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| In [[telecommunication]]s, '''standing wave ratio''' ('''SWR''') is the [[ratio]] of the [[amplitude]] of a partial [[standing wave]] at an antinode (maximum) to the amplitude at an adjacent [[node (physics)|node]] (minimum), in an electrical [[transmission line]].
| | Consequently, teams of people who all have exactly the same core speciality, whatever that might be, frequently face a challenge that is similar.<br>It will not matter whether the team is comprised of nurses, software engineers or fire-fighters. The chances are that all made a decision to [http://www.bing.com/search?q=transfer&form=MSNNWS&mkt=en-us&pq=transfer transfer] into that job for reasons that are related, with similar passions and similar abilities. Far more than that, they are also required to structure a de Briefing session to help the group recognize ways in which this groupthink problem can be solved.<br><br> |
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| The SWR is usually defined as a [[voltage]] ratio called the '''VSWR''', (sometimes pronounced "viswar"<ref name="Knott">{{cite book
| | [http://www.riversidemediagroup.com/uggboots.asp UGG Boots Sale] All groups need procedures include strengths to how the team does it and what it does and to [http://www.riversidemediagroup.com/uggboots.asp UGG Boots Sale] support most teams. Specialists [http://www.riversidemediagroup.com/uggboots.asp http://www.riversidemediagroup.com/uggboots.asp] teams regularly want at effectively adding a dissenting voice, some of those to be targeted. It is simple enough to add a product to the schedule for every single meeting that the team has collectively, by way of example, that stipulates that no decisions could be made without some one suggesting an option that's then discussed for at least five minutes.<br><br>It might sound a small change, plus it's, to what the team produce in the conclusion of this kind of session but it could make this type of difference. Professional [http://www.riversidemediagroup.com/uggboots.asp UGG Boots USA] michigan team building activities will most likely be structured so as to aid the participants determine the group strengths which exist within the people as well as reveal how a team's favoured processes don't always enable those strengths to be utilised as effectively as they could be for the benefit of the group.<br><br>While that makes the best for many teams, specialist teams of all sorts want something distinct. They need tasks that emphasize such [http://www.riversidemediagroup.com/uggboots.asp UGG Boots USA] a group's inclination to accept the first notion that somebody comes up with, the insufficient challenge within the group as well as the lost opportunities that are the inescapable effects of this easy-going staff environment.<br><br>For diverse teams to reach their full potential, the people within them need to work in this kind of manner as to exploit the various potencies together. For the homogeneous professionals groups the the task is almost the reverse. Whereas varied teams often have lots of clashes within them due to the [https://Www.vocabulary.com/dictionary/differences differences] between the team members, groups who are full f related folks can instead suffer from something which is called "groupthink".<br><br>That is, all of them are are happy with what one or two individuals are saying over something significant, so that they settle for what has been said. When everyone is happy with something, why whenever they they try and improve upon it? Well, without a contrary perspective, they lack the normal, inherent team power to challenge thoughts and challenge is a key ingredient in successful team working.<br>Without it, great strides in group improvement is not likely in the extreme. Tools like lateral thinking methods may also be added to the mixture to assist a team really appear with options that were fairly different. Add these to the problem added and specialist teams will find that they actually can improve considerably in a brief space of time.<br><br>And well chosen team-building actions are nicely [http://www.riversidemediagroup.com/uggboots.asp UGG Boots] placed to help them see that and implement those developments fast. |
| | last1 = Knott
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| | first1 = Eugene F.
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| | last2 = Shaeffer
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| | first2 = John F.
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| | last3 = Tuley
| |
| | first3 = Michael T.
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| | title = Radar cross section
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| | series = SciTech Radar and Defense Series
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| | edition = 2nd
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| | publisher = SciTech Publishing
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| | year = 2004
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| | page = 374
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| | url = http://books.google.co.uk/books?id=0WuGjb8sqCUC&pg=PA374#v=onepage&q&f=false
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| | isbn = 978-1-891121-25-8}}</ref>
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| <ref name="Schaub">{{cite book
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| | last1 = Schaub
| |
| | first1 = Keith B.
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| | last2 = Kelly
| |
| | first2 = Joe
| |
| | title = Production testing of RF and system-on-a-chip devices for wireless communications
| |
| | series = Artech House microwave library
| |
| | publisher = Artech House
| |
| | year = 2004
| |
| | page = 93
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| | url = http://books.google.co.uk/books?id=26RfoKg2UxIC&pg=PA93#v=onepage&q&f=false
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| | isbn = 978-1-58053-692-9}}</ref>), for ''voltage standing wave ratio''. For example, the VSWR value 1.2:1 denotes a maximum standing wave amplitude that is 1.2 times greater than the minimum standing wave value. It is also possible to define the SWR in terms of [[Current (electricity)|current]], resulting in the ISWR, which has the same numerical value. The ''power standing wave ratio'' (PSWR) is defined as the square of the VSWR. To avoid confusion, wherever SWR is used without modification in this article, assume it is referring to the VSWR.
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| SWR is used as an efficiency measure for transmission lines, electrical cables that conduct [[radio frequency]] signals, used for purposes such as connecting [[transmitter|radio transmitters]] and receivers with their [[Antenna (radio)|antenna]]s, and distributing [[cable television]] signals. A problem with transmission lines is that [[Impedance matching|impedance mismatches]] in the cable tend to reflect the radio waves back toward the source end of the cable, preventing all the power from reaching the destination end. SWR measures the relative size of these reflections. An ideal transmission line would have an SWR of 1:1, with all the power reaching the destination and no reflected power. An infinite SWR represents complete reflection, with all the power reflected back down the cable. The SWR of a transmission line can be measured with an instrument called an [[SWR meter]], and checking the SWR is a standard part of installing and maintaining transmission lines.
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| ==Relationship to the reflection coefficient==
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| The voltage component of a standing wave in a uniform [[transmission line]] consists of the forward wave (with amplitude <math>V_f</math>) superimposed on the reflected wave (with amplitude <math>V_r</math>).
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| Reflections occur as a result of discontinuities, such as an imperfection in an otherwise uniform transmission line, or when a transmission line is terminated with other than its [[characteristic impedance]]. The [[reflection coefficient]] <math>\Gamma</math> is defined thus:
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| :<math>\Gamma = {V_r \over V_f}.</math>
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| <math>\Gamma</math> is a [[complex number]] that describes both the magnitude and the phase shift of the reflection. The simplest cases, when the imaginary part of <math>\Gamma</math> is zero, are:
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| * <math>\Gamma=-1</math>: maximum negative reflection, when the line is short-circuited,
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| * <math>\Gamma=0</math>: no reflection, when the line is perfectly matched,
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| * <math>\Gamma=+1</math>: maximum positive reflection, when the line is open-circuited.
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| For the calculation of SWR, only the [[magnitude (mathematics)|magnitude]] of <math>\Gamma</math>, denoted by <math>\rho</math>, is of interest. Therefore, we define
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| :<math>\rho = | \Gamma | </math>.
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| At some points along the line the two waves [[Interference (wave propagation)|interfere]] constructively, and the resulting amplitude <math>V_\max</math> is the sum of their amplitudes:
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| :<math>V_\max = V_f + V_r = V_f + \rho V_f = V_f (1 + \rho).\,</math> | |
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| At other points, the waves interfere destructively, and the resulting amplitude <math>V_\min</math> is the difference between their amplitudes:
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| :<math>V_\min = V_f - V_r = V_f - \rho V_f = V_f ( 1 - \rho).\,</math>
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| The voltage standing wave ratio is then equal to:
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| :<math>VSWR = {V_\max \over V_\min} = {{1 + \rho} \over {1 - \rho}}.</math>
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| <!-- Commented out because image was deleted: [[File:VSWR.png]] -->
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| As <math>\rho</math>, the magnitude of <math>\Gamma</math>, always falls in the range [0,1], the SWR is always ≥ +1.
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| The SWR can also be defined as the ratio of the maximum amplitude of the [[electric field strength]] to its minimum amplitude, <math>E_\max/E_\min</math>.
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| Since power is proportional to V<sup>2</sup>, VSWR can be expressed in terms of forward and reflected power as follows:
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| :<math> \frac {P_r}{P_f} = \left ( \frac {VSWR - 1}{VSWR + 1} \right )^2 </math>
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| ==Further analysis==
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| {{accuracy-section|Further analysis section|reason=see talk|date=November 2013}}
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| If the standing waves are only the result of a mismatch between the characteristic impedance and load impedance of the line, the VSWR can be expressed as one of the two equations below (pick the one that gives a value greater than 1):
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| :<math>VSWR = \frac{Z_\text{0}}{R_\text{L}} </math> {{space}}{{space}}{{space}}{{space}}{{space}}{{space}}'''or''' {{space}}{{space}}{{space}}{{space}}{{space}}{{space}}<math>VSWR = \frac{R_\text{L}}{Z_\text{0}}</math>
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| To understand the standing wave ratio in detail, we need to calculate the voltage (or, equivalently, the electrical field strength) at any point along the transmission line at any moment in time. We can begin with the forward wave, whose voltage as a function of time ''t'' and of distance ''x'' along the transmission line is:
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| :<math>V_f(x,t) = A \sin (\omega t - kx),\,</math>
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| where ''A'' is the amplitude of the forward wave, ω is its [[angular frequency]] and ''k'' is the wave number (equal to ω divided by the speed of the wave). The voltage of the reflected wave is a similar function, but spatially reversed (the sign of ''x'' is inverted) and attenuated by the reflection coefficient ρ:
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| :<math>V_r(x,t) = \rho A \sin (\omega t + kx).\,</math>
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| The total voltage <math>V_t</math> on the transmission line is given by the [[superposition principle]], which is just a matter of adding the two waves:
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| :<math>V_t(x,t) = A \sin (\omega t - kx) + \rho A \sin (\omega t + kx).\,</math>
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| Using standard [[trigonometry|trigonometric]] identities, this equation can be converted to the following form:
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| :<math>V_t(x,t) = A \sqrt {4\rho\cos^2 kx+(1-\rho)^2} \cos(\omega t + \phi),\,</math>
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| where <math>{\tan \phi}={{(1+\rho)}\over{(1-\rho)}}\cot(kx).</math>
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| This form of the equation shows, if we ignore some of the details, that the maximum voltage over time ''V''<sub>mot</sub> at a distance ''x'' from the transmitter is the periodic function
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| :<math>V_\mathrm{mot} = A \sqrt {4\rho\cos^2 kx+(1-\rho)^2}.</math>
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| This varies with ''x'' from a minimum of <math>A(1-\rho)</math> to a maximum of <math>A(1+\rho)</math>, as we saw in the earlier, simplified discussion. A graph of <math>V_\mathrm{mot}</math> against ''kx'', for a range of ''ρ'', is shown below. The maximum and minimum of ''V''<sub>mot</sub> in a period are <math>V_\min</math> and <math>V_\max</math> and are the values used to calculate the SWR.
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| [[File:Standing Wave Ratio.svg|500px|center|frame|Standing wave ratio for a range of ''ρ''. In this graph, ''A'' and ''k'' are set to unity.]]
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| Note that this graph does not show the instantaneous voltage profile, ''V''<sub>t</sub>(x,t), along the transmission line. It only shows ''V''<sub>t</sub>(x) or the voltage amplitude as a function of space at a single point in time. The instantaneous voltage is a function of both time and distance, so could only be shown fully by a three-dimensional or animated graph.
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| ==Practical implications of SWR==
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| The most common case for measuring and examining SWR is when installing and tuning transmitting [[Antenna (radio)|antenna]]s. When a transmitter is connected to an antenna by a [[feed line]], the [[Electrical impedance|impedance]] of the antenna and feed line must match exactly for maximum energy transfer from the feed line to the antenna to be possible. The impedance of the antenna varies based on many factors including: the antenna's natural [[resonance]] at the [[Antenna (radio)#Resonant frequency|frequency]] being transmitted, the antenna's height above the ground, and the size of the conductors used to construct the antenna.<ref name="ARRL20.2">{{cite book
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| | last = Hutchinson
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| | first = Chuck, ed.
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| | title = The ARRL Handbook for Radio Amateurs 2001
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| | publisher = ARRL—the national association for Amateur Radio
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| | year = 2000
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| | location = Newington, CT
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| | page = 20.2
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| | isbn = 0-87259-186-7}}</ref>
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| When an antenna and feedline do not have matching impedances, some of the electrical energy cannot be transferred from the feedline to the antenna.<ref name="ARRL19.4">{{cite book
| |
| | last = Hutchinson
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| | first = Chuck, ed.
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| | title = The ARRL Handbook for Radio Amateurs 2001
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| | publisher = ARRL—the national association for Amateur Radio
| |
| | year = 2000
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| | location = Newington, CT
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| | pages = 19.4–19.6
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| | isbn = 0-87259-186-7}}</ref>
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| Energy not transferred to the antenna is reflected back towards the transmitter.<ref name="QST">{{cite journal
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| | last = Ford
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| | first = Steve
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| | title = The SWR Obsession
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| | journal = QST
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| | volume = 78
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| | issue = 4
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| | pages = 70–72
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| | publisher = ARRL—The national association for Amateur Radio
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| | location = Newington, CT
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| |date=April 1997
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| | url = http://www.arrl.org/tis/info/pdf/49470.pdf
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| |format=PDF| accessdate = 2008-09-26 }}</ref>
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| It is the interaction of these reflected waves with forward waves which causes standing wave patterns.<ref name="ARRL19.4" /> Reflected power has three main implications in radio transmitters: Radio Frequency (RF) energy losses increase, distortion on transmitter due to reflected power from load<ref name="ARRL19.4" /> and damage to the transmitter can occur.<ref name="ARRL19.13">{{cite book
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| | last = Hutchinson
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| | first = Chuck, ed.
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| | title = The ARRL Handbook for Radio Amateurs 2001
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| | publisher = ARRL—the national association for Amateur Radio
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| | year = 2000
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| | location = Newington, CT
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| | page = 19.13
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| | isbn = 0-87259-186-7}}</ref>
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| Matching the impedance of the antenna to the impedance of the feed line is typically done using an [[antenna tuner]]. The tuner can be installed between the transmitter and the feed line, or between the feed line and the antenna. Both installation methods will allow the transmitter to operate at a low SWR, however if the tuner is installed at the transmitter, the feed line between the tuner and the antenna will still operate with a high SWR, causing additional RF energy to be lost through the feedline.
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| Many [[amateur radio]] operators consider any impedance mismatch a serious matter.<ref name="ARRL20.2" /> Power loss will increase as the SWR increases. For example, a [[dipole antenna]] tuned to operate at 3.75 MHz—the center of the 80 meter amateur radio band—will exhibit an SWR of about 6:1 at the edges of the band. However, if the antenna is fed with 250 feet of RG-8A coax, the loss due to standing waves is 2.2dB, which may seem like a small loss, but is on a logarithmic scale. If running a typical 100W transmitter on the HF band, 2.2dB of loss would reduce the output power to 60W. That is a 40% reduction in power.<ref name="ARRL19.4" /> Feed line loss typically increases with frequency, so [[VHF]] and above antennas must be matched closely to the feedline. The same 6:1 mismatch to 250 feet of RG-8A coax would incur 10.8dB of loss at 146 MHz.<ref name="ARRL19.4" /> However, a length of 250 feet would not likely be used for 2m VHF radios. Antennas for the 80m band frequently involve large or complex designs typically mounted on a tall tower with great distances needed between buildings and thus the transmitter. VHF requires a much smaller antenna, and unless being used on a high powered repeater, does not have a very tall tower. The most common usage of 2m band is mobile single or dual band VHF or VHF/UHF mobiles. Also in part due to the typical output power of a VHF band is 50W, due to the FCC requirement of RF exposure evaluations needing to be conducted on power greater than 50W in the 2m band. This 50W with the 250 feet of cable would be reduced to 5W with 10dB of loss. On the less common occasions where a long transmission line is needed for 146 MHz, a higher quality low-loss transmission line would be used instead of the relatively cheap RG-8A.
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| ==Implications of SWR on medical applications==
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| SWR can also have a detrimental impact upon the performance of microwave based medical applications. In microwave electrosurgery an antenna that is placed directly into tissue may not always have an optimal match with the feedline resulting in an SWR. The presence of SWR can affect monitoring components used to measure power levels impacting the reliability of such measurements.<ref name="ARRL19.5">{{cite web
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| | url = http://www.microwaves101.com/encyclopedia/medical_VSWR.cfm
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| | title = Problems with VSWR in medical applications
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| | publisher =
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| | year =
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| | location =
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| | page = }}</ref>
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| == See also ==
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| * [[Return loss]]
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| * [[Time-domain reflectometer]]
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| * [[SWR meter]]
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| * [[Electrical impedance|Impedance]]
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| * [[Mismatch loss]]
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| ==References==
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| {{Reflist}}
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| *{{FS1037C MS188}}
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| ==Further reading==
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| * [http://www.hpmemory.org/an/pdf/an_1287-1.pdf ''Understanding the Fundamental Principles of Vector Network Analysis''], [[Hewlett Packard]] Application note 1287-1, 1997
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| ==External links==
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| * [http://www.fourier-series.com/rf-concepts/reflection.html Reflection and VSWR] A flash demonstration of transmission line reflection and SWR
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| * [http://cgi.www.telestrian.co.uk/cgi-bin/www.telestrian.co.uk/vswr.pl VSWR]—An online conversion tool between SWR, return loss and reflection coefficient
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| * [http://www.emtalk.com/vswr.php Online VSWR Calculator]
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| {{DEFAULTSORT:Standing Wave Ratio}}
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| [[Category:Antennas (radio)]]
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| [[Category:Wave mechanics]]
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| [[Category:Radio electronics]]
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| [[Category:Engineering ratios]]
| |
Consequently, teams of people who all have exactly the same core speciality, whatever that might be, frequently face a challenge that is similar.
It will not matter whether the team is comprised of nurses, software engineers or fire-fighters. The chances are that all made a decision to transfer into that job for reasons that are related, with similar passions and similar abilities. Far more than that, they are also required to structure a de Briefing session to help the group recognize ways in which this groupthink problem can be solved.
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That is, all of them are are happy with what one or two individuals are saying over something significant, so that they settle for what has been said. When everyone is happy with something, why whenever they they try and improve upon it? Well, without a contrary perspective, they lack the normal, inherent team power to challenge thoughts and challenge is a key ingredient in successful team working.
Without it, great strides in group improvement is not likely in the extreme. Tools like lateral thinking methods may also be added to the mixture to assist a team really appear with options that were fairly different. Add these to the problem added and specialist teams will find that they actually can improve considerably in a brief space of time.
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