Koretsky 0. Randall D. Knight 0. George Odian 0. John Kenkel 0. Trott 0. Carl S. Warren 2. Warren 0. Abraham Silberschatz 1. Frederick S. Hillier 1. William Stallings 1. Morris Mano 1. David Irwin 0. Morris Mano 0.
Michael F. With a short circuit replacing the load, a minimum is found at a point on the line marked by a small spot of puce paint. The 1m distance is therefore 3.
Therefore, with the actual load installed, the Vmin position as stated would be 3. This being the case, the normalized load impedance will lie on the positive real axis of the Smith chart, and will be equal to the standing wave ratio.
This point is to be transformed to a location at which the real part of the normalized admittance is unity. The stub is connected at either of these two points. The stub input admittance must cancel the imaginary part of the line admittance at that point.
This point is marked on the outer circle and occurs at 0. The length of the stub is found by computing the distance between its input, found above, and the short-circuit position stub load end , marked as Psc.
The length of the main line between its load and the stub attachment point is found on the chart by measuring the distance between yL and yin2 , in moving clockwise toward generator. This occurs at 0. The attachment point is found by transforming yL to yin1 , where the former point is located at 0.
The lossless line shown in Fig. For the line to be matched, it is required that the sum of the normalized input admittances of the shorted stub and the main line at the point where the stub is connected be unity.
So the input susceptances of the two lines must cancel. This line is one-quarter wavelength long, so the normalized load impedance is equal to the normalized input admittance. To cancel the input normalized susceptance of We therefore write 2. The two-wire lines shown in Fig. In this case, we have a series combination of the loaded line section and the shorted stub, so we use impedances and the Smith chart as an impedance diagram.
The requirement for matching is that the total normalized impedance at the junction consisting of the sum of the input impedances to the stub and main loaded section is unity.
In the transmission line of Fig. First, the load voltage is found by adding voltages along the right side of the voltage diagram at the indicated times. The load voltage as a function of time is found by accumulating voltage values as they are read moving up along the right hand boundary of the chart. In the charged line of Fig. This problem accompanies Example Plots of the voltage and current at the resistor are then found by accumulating values from the left sides of the two charts, producing the plots as shown.
A simple frozen wave generator is shown in Fig. Determine and plot the load voltage as a function of time: Closing the switches sets up a total of four voltage waves as shown in the diagram below. Note that in Problem Given, a MHz uniform plane wave in a medium known to be a good dielectric.
We use the good dielectric approximations, Eqs. Perfectly-conducting cylinders with radii of 8 mm and 20 mm are coaxial. The external and internal regions are non-conducting. The inner and outer dimensions of a copper coaxial transmission line are 2 and 7 mm, respec- tively. The dielectric is lossless and the operating frequency is MHz. A hollow tubular conductor is constructed from a type of brass having a conductivity of 1. The inner and outer radii are 9 mm and 10 mm respectively.
Calculate the resistance per meter length at a frequency of a dc: In this case the current density is uniform over the entire tube cross-section. Most microwave ovens operate at 2.
A good conductor is planar in form and carries a uniform plane wave that has a wavelength of 0. The outer conductor thickness is 0. Use information from Secs. The result is squared, terms collected, and the square root taken. Consider a left-circularly polarized wave in free space that propagates in the forward z direc- tion.
Since the wave propagates in the positive y direction and has equal x and z amplitudes, we identify the polarization as left circular. With the dielectric constant greater for x-polarized waves, the x component will lag the y component in time at the out- put. Suppose that the length of the medium of Problem Given the general elliptically-polarized wave as per Eq. What percentage of the incident power density is transmitted into the copper?
Next we apply Eq. A uniform plane wave in region 1 is normally-incident on the planar boundary separating regions 1 and 2. There are two possible answers. Its intrinsic impedance is therefore approximated well by Eq. Solve for z to obtain ln 8.
This is found using Eq. This is given by Eq. Pi Try measuring that. A MHz uniform plane wave in normally-incident from air onto a material whose intrinsic impedance is unknown. A 50MHz uniform plane wave is normally incident from air onto the surface of a calm ocean. The transmitted power fraction thus increases. A left-circularly-polarized plane wave is normally-incident onto the surface of a perfect con- ductor.
Determine the standing wave ratio in front of the plate. Repeat Problem We can now evaluate the phase shift for the three given cases.
The slabs are to be positioned parallel to one another, and the combination lies in the path of a uniform plane wave, normally-incident.
The slabs are to be arranged such that the air spaces between them are either zero, one-quarter wavelength, or one-half wavelength in thickness. Specify an arrangement of slabs and air spaces such that a the wave is totally transmitted through the stack: In this case, we look for a combination of half-wave sections.
Let the inter-slab distances be d1 , d2 , and d3 from left to right. Two possibilities are i. Thus every thickness is one-quarter wavelength. The 50MHz plane wave of Problem Next we need the angle of refraction, which means that we need to know the refractive index of seawater at 50MHz. Therefore, for s polarization,.
The fraction transmitted is then 0. The transmitted wave, while having all the incident p-polarized power, will have a reduced s-component, and so this wave will be right-elliptically polarized. A dielectric waveguide is shown in Fig. The prism of Fig. In the Brewster prism of Fig.
The light is incident from air, and the returning beam also in air may be displaced sideways from the incident beam. More than one design is possible here. Using the result of Example For this to work, the Brewster angle must be greater than or equal to the critical angle. Over a small wavelength range, the refractive index of a certain material varies approximately.
All frequency components arrive simultaneously. Describe the pulse at the output of the second channel and give a physical explanation for what happened. The pulse, if originally transform-limited at input, will emerge, again transform-limited, at its original width. Two aluminum-clad steel conductors are used to construct a two-wire transmission line.
The radius of the steel wire is 0. The dielectric is air, and the center-to-center wire separation is 4 in. Furthermore, the skin depth is considerably less than the aluminum layer thickness, so the bulk of the current resides in the aluminum, and we may neglect the steel. Each conductor of a two-wire transmission line has a radius of 0.
Pertinent dimensions for the transmission line shown in Fig. The conductors and the dielectric are non-magnetic. A transmission line constructed from perfect conductors and an air dielectric is to have a maximum dimension of 8mm for its cross-section.
The line is to be used at high frequencies. Line 1 is of 4mm width; line 2 unfortunately has been fabricated with a 5mm width. Determine the power loss in dB for waves transmitted through the junction. How many modes propagate?
If the operating frequency is 32 GHz, which modes will propagate? For the guide of Problem Assume a propagation distance of 10 cm: From Problem The So the answer is yes.
In the guide of Figure To summarize, as frequency is lowered, the ray angle in guide 1 decreases, which leads to the incident angle at the interface increasing to eventually reach and surpass the critical angle.
Two rectangular waveguides are joined end-to-end. Integrate the result of Problem This was considered in the discussion leading to Eq. Using the result of Problem The reasoning of part a applies to all modes, so the answer is the same, or 2.
An asymmetric slab waveguide is shown in Fig. The minimum wave angle is thus determined by the greater of the two critical angles. Therefore, the percentage reduction required in the core radius will be 1. The answer to this can be found by inspecting Eq. Prepare a curve, r vs. Both are circles. Since we are in the far zone, applies. The radiated power and radiation resistance are down to a factor of 0. A dipole antenna in free space has a linear current distribution.
If the length is 0. A monopole antenna in free space, extending vertically over a perfectly conducting plane, has a linear current distribution. If the length of the antenna is 0. This reduces the radiation resistance of the equivalent dipole antenna by a factor of one-half. Therefore, with the actual load installed, the Vmin position as stated would be 3. This being the case, the normalized load impedance will lie on the positive real axis of the Smith chart, and will be equal to the standing wave ratio.
This point is to be transformed to a location at which the real part of the normalized admittance is unity. The stub is connected at either of these two points. The stub input admittance must cancel the imaginary part of the line admittance at that point. This point is marked on the outer circle and occurs at 0. The length of the stub is found by computing the distance between its input, found above, and the short-circuit position stub load end , marked as Psc.
The length of the main line between its load and the stub attachment point is found on the chart by measuring the distance between yL and yin2 , in moving clockwise toward generator. This occurs at 0. The attachment point is found by transforming yL to yin1 , where the former point is located at 0. The lossless line shown in Fig. For the line to be matched, it is required that the sum of the normalized input admittances of the shorted stub and the main line at the point where the stub is connected be unity.
So the input susceptances of the two lines must cancel. This line is one-quarter wavelength long, so the normalized load impedance is equal to the normalized input admittance.
To cancel the input normalized susceptance of We therefore write 2. The two-wire lines shown in Fig. In this case, we have a series combination of the loaded line section and the shorted stub, so we use impedances and the Smith chart as an impedance diagram. The requirement for matching is that the total normalized impedance at the junction consisting of the sum of the input impedances to the stub and main loaded section is unity. In the transmission line of Fig.
First, the load voltage is found by adding voltages along the right side of the voltage diagram at the indicated times. The load voltage as a function of time is found by accumulating voltage values as they are read moving up along the right hand boundary of the chart. In the charged line of Fig. This problem accompanies Example Plots of the voltage and current at the resistor are then found by accumulating values from the left sides of the two charts, producing the plots as shown.
A simple frozen wave generator is shown in Fig. Determine and plot the load voltage as a function of time: Closing the switches sets up a total of four voltage waves as shown in the diagram below. Note that in Problem Given, a MHz uniform plane wave in a medium known to be a good dielectric.
Also, the specified distance in part f should be 10m, not 1km. We use the good dielectric approximations, Eqs. Perfectly-conducting cylinders with radii of 8 mm and 20 mm are coaxial. The external and internal regions are non-conducting. The inner and outer dimensions of a copper coaxial transmission line are 2 and 7 mm, respec- tively. The dielectric is lossless and the operating frequency is MHz.
A hollow tubular conductor is constructed from a type of brass having a conductivity of 1. The inner and outer radii are 9 mm and 10 mm respectively. Calculate the resistance per meter length at a frequency of a dc: In this case the current density is uniform over the entire tube cross-section.
Most microwave ovens operate at 2. A good conductor is planar in form and carries a uniform plane wave that has a wavelength of 0. The outer conductor thickness is 0. Use information from Secs. The result is squared, terms collected, and the square root taken. Consider a left-circularly polarized wave in free space that propagates in the forward z direc- tion.
Since the wave propagates in the positive y direction and has equal x and z amplitudes, we identify the polarization as left circular. With the dielectric constant greater for x-polarized waves, the x component will lag the y component in time at the out- put. Suppose that the length of the medium of Problem Given the general elliptically-polarized wave as per Eq.
What percentage of the incident power density is transmitted into the copper? Next we apply Eq. A uniform plane wave in region 1 is normally-incident on the planar boundary separating regions 1 and 2. There are two possible answers. Its intrinsic impedance is therefore approximated well by Eq. Solve for z to obtain ln 8. This is found using Eq. This is given by Eq. Pi Try measuring that. A MHz uniform plane wave in normally-incident from air onto a material whose intrinsic impedance is unknown.
A 50MHz uniform plane wave is normally incident from air onto the surface of a calm ocean. The transmitted power fraction thus increases. A left-circularly-polarized plane wave is normally-incident onto the surface of a perfect con- ductor.
Determine the standing wave ratio in front of the plate. Repeat Problem We can now evaluate the phase shift for the three given cases. The slabs are to be positioned parallel to one another, and the combination lies in the path of a uniform plane wave, normally-incident.
The slabs are to be arranged such that the air spaces between them are either zero, one-quarter wavelength, or one-half wavelength in thickness. Specify an arrangement of slabs and air spaces such that a the wave is totally transmitted through the stack: In this case, we look for a combination of half-wave sections. Let the inter-slab distances be d1 , d2 , and d3 from left to right.
Two possibilities are i. Thus every thickness is one-quarter wavelength. The 50MHz plane wave of Problem Next we need the angle of refraction, which means that we need to know the refractive index of seawater at 50MHz. Therefore, for s polarization,. The fraction transmitted is then 0. The transmitted wave, while having all the incident p-polarized power, will have a reduced s-component, and so this wave will be right-elliptically polarized.
A dielectric waveguide is shown in Fig. The prism of Fig. In the Brewster prism of Fig. The light is incident from air, and the returning beam also in air may be displaced sideways from the incident beam. More than one design is possible here. Using the result of Example For this to work, the Brewster angle must be greater than or equal to the critical angle. Over a small wavelength range, the refractive index of a certain material varies approximately. All frequency components arrive simultaneously.
Describe the pulse at the output of the second channel and give a physical explanation for what happened. The pulse, if originally transform-limited at input, will emerge, again transform-limited, at its original width. Two aluminum-clad steel conductors are used to construct a two-wire transmission line. The radius of the steel wire is 0. The dielectric is air, and the center-to-center wire separation is 4 in. Furthermore, the skin depth is considerably less than the aluminum layer thickness, so the bulk of the current resides in the aluminum, and we may neglect the steel.
Each conductor of a two-wire transmission line has a radius of 0. Pertinent dimensions for the transmission line shown in Fig. The conductors and the dielectric are non-magnetic. A transmission line constructed from perfect conductors and an air dielectric is to have a maximum dimension of 8mm for its cross-section. The line is to be used at high frequencies. Line 1 is of 4mm width; line 2 unfortunately has been fabricated with a 5mm width. Determine the power loss in dB for waves transmitted through the junction.
How many modes propagate? If the operating frequency is 32 GHz, which modes will propagate? For the guide of Problem Assume a propagation distance of 10 cm: From Problem The So the answer is yes. In the guide of Figure To summarize, as frequency is lowered, the ray angle in guide 1 decreases, which leads to the incident angle at the interface increasing to eventually reach and surpass the critical angle.
Two rectangular waveguides are joined end-to-end. Integrate the result of Problem This was considered in the discussion leading to Eq. Using the result of Problem The reasoning of part a applies to all modes, so the answer is the same, or 2. An asymmetric slab waveguide is shown in Fig. The minimum wave angle is thus determined by the greater of the two critical angles.
Therefore, the percentage reduction required in the core radius will be 1. The answer to this can be found by inspecting Eq. Using these values, along with our new equation, we write 0. Prepare a curve, r vs. Both are circles. Since we are in the far zone, applies. The radiated power and radiation resistance are down to a factor of 0.
A dipole antenna in free space has a linear current distribution. If the length is 0. A monopole antenna in free space, extending vertically over a perfectly conducting plane, has a linear current distribution.
If the length of the antenna is 0. This reduces the radiation resistance of the equivalent dipole antenna by a factor of one-half. Additionally, the linear current distribution reduces the radi- ation resistance of a dipole having uniform current by a factor of one-fourth. The construction and arguments are similar to those used in the discussion of the electric dipole in Sec. It comprises concise chapters which introduce the history, key lines of inquiry relating to both health and performance, technology, certifications, professional associations, and career opportunities associated with each area.
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