Just a few odds and ends. Consider the
following which is called a "cascaded line"
problem. These are problems where we have two differenttransmission lines, with different characteristic
impedances. Since we will give all of the distances inwavelengths,λ, we will assume that theλwe are
talking about is the appropriate one for the line involved. Ifthe phase velocities on the two lines is the same, then the
physical lengths would correspond as well. The approach isrelatively straight-forward. First let's plot
on the
Smith Chart . Then we
have to rotate
so that we can find
, the normalized impedance at point A, the junction
between the two lines
.
Cascaded line
Smith diagram
Thus, we find
. Now we have to
renormalize the impedance
so we can move to the line with the new impedance
. Since
,
. This is the load for the second length of line, so let's find
, which is easily found to be
, so this can be plotted on the
Smith Chart . Now we have to rotate around
another
so that we can find
. This appear to have a value of about
, so
.
Towards the generator
More smith charts
Even more smith charts
There is one application of the cascaded line problem that is
used quite a bit in practice. Consider the following: We assumethat we have a matched line with impedance
and we connect it to another line whose impedance is
. If we connect the two of them
together directly, we will have a reflection coefficient at thejunction given by
Simplified cascaded line
Now let's imagine that we have inserted a section of line with length
and impedance
. At point A, the junction
between the first line and the matchng section, we can find thenormalized impedance as
Another cascaded line
We take this impedence and rotate around on the Smith Chart
to find
where we have taken advantage of the fact that when we
go half way around the Smith Chart, the impedance we get is justthe inverse of what we had originally (half way around turns
into
).
Thus
If we want to have a match for line with impedence
, then
should equal
and hence:
or
This piece of line is called a
quarter wave matching
section and is a convenient way to connect two lines of
different impedance.
Questions & Answers
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
