There
is a way that we can
make things a good bit easier for ourselves however. The onlydrawback is that we have to do some complex analysis first, and
look at a
bilinear transform ! Let's do one more
substitution, and define another complex vector, which we cancall
:
The vector
is just the rotating part of the crank diagram which
we have been looking at
. It has a
magnitude equal to that of the reflection coefficient, and itrotates around at a rate
as we move down the line. For every
there is a corresponding
which is given by:
The vector r(s)
Now, it turns out to be easier if we talk about a
normalized
impedance , which we get by dividing
by
.
which we can solve for
This relationship is called a
bilinear
transform . For every
that we can imagine, there is one and only one
and for every
there is one and only one
. What we would like to be able to do, is find
, given an
. The reason for this should be readily
apparent. Whereas, as we move along in
,
behaves in a most difficult manner (dividing one
phasor by another),
simply rotates around on the complex plane. Given one
it is
easy to find another
. We just rotate around!
We shall find the required relationship in a
graphical manner. Suppose I have a complex plane, representing
. And then suppose I have some point "A" on that plane
and I want to know what impedance it represents. I just readalong the two axes, and find that, for the example in
, "A" represents an impedance of
. What I would like to do would be to get a grid
similar to that on the
plane, but on the
plane instead. That way, if I knew one impedence (say
then I could find any other impedance, at any other
, by simply rotating
around by
, and then reading off the new
from the grid I had developed. This is what we shall
attempt to do.
The complex impedance plane
Let's start with
and re-write it as:
In order to use
, we are going to have to
interpret it in a way which might seem a little odd to you. Theway we will read the equation is to say: "Take
and add 1 to it. Invert what you get, and multiply by
-2. Then add 1 to the result." Simple isn't it? The only hardpart we have in doing this is inverting
. This, it turns out, is pretty easy once we learn one
very important fact.
The
one fact about algebra
on the complex plane that we need is as follows. Consider avertical line,
, on the complex
plane, located a distance
away
from the imaginary axis
. There are a lot
of ways we could express the line
, but we will choose one which
will turn out to be convenient for us. Let's let:
A vertical line, s, a distance, d, away from the
imaginary axis
Now we ask ourselves the question: what is the inverse of s?
We can substitute for
:
And then, since
A plot of 1/s
A careful look at
should allow you to
convince yourself that
is an equation for
a circle on the complex plane, with a diameter
. If
is not parallel to
the imaginary axis, but rather has its perpendicular to theorigin at some angle
, to make a line
. Since
, taking
simply will give us a circle with a diameter of
, which has been rotated by an angle
from the real axis
. And so we come to the
one fact we have to keep in mind:
"The inverse of a
straight line on the complex plane is a circle, whose diameteris the inverse of the distance between the line and the
origin."
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
Got questions? Join the online conversation and get instant answers!
