
The NLTL with the charge voltage
relationship,is anexact Toda lattice and is therefore anExact soliton
system,withnoapproximation.
2.2) LOSSY NLTL:
In NLTL Two major forms of loss,Thefirst
is frequency independent loss which is caused by Series resistancein
inductance and a resistor parallel in capacitor.The Loss term is
17. Page | 17
The second formof loss is Frequency dependant loss which is caused by
the resistance in series with the capacitor.The Loss term is given by
18. Page | 18
3
SOLITON OSCILLATOR
3.1) Basic Topology:
We begin by considering a
closed loop NLTL as shown, if only unidirectional propagation is
allowed, the possiblesoliton propagation modes on the ring are
the ones that satisfy the periodic boundary condition
l ,
where and are circumferenceof
the
ring and the spacing between neighboring solitons repeatedly .
19. Page | 19
Our starting idea to constructan
electrical soliton oscillator was to break the ring NLTL and
insert an non inverting amplifier as shown
20. Page | 20
The purposeof the
amplifier is to enable initial start up fromnoise and to
compensate for systemloss in steady state as is commonly done
in LC or Standing wave oscillator. The ultimate goal of the circuit is
to self generate and self sustain one of the soliton modes of the
ring NLTL. However the oscillation stability depends strongly on
the amplifier characteristics.
For the oscillator to generate
a stable soliton pulse train it is essential for the amp to tame the
complex soliton dynamics of NLTL
21. Page | 21
3.2) Instability mechanism
Here we examine the dynamics with two
commonly used amplifiers .This will lead us to identify the instability
mechanisms associated with the oscillator which is key to constructing a stable
soliton oscillator
3.2.1) Voltage limiting Amplifier:
Let us first consider the
case wherea standard voltage limiting non inverting amplifier is
used in the circuit. The transfer function of this amplifier is shown
.the amplifier is biased at a fixed operating point.
Behavioral simulations using matlab show that the circuit indeed
self starts into oscillations but the oscillation is unstable with
significant amplitude and pulse repetition variation often tending
towards whatappears to be a chaotic stageas shown.
The oscillation instability arises from
signal clipping in the amplifier in connection with the unique
22. Page | 22
NLTL properties. To see this assumeA soliton pulse appears at the
input of the amplifier at a certain time. This soliton pulse after
passing through the amplifier will turn into a squarepulse due to
clipping of the amplifiers.
This squarepulse will break up into
severalsolitons with different amplitudes while propagating down
the NLTL. The multiple soliton pulses will travel at different
speeds, eventually appearing again at the input of the amplifier.
This process repeats itself creating many soliton pulses with
various amplitudes in the loop. These soliton pulses propagate
with different speeds and continually collide with one another
causing time shifts and amplitude variations making the
oscillations unstable.
3.2.2) Linear Amplifier
The discussion aboveshows thatsignal
distortion has a negative impact on the oscillation stability,
suggesting that one might be able to attain a stable soliton
oscillation if the signal distortion is mitigated. Ballentyne et al
implemented such a systemusing a linear amplifier whose
transfer function is shown. By using the linear amplifier and
adding additional frequency dependant loss to the NLTL, he could
producea periodic soliton pulse train as shown.
23. Page | 23
In the same systemhowever other
oscillations uncontrollably appeared with slight changes in gain
termination or with external perturbations indicating a lack of
robustness. Thesewaveforms sometimes contain multiple soliton
with varying amplitudes and pulses continuously moved related to
one another and collided while Ballentyne’s systemis invaluable
for providing an opportunity to examine soliton dynamics Itis not
able to reproducea stable soliton pulse train.
24. Page | 24
3.3) Identification of three instability mechanisms:
First, perturbations arising
frominherent noise and frominhomogeneities on the NLTL can
excite various solitons in addition to the desired soliton pulsetrain.
The non linear collisions between the perturbing solitons and the
existing soliton pulse train result in significant pulseshifts and
amplitude variations, leading to unstable oscillations.
25. Page | 25
Second,unless itis ensured that a
single mode is generated every time, non linear inter mode collisions
on the NLTL could lead to instability.
Summarising to attain a stable robust
solition oscillation, the amplifier should posses the following three
capabilities
Distortion Reduction
Perturbation Rejection
Single mode selection
3.4) NLTL soliton oscillator working model:
The amplifier incorporates an adaptive bias control that
exploits the amplifiers non linear transfer function this
approach allows the simultaneous satisfaction of three
stability requirements mentioned above
3.4.1) OPERATING PRINCIPLE :
The self sustained oscillator is shown in the circuit below.
The critical difference in the amplifier is that instead of
allowing the non linearity to destabilize the oscillation,we
take advantage of it to provide stability.This is done by
using adaptive bias control to move the bias point as the dc
component of the amplifier output.
26. Page | 26
3.4.2) Bias Adjustment:
The bias of the amplifier is adjusted by using the change in
dc component of the output as the oscillation grows from a
low amplitude signal at start up to a large signal pulse based
oscillation in steady state. Other methods may be used to
make this bias adjustment such as output peak deduction ,
however using the dc component allows us to adjust the
bias for both amplitude changes and mode changes which is
critical for single mode selection.
27. Page | 27
3.4.3) Amplifier operation :
The non linear transfer
function off the amplifier together with the movable bias scheme
allows us to simultaneously meet the three stability requirements.
The transfer curve may be divided into attenuation ,gain and
voltage limiting regions. In the attenuation regions the tangential
slope at any point is less than one while in the gain region it is
always greater than one. In the voltage limiting region the
tangential slope is also less than one but was termed voltage
limiting region due to the clipping of large input voltages that fall
in the region.
28. Page | 28
Initially, the amplifier is biased at
A in the gain region, which allows start up from ambient noise. As
the oscillation grows and forms into pulses the dc component
steadily increases. The amplifier uses this increase in the dc
component to lower its bias point. This reduce bias corresponds to
a net overall gain reduction, since a portion of the pulse enters
the attenuation region thereby reducing the amount of the pulse
that receives gain. The bias point keeps moving down on the
transfer curve to the steady state bias point B in the attenuation
region, where the net overall gain of the amplifier becomes equal
to the loss in the system. This adaptive bias control resolves all the
three issues mentioned above.
30. Page | 30
3.5) Stability Mechanisms-Solutions:
3.5.1) Distortion reduction
In the steady state, the input bias has been
sufficiently reduced so that the peak portion of the input
and output pulses do not go into the voltage limiting region
of the amplifier transfer curve, thereby preventing
significant signal distortion.
3.5.2) Perturbation Rejection:
In a steady state, small perturbations at the input of
the amplifier are attenuated at the output since they fall in
the attenuation region of the transfer curve. This
perturbation rejection is possible since the steady state bias
point B has been reduce into the attenuation region. The
higher portions of the pulses lying in the gain region still
receive enough gain to compensate loss
This threshold dependant gain-attenuation mechanism vital
for stabilizing our soliton oscillator has been employed in
optical mode locked systems which is known as saturable
absorption.
31. Page | 31
3.5.3) Single Mode Selection :
It is also made possible by the adaptive bias control. since a
higher mode has a higher dc component and a lower steady
state bias due to adaptive bias control, the higher mode
receives a lower gain. We can take advantage of this mode-
dependant gain to select a particular mode. only those
modes with sufficient gain to overcome the loss of the
system can be sustained in steady state oscillations. when
more than one mode has sufficient gain, only the highest
mode is stable since any small perturbations to a lower
mode will grow into a soliton resulting in a higher mode
oscillation. Consequently, the mode dependant gain allows
only one soliton pulse train mode.
33. Page | 33
4
REFLECTION SOLITON
OSCILLATOR
4.1) INTRODUCTION:
ELECTRICAL oscillators that can generate a
periodic train of short-duration pulses can be useful in a number of
applications, including high speed sampling, time domain reflectometry,
ultra wideband radars, and high power RF generation. A few different
types of such pulse oscillators have been developed. we introduce a new
type of pulse oscillator.
4.2) Cutler’s Oscillator:
In 1955, Cutler arranged an amplifier and
a linear transmission line in a circular topology , which self-generated a
34. Page | 34
stable periodic train of short-duration pulses. Theamplifier provides gain
for a signal beyond a certain threshold, and attenuates a signal below
that threshold. This level-dependent gain is the key to the stable pulse
oscillation. More specifically: first, the level-dependent gain sharpens
the amplifier’s input signal, enabling pulse formation; second, the level-
dependent gain, especially the attenuation below the threshold,
suppresses small perturbations (e.g., noise, reflection) that could grow
into undesired pulses and disrupt a stable pulse oscillation.
In the steady state, a pulse circulates in the
loop. The transmission line is to introduce a delay between one pulse
event and the next at any point in the loop.
4.3) Haus’s Oscillator:
In 1978, Haus et al. altered Cutler’s oscillator.
Instead of circulating a pulse, a pulse is made travel back and forth on a
transmission line through reflection at both ends of the line. Like in
Cutler’s oscillator, level-dependent gain is needed for pulse formation
and oscillation stabilization. It is realized as a combination of a constant
gain (which occurs in reflection at one line end terminated with an
approximately constant negative resistance) and a level-dependent
attenuation(which occurs in reflection at the other line end terminated
with a level-dependent positive resistance).
35. Page | 35
In Cutler and Haus’s oscillators, the
transmission line serves as a simple pulse propagation medium. An
interesting design alteration to obtain much sharper pulses would be to
incorporate a pulse-sharpening mechanism into the line, in addition to
the pulse sharpening provided by the level-dependent gain. we attained
a circuit that robustly self-generated astable, periodic train of much
sharper pulses ,By replacing, in Cutler’s circular topology, a linear
transmission line with a nonlinear transmission line (NLTL) [a
transmission line periodically loaded with varactors (nonlinear
capacitors)], which had been long known for its superb pulse sharpening
capability. The sharp pulses on the NLTL, which possess uniquenonlinear
properties, are known as solitons. Thus, we called the oscillator electrical
soliton oscillator.
Solitons circulating in the oscillatory
loop exhibit rich nonlinear dynamics, and unless suitably controlled, they
tend to form a soliton pulse train with significant variations in the pulse
amplitude and repetition rate. The key to our success in overcoming this
oscillation instability and building the soliton oscillator of that robustly
self-generated a train of solitons with constant soliton amplitude and
repetition rate was to realize that the level-dependent gain used for
pulse sharpening and oscillation stabilization in Cutler’s oscillator is also
effective in stabilizing the soliton oscillation.
However, since the soliton oscillator
has a much stronger tendency towards instability due to soliton’s
36. Page | 36
nonlinear dynamics, its stabilization demanded more from the
amplifier’s level-
dependent gain. In the soliton oscillator, the dominant pulse sharpening
mechanism is provided not by the level-dependent gain, but by the
NLTL.
37. Page | 37
This work starts by replacing the
linear transmission line in Haus’s oscillator with an NLTL to establish a
dominant
pulse sharpening mechanism in the pulse propagation medium. The
level-dependent gain needed for soliton oscillation stability is
incorporated in a single one-port amplifier connected to one end of the
NLTL: it produces a negative resistance for a voltage beyond a certain
threshold and a positive resistance for a voltage below that threshold,
and thus, the reflection from the amplifier end provides gain for the
main upper portion of a pulse to compensate loss, while attenuating
small perturbations. The other end of the NLTL is open for reflection. In
Haus’s oscillator where pulse sharpening is achieved solely through the
level dependent gain, the pulse sharpening is limited by the bandwidth
of the active circuit providing the level-dependent gain.In contrast, our
reflection soliton oscillator, where the pulse sharpening executed
38. Page | 38
dominantly by the NLTL is not limited by the amplifier bandwidth,
achieves substantially more pulse sharpening.
39. Page | 39
5
REFLECTION SOLITON
OSCILLATOR—OPERATING
PRINCIPLE
Our reflection soliton oscillator
consists of an NLTL terminated with a one-portamplifier at one end and
an electrical open at the other end In the steady state, a pulse travels
back and forth on the NLTL. The pulse reflected at the amplifier end
travels down the NLTL towards the open, during which the NLTL
compresses thepulse, forming it into a sharp soliton. As the soliton
reaches the open, it is reflected to travel back towards the amplifier,
during which the soliton lowers amplitude and broadens width in a
particular manner due to
loss in the NLTL.
Once the damped soliton reaches the
amplifier, a reflection with level-dependent gain occurs, which
compensates loss and reinforces oscillation stability. The reflected pulse
40. Page | 40
is not a soliton, as the amplifier deforms the soliton shape. The reflected
reenergized pulse repeats the spatial dynamics described above, again
forming into a soliton as it propagates down the NLTL toward the open.
5.1) Reflection at the AmplifierEnd
The reflection with level-dependent gain at
the amplifier end is achieved as follows. The output impedance of the
amplifier seen by the NLTL, is a function of voltage at that output node.
If wedenote the averagecharacteristic impedance of the NLTL as , the
reflection coefficient at the amplifier end with a voltage of is given by
41. Page | 41
Since , we see that
Therefore, for the amplifier to providea gain for a voltage larger
than a certain threshold and to attenuate a signal smaller than the
threshold, we are to have for abovethe threshold, and
.
Let us examine what would happen if the
level-dependent gain is not in force, or more specifically ,if
regardless of and all signal levels receive gain upon reflection from
the amplifier end. Supposea desired soliton pulse and a small parasitic
soliton pulse produced by a perturbation (e.g.,noise) in the oscillator.
Both of these pulses will be reflected with gain at the amplifier end, and
the parasitic pulse will persist, as the amplifier in this scenario does not
attenuate low-level signals.
Since the two reflected pulses have
different Amplitudes, they propagate at different velocities (a taller
pulse propagates faster than a shorter pulse—this is a key soliton
property thus eventually colliding with each other. This collision, which is
a nonlinear process, causes pulseamplitude modulation at the moment
42. Page | 42
of collision ,and pulse position modulation after the collision, right—the
taller pulse would appear as the dashed one in the different position,
were it not for the collision), which is another key soliton property.
Therefore, the pulse train produced
with gain at all signal levels exhibits significant variations in pulse
amplitude and repetition rate. In contrast, when level-dependent gain is
in force, small perturbation falls in the attenuation region to be
suppressed ,no soliton collision occurs, and the instability is prevented.
5.2) Reflection at the Open End
The pulsereflection at the open end of
the NLTL, is interesting and useful, as it offers an extra pulse sharpening
mechanism, in addition to the sharpening that occurs during pulse
propagation on the NLTL. At the open end, the incoming pulse is
reflected into a same shapepulse. The incoming and reflected pulses
(voltages) superposeto increase the joint voltage at the open end. If a
linear line is used, the joint voltage at the open end is twice the incoming
voltage.
43. Page | 43
In caseof the NLTL, the joint voltage
is larger than twice the incoming voltage. This is due to the voltage
dependence of the capacitance of the varactor at the open end. The
superposed (thus increased) voltagereduces the capacitance, and to
conservethe total energy despite the reduced capacitance, the
superposed voltageshould be larger than twice the incoming voltage.
This pulse amplification at the open
end by a factor larger than two translates to pulse sharpening. In an
NLTL constructed in the formof a ladder network of inductor–varactor
sections, the time integration of an arbitrary pulsevoltage at the
Nth node is constant, independent of the position.
In other words, if one measures the area
under the time-domain voltage waveform thearea will remain the
same, independently of n.
45. Page | 45
6
REFLECTION SOLITON
OSCILLATOR—AMPLIFIER
DESIGN
6.1) Need for an Adaptive Bias Scheme
The reflection amplifier should
be capable of level-dependent amplification such that small
perturbations are rejected to ensureoscillation stability, while the
main portion of the soliton is amplified to compensateloss. An
important notion is that this level-dependent gain is whatis
required in the steady state. In contrast, in the initial startup
transient, the level-dependent gain should be actually avoided, as
small perturbations should be amplified to enable oscillation
startup.
To achieve these two
contradicting gain characteristics in the same amplifier, an
adaptive bias schemecan be employed to shiftthe gain
46. Page | 46
characteristic of the amplifier fromfull gain to level-dependent
gain as the oscillation grows froman initial transient into a steady-
state pulse train. Such an adaptive bias schemehas been actually
implemented in various forms in all of the previous pulse
oscillator.
6.2) One-Port Reflection Amplifier With an Adaptive Bias
The basic circuit
arrangementis two inverters put back to back: transistors and
formone inverter; transistors and formthe other
inverter. The underlying design idea is that the real part of the
output impedance of the amplifier, seen by the NLTL, can
assumepositive or negative values, depending on the ON/OFF
status of i.e., depending on the voltage difference between
and .If is ON with the back-to-back inverters
are in force and a positivefeedback is set up, yielding
.If is OFF with the back-to-back inverters do not
Work, leading to
48. Page | 48
In the beginning of the startup transient, assume
certain initial bias values. The amplifier is arranged in such a way
that in this initial stage and is ON, thus ensuring
and enabling an oscillation startup.
As can be seen, the initial bias
sits in the gain region where and thus a small
perturbation around the bias receives gain to grow into a pulse
49. Page | 49
train.As the oscillation grows, a train of pulses starts appearing at
the output node of the amplifier.When a pulsearrives at the
amplifier fromthe NLTL, goes up.
Following , the emitter voltage of is increased,
charging capacitor .Dueto the time constantassociated
with this charging of is much smaller than the time
constantof the network.
Now as the pulseleaves the amplifier and is decreased, is
turned off because is still high, and the charge stored on
starts being discharged through the network with a time
constantof the discharging of the absenceof a pulse is
50. Page | 50
slower than its charging in the presence of a pulse. We set the
value of larger than the pulse repetition period so that by
the time the next pulse arrives, thedischarging has not been
sufficient to empty whatwas charged during the previous pulse
event and thus, has been increased overall.As this process is
repeated with continued arrivals and departures of pulses, the
overall charges in are increased at every pulse event, and the
dc average(bias) of goes up. In this way, once the steady
state is reached (wewill explain shortly how the dc averageof
eventually settles to a constantvalue), the bias of
assumes a value larger than that during the initial startup.
Due to this increased in the
steady state, turning on to generate a negative and to
producegain requires a higher level of voltage at .This
corresponds to the fact that in the steady state, the
versus curveis shifted to the right, as hypothetically. negative
or gain, is attainable at higher voltages. The steady-state
bias (dc average) of has been shifted to the right as well due
to the increased pulse height, but this shift is not as large as the
shift in the impedance curve, and thus, the steady state bias lies in
the attenuation region.
Overall, the steady-statepulses
lie across the attenuation and gain regions, and only the higher
portion of the pulses will be amplified, while their lower portion
and any small undesired perturbations will be suppressed: the
51. Page | 51
level-dependent gain has thus been set up in the steady state.
Shortly before, we asserted that the increase in the dc averageof
during the initial startup transienteventually settles down to
a constant value, which wewill explain now.
During the very initial transient,
the charging is faster than the discharging dueto the
strong action of hat is ON during the pulseevent, thus causing
the increasein As the steady state is approached, turns
on during the higher portion of a pulse,butturns off during the
lower portion of the pulse, and thus, the effect of which is not
always ONeven during the pulse event, has become weaker, and
thus, the charging is not as fast. Dueto this slowing down in
the charging rate, at a certain point, the charging during the
pulse event and the discharging during the absenceof the pulse
balance each other out, thus causing the dc average of to
settle at a constant value.
Fromthe foregoing description, it is
clear that should be larger than the pulse repetition period
to ensurea slow discharging between two adjacent pulse
events so that can grow during the initial startup. In our case,
52. Page | 52
6.3) Improved – Network
In the initial transient, it is
common to see two competing large pulses that appear
successively wellwithin the intended pulse repetition period. The
amplifier should be able to select only one of them, while
eliminating the other, so that the oscillator can eventually
producea periodic train of soliton pulses with a constant
amplitude and a constantpulse repetition rate. Consider two such
pulses. If the increase in during the firstpulse is not fast
enough, is still low for the second pulse, and thus, the second
pulse receives a large enough gain to be undesirably sustained. To
prevent this, should rise fastenough during the firstpulse so
that by the time the second pulse arrives, is high enough to
introduce enough loss for the second pulse to eliminate it.
To this end, we introduced an
network in series with the original .
.. This extra network allows for to track fast for the
firstpulse so that the second pulsecan be suppressed.
57. Page | 57
We employ a one port amplifier,
during the initial stages the dc operating point is in the
saturation region. It shifts to the cut off region in due course of
time. The reason being the implementation of the level
dependant gain. In the initial stages we implement the normal
gain circuit which produces oscillations and as the reflection
occurs level dependant gain operates, thereby amplifying the
output above a threshold value and attenuating the output
below the threshold value. This level dependant gain has a vital
advantage of removing the small perturbation and other
distortions which have amplitudes below the threshold level
and producing the necessary output without noise.
60. Page | 60
The length of the NLTL which determines the stable Gaussian
output being produced is varied thereby determining the exact
no of the elements forming the NLTL. In the above circuit since
the length of the NLTL is very large the Gaussian output that is
obtained is not stable
68. Page | 68
8
COMPARISON WITH
CIRCULAR SOLITON
OSCILLATOR
The design spirit of our reflection soliton
oscillator, and its utilization of the level-dependent gain for soliton
oscillation stabilization ,originate fromour earlier work on the circular
soliton oscillator. We compare the two oscillators’ performanceand
design merits.
8.1) Energy Efficiency:
In the circular soliton oscillator, the
energy of a circulating pulse is dissipated in a termination network at
the input of the two-portamplifier to preventa reflection. It is the
voltage of the circulating pulse that is sensed and amplified by the
amplifier to recreate a pulsed energy at the output of the amplifier. This
69. Page | 69
energy dissipation and recreation at each cycle of pulsecirculation
corresponds to an energetically inefficient operation. In contrast, in the
reflection soliton oscillator, the one-port amplifier pushesback the
oncoming pulse energy, while adding some energy to compensate for
loss, and thus, energy is recycled with no intentional energy dissipation.
Overall, the reflection soliton oscillator utilizes energy more efficiently.
8.2) Pulsewidth:
The reflection at the open end of
the NLTL in the reflection soliton oscillator sharpens thepulse at that
end. This is an extra sharpening mechanism,in addition to the pulse
sharpening that occurs during the propagation on the NLTL. Such a
reflection-mediated pulse sharpening does not exist in the circular
soliton oscillator, and thus, the reflection soliton Oscillator can
potentially achieve a narrower pulsewidth.
8.3) Circuit Size:
To achieve a pulse repetition rate
of for a pulse propagation speed of , the reflection soliton oscillator
requires an NLTL length of approximately while the circular
70. Page | 70
soliton oscillator requires a twice longer NLTL length (these are
Approximations becausedelays caused by amplifiers will somewhat
affect the pulserepetition rate). Given that the NLTL is by far the largest
part of both circuits, the reflection soliton oscillator will havean almost
twice smaller physicalsize than the circular soliton oscillator.
71. Page | 71
References:
[1] M. Kahrs, “50 years of RF and microwavesampling,” IEEE Trans.
Microw. Theory Tech., vol. 51, no. 6, pp. 1787–1805, Jun. 2003.
[2] R. Y. Yu, M. Reddy, J. Pusl, S. T. Allen, M. Case, and M. J. W.
Rodwell, “Millimeter-wave on-wafer waveformand network
measurements
using active probes,” IEEETrans. Microw. Theory Tech.,
vol. 43, no. 4, pp. 721–729, Apr. 1995.
[3] G. F. Ross, “Transmission and reception systemfor generating and
receiving
base-band pulseduration pulse signals withoutdistortion for
shortbase-band communication system,” U.S. Patent 3 728 632, Apr.
17, 1973.
[4] C. C. Cutler, “The regenerative pulse generator,” Proc. IRE, vol. 43, no.
2, pp. 140–148, Feb. 1955.
[5] L. A. Glasser and H. A. Haus, “Microwavemode locking at �-band
using solid-state devices,” IEEE Trans. Microw. Theory Tech., vol.
MTT-26, no. 2, pp. 62–69, Feb. 1978.
[6] D. Ricketts, X. Li, and D. Ham, “Electrical soliton oscillator,” IEEE
Trans. Microw. Theory. Tech., vol. 54, no. 1, pp. 373–382, Jan. 2006.
[7] D. Ricketts, X. Li, N. Sun, K. Woo, and D. Ham, “On the self-generation
of electrical soliton pulses,” IEEE J. Solid-State Circuits, vol. 42,
no. 8, pp. 1657–1668,Aug. 2007.
72. Page | 72
[8] R. Landauer, “Shock waves in nonlinear transmission lines and their
effect on parametric amplification,” IBM J. Res. Develop., vol. 4, no. 4,
pp. 391–401, Oct. 1960.
[9] R. Hirota and K. Suzuki, “Theoretical and experimental studies of
lattice
solitons in nonlinear lumped networks,” Proc. IEEE, vol. 61, no.
10, pp. 1483–1491, Oct. 1973.
[10] M. Rodwell et al., “Active and nonlinear wave propagation devices
in
ultrafastelectronics and optoelectronics,” Proc. IEEE, vol. 82, no. 7,
pp. 1037–1059,Jul. 1994.
[11] M. Case, M. Kamegawa, R. Y. Yu, M. J. W. Rodwell, and J. Franklin,
“Impulsecompression using soliton effects in a monolithic GaAs circuit,”
Appl. Phys. Lett., vol. 68, no. 2, pp. 173–175, Jan. 14, 1991.
[12] M. Tan, C. Y. Su, and W. J. Anklam, “7�electrical pulsecompression
on an inhomogeneous nonlinear transmission line,” Electron. Lett., vol.
24, no. 4, pp. 213–215, Feb. 1988.
[13] M. Remoissenet,WavesCalled Solitons: Conceptsand Experiments.
New York: Springer, 1999.
