Coaxial cable is a accurate affectionate of manual line, so the ambit models developed for accepted manual curve are appropriate. See Telegrapher's equation.
Schematic representation of the elementary apparatus of a manual line.
Schematic representation of a coaxial manual line, assuming the appropriate impedance Z0.
edit Physical parameters
In the afterward section, these symbols are used:
Breadth of the cable, h.
Outside bore of close conductor, d.
Central bore of the shield, D.
Dielectric connected of the insulator, \epsilon. The dielectric connected is generally quoted as the about dielectric connected \epsilon_r referred to the dielectric connected of chargeless amplitude \epsilon_0: \epsilon = \epsilon_r \epsilon_0. If the insulator is a admixture of altered dielectric abstracts (e.g., polyethylene cream is a admixture of polyethylene and air), again the appellation able dielectric connected \epsilon_{eff} is generally used.
Magnetic permeability of the insulator, μ. Permeability is generally quoted as the about permeability μr referred to the permeability of chargeless amplitude μ0: μ = μrμ0. The about permeability will about consistently be 1.
edit Fundamental electrical parameters
Blow capacitance per assemblage length, in farads per metre.6
\left(\frac{C}{h}\right) = {2 \pi \epsilon \over \ln(D/d)}= {2 \pi \epsilon_0 \epsilon_r \over \ln(D/d)}
Series inductance per assemblage length, in henrys per metre.
\left(\frac{L}{h}\right) = {\mu \over 2 \pi} \ln(D/d)= {\mu_0 \mu_r \over 2 \pi} \ln(D/d)
Series attrition per assemblage length, in ohms per metre. The attrition per assemblage breadth is just the attrition of close aqueduct and the absorber at low frequencies. At college frequencies, derma aftereffect increases the able attrition by circumscribed the advice to a attenuate bandage of anniversary conductor.
Blow conductance per assemblage length, in siemens per metre. The blow conductance is usually actual baby because insulators with adequate dielectric backdrop are acclimated (a actual low accident tangent). At top frequencies, a dielectric can accept a cogent arresting loss.
edit Derived electrical parameters
Appropriate impedance in ohms (Ω). Neglecting attrition per assemblage breadth for a lot of coaxial cables, the appropriate impedance is bent from the capacitance per assemblage breadth (C) and the inductance per assemblage breadth (L). The simplified announcement is (Z_0 = \sqrt{L/C}). Those ambit are bent from the arrangement of the close (d) and alien (D) diameters and the dielectric connected (\epsilon). The appropriate impedance is accustomed by7
Z_0=\frac{1}{2\pi}\sqrt{\frac{\mu}{\epsilon}}\ln\frac{D}{d}\approx\frac {138 \Omega}{\sqrt{\epsilon_r}}\log_{10}\frac {D} {d}
Assuming the dielectric backdrop of the actual central the cable do not alter appreciably over the operating ambit of the cable, this impedance is abundance absolute aloft about 5 times the absorber blow frequency. For archetypal coaxial cables, the absorber blow abundance is 600 (RG-6A) to 2,000 Hz (RG-58C).8
Abrasion (loss) per assemblage length, in decibels per meter. This is abased on the accident in the dielectric actual bushing the cable, and arresting losses in the centermost aqueduct and alien shield. These losses are abundance dependent, the losses adequate college as the abundance increases. Derma aftereffect losses in the conductors can be bargain by accretion the bore of the cable. A cable with alert the bore will accept bisected the derma aftereffect resistance. Ignoring dielectric and added losses, the beyond cable would bisect the dB/meter loss. In designing a system, engineers accede not alone the accident in the cable but aswell the accident in the connectors.
Acceleration of propagation, in meters per second. The acceleration of advancement depends on the dielectric connected and permeability (which is usually 1).
v={1 \over \sqrt{\epsilon \mu}} = {c \over \sqrt{\epsilon_r \mu_r}}
Single-mode band. In coaxial cable, the ascendant approach (the approach with the everyman blow frequency) is the TEM mode, which has a blow abundance of zero; it propagates all the way down to d.c. The approach with the next everyman blow is the TE11 mode. This approach has one 'wave' (two reversals of polarity) in traveling about the ambit of the cable. To a adequate approximation, the action for the TE11 approach to bear is that the amicableness in the dielectric is no best than the boilerplate ambit of the insulator; that is that the abundance is at least
f_c \approx {1 \over \pi ({D + d \over 2}) \sqrt{\mu \epsilon} }= {c \over \pi ({D + d \over 2}) \sqrt{\mu_r \epsilon_r} }.
Hence, the cable is single-mode from to d.c. up to this frequency, and ability in convenance be acclimated up to 90%9 of this frequency.
Aiguille Voltage. The aiguille voltage is set by the breakdown voltage of the insulator. One website10 gives:
V_p = 1150 \ S_\mathrm{mils} \ d_\mathrm{in} \ \log_{10}(D/d)
where
Smils is the insulator's breakdown voltage in volts per mil
din is the close bore in inches
The 1150 agency converts inches (diameter) to mils (radius) and log10 to ln.
The aloft announcement may be rewritten11 as
V_p = 0.5 \ S \ d \ \ln(D/d)
where
S is the insulator's breakdown voltage in volts per meter
d is the close bore in meters
The affected aiguille voltage is generally bargain by a assurance factor.
edit Choice of impedance
The best coaxial cable impedances in high-power, high-voltage, and low-attenuation applications were experimentally bent at Bell Laboratories in 1929 to be 30, 60, and 77 Ω, respectively. For a coaxial cable with air dielectric and a absorber of a accustomed close diameter, the abrasion is minimized by allotment the bore of the close aqueduct to accord a appropriate impedance of 76.7 Ω.12 If added accepted dielectrics are considered, the best-loss impedance drops down to a amount amid 52–64 Ω. Maximum ability administration is accomplished at 30 Ω.13
The almost impedance appropriate to bout a centre-fed dipole antenna in chargeless amplitude (i.e., a dipole after arena reflections) is 73 Ω, so 75 Ω allure was frequently acclimated for abutting shortwave antennas to receivers. These about absorb such low levels of RF ability that power-handling and high-voltage breakdown characteristics are unimportant if compared to attenuation. Likewise with CATV, although abounding advertisement TV installations and CATV headends use 300 Ω bankrupt dipole antennas to accept off-the-air signals, 75 Ω allure makes a adequate 4:1 balun agent for these as able-bodied as possessing low attenuation.
The addition beggarly amid 30 Ω and 77 Ω is 53.5 Ω; the geometric beggarly is 48 Ω. The alternative of 50 Ω as a accommodation amid power-handling adequacy and abrasion is in accepted cited as the acumen for the number.citation needed 50 Ω aswell works out able-bodied because it corresponds actual carefully to the drive impedance of a half-wave dipole in absolute environments, and provides an adequate bout to the drive impedance of a quarter-wave monopole, as well.
RG-62 is a 93 Ω coaxial cable originally acclimated in mainframe computer networks in the 1970s and aboriginal 1980s (it was the cable acclimated to affix IBM 3270 terminals to IBM 3274/3174 terminal array controllers). Later, some manufacturers of LAN equipment, such as Datapoint for ARCNET, adopted RG-62 as their coaxial cable standard. The cable has the everyman capacitance per unit-length if compared to added coaxial cables of agnate size. Capacitance is the adversary of square-wave abstracts manual (in particular, it slows down bend transitions), and this is a abundant added important agency for baseband agenda abstracts manual than ability administration or attenuation.
All of the apparatus of a coaxial arrangement should accept the aforementioned impedance to abstain centralized reflections at access amid components. Such reflections may could could could cause arresting abrasion and ghosting TV account display; assorted reflections may could could could cause the aboriginal arresting to be followed by added than one echo. In analog video or TV systems, this causes ghosting in the image. Reflections aswell acquaint continuing waves, which could could could cause added losses and can even aftereffect in cable dielectric breakdown with high-power manual (see Impedance matching). Briefly, if a coaxial cable is open, the abortion has absolute resistance, this causes reflections; if the coaxial cable is short-circuited, the abortion attrition is zero, there will be reflections with the adverse polarity. Now amid this aught and absolute attrition termination, one can acquisition a abortion attrition that causes no reflection.
Schematic representation of the elementary apparatus of a manual line.
Schematic representation of a coaxial manual line, assuming the appropriate impedance Z0.
edit Physical parameters
In the afterward section, these symbols are used:
Breadth of the cable, h.
Outside bore of close conductor, d.
Central bore of the shield, D.
Dielectric connected of the insulator, \epsilon. The dielectric connected is generally quoted as the about dielectric connected \epsilon_r referred to the dielectric connected of chargeless amplitude \epsilon_0: \epsilon = \epsilon_r \epsilon_0. If the insulator is a admixture of altered dielectric abstracts (e.g., polyethylene cream is a admixture of polyethylene and air), again the appellation able dielectric connected \epsilon_{eff} is generally used.
Magnetic permeability of the insulator, μ. Permeability is generally quoted as the about permeability μr referred to the permeability of chargeless amplitude μ0: μ = μrμ0. The about permeability will about consistently be 1.
edit Fundamental electrical parameters
Blow capacitance per assemblage length, in farads per metre.6
\left(\frac{C}{h}\right) = {2 \pi \epsilon \over \ln(D/d)}= {2 \pi \epsilon_0 \epsilon_r \over \ln(D/d)}
Series inductance per assemblage length, in henrys per metre.
\left(\frac{L}{h}\right) = {\mu \over 2 \pi} \ln(D/d)= {\mu_0 \mu_r \over 2 \pi} \ln(D/d)
Series attrition per assemblage length, in ohms per metre. The attrition per assemblage breadth is just the attrition of close aqueduct and the absorber at low frequencies. At college frequencies, derma aftereffect increases the able attrition by circumscribed the advice to a attenuate bandage of anniversary conductor.
Blow conductance per assemblage length, in siemens per metre. The blow conductance is usually actual baby because insulators with adequate dielectric backdrop are acclimated (a actual low accident tangent). At top frequencies, a dielectric can accept a cogent arresting loss.
edit Derived electrical parameters
Appropriate impedance in ohms (Ω). Neglecting attrition per assemblage breadth for a lot of coaxial cables, the appropriate impedance is bent from the capacitance per assemblage breadth (C) and the inductance per assemblage breadth (L). The simplified announcement is (Z_0 = \sqrt{L/C}). Those ambit are bent from the arrangement of the close (d) and alien (D) diameters and the dielectric connected (\epsilon). The appropriate impedance is accustomed by7
Z_0=\frac{1}{2\pi}\sqrt{\frac{\mu}{\epsilon}}\ln\frac{D}{d}\approx\frac {138 \Omega}{\sqrt{\epsilon_r}}\log_{10}\frac {D} {d}
Assuming the dielectric backdrop of the actual central the cable do not alter appreciably over the operating ambit of the cable, this impedance is abundance absolute aloft about 5 times the absorber blow frequency. For archetypal coaxial cables, the absorber blow abundance is 600 (RG-6A) to 2,000 Hz (RG-58C).8
Abrasion (loss) per assemblage length, in decibels per meter. This is abased on the accident in the dielectric actual bushing the cable, and arresting losses in the centermost aqueduct and alien shield. These losses are abundance dependent, the losses adequate college as the abundance increases. Derma aftereffect losses in the conductors can be bargain by accretion the bore of the cable. A cable with alert the bore will accept bisected the derma aftereffect resistance. Ignoring dielectric and added losses, the beyond cable would bisect the dB/meter loss. In designing a system, engineers accede not alone the accident in the cable but aswell the accident in the connectors.
Acceleration of propagation, in meters per second. The acceleration of advancement depends on the dielectric connected and permeability (which is usually 1).
v={1 \over \sqrt{\epsilon \mu}} = {c \over \sqrt{\epsilon_r \mu_r}}
Single-mode band. In coaxial cable, the ascendant approach (the approach with the everyman blow frequency) is the TEM mode, which has a blow abundance of zero; it propagates all the way down to d.c. The approach with the next everyman blow is the TE11 mode. This approach has one 'wave' (two reversals of polarity) in traveling about the ambit of the cable. To a adequate approximation, the action for the TE11 approach to bear is that the amicableness in the dielectric is no best than the boilerplate ambit of the insulator; that is that the abundance is at least
f_c \approx {1 \over \pi ({D + d \over 2}) \sqrt{\mu \epsilon} }= {c \over \pi ({D + d \over 2}) \sqrt{\mu_r \epsilon_r} }.
Hence, the cable is single-mode from to d.c. up to this frequency, and ability in convenance be acclimated up to 90%9 of this frequency.
Aiguille Voltage. The aiguille voltage is set by the breakdown voltage of the insulator. One website10 gives:
V_p = 1150 \ S_\mathrm{mils} \ d_\mathrm{in} \ \log_{10}(D/d)
where
Smils is the insulator's breakdown voltage in volts per mil
din is the close bore in inches
The 1150 agency converts inches (diameter) to mils (radius) and log10 to ln.
The aloft announcement may be rewritten11 as
V_p = 0.5 \ S \ d \ \ln(D/d)
where
S is the insulator's breakdown voltage in volts per meter
d is the close bore in meters
The affected aiguille voltage is generally bargain by a assurance factor.
edit Choice of impedance
The best coaxial cable impedances in high-power, high-voltage, and low-attenuation applications were experimentally bent at Bell Laboratories in 1929 to be 30, 60, and 77 Ω, respectively. For a coaxial cable with air dielectric and a absorber of a accustomed close diameter, the abrasion is minimized by allotment the bore of the close aqueduct to accord a appropriate impedance of 76.7 Ω.12 If added accepted dielectrics are considered, the best-loss impedance drops down to a amount amid 52–64 Ω. Maximum ability administration is accomplished at 30 Ω.13
The almost impedance appropriate to bout a centre-fed dipole antenna in chargeless amplitude (i.e., a dipole after arena reflections) is 73 Ω, so 75 Ω allure was frequently acclimated for abutting shortwave antennas to receivers. These about absorb such low levels of RF ability that power-handling and high-voltage breakdown characteristics are unimportant if compared to attenuation. Likewise with CATV, although abounding advertisement TV installations and CATV headends use 300 Ω bankrupt dipole antennas to accept off-the-air signals, 75 Ω allure makes a adequate 4:1 balun agent for these as able-bodied as possessing low attenuation.
The addition beggarly amid 30 Ω and 77 Ω is 53.5 Ω; the geometric beggarly is 48 Ω. The alternative of 50 Ω as a accommodation amid power-handling adequacy and abrasion is in accepted cited as the acumen for the number.citation needed 50 Ω aswell works out able-bodied because it corresponds actual carefully to the drive impedance of a half-wave dipole in absolute environments, and provides an adequate bout to the drive impedance of a quarter-wave monopole, as well.
RG-62 is a 93 Ω coaxial cable originally acclimated in mainframe computer networks in the 1970s and aboriginal 1980s (it was the cable acclimated to affix IBM 3270 terminals to IBM 3274/3174 terminal array controllers). Later, some manufacturers of LAN equipment, such as Datapoint for ARCNET, adopted RG-62 as their coaxial cable standard. The cable has the everyman capacitance per unit-length if compared to added coaxial cables of agnate size. Capacitance is the adversary of square-wave abstracts manual (in particular, it slows down bend transitions), and this is a abundant added important agency for baseband agenda abstracts manual than ability administration or attenuation.
All of the apparatus of a coaxial arrangement should accept the aforementioned impedance to abstain centralized reflections at access amid components. Such reflections may could could could cause arresting abrasion and ghosting TV account display; assorted reflections may could could could cause the aboriginal arresting to be followed by added than one echo. In analog video or TV systems, this causes ghosting in the image. Reflections aswell acquaint continuing waves, which could could could cause added losses and can even aftereffect in cable dielectric breakdown with high-power manual (see Impedance matching). Briefly, if a coaxial cable is open, the abortion has absolute resistance, this causes reflections; if the coaxial cable is short-circuited, the abortion attrition is zero, there will be reflections with the adverse polarity. Now amid this aught and absolute attrition termination, one can acquisition a abortion attrition that causes no reflection.
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