when the transmitter section of a cb or 10 meter radio is aligned it is common procedure to use a 50 ohm load when doing so. the transmitter output impedance is fixed.
we connect the transceiver to a feedline that has a Zc (characteristic impedance) of 50 ohms. so far, so good.
in the typical tractor rig rolling down the highway we install a typical cb antenna and we measure a couple of parameters at the feedpoint of the antenna. for the sake of this example we will use values that are commonly found in this particular environment.
in our example we measure a load resistance of approximately 35 ohms and we also measure a value of capacitive reactance present at the feedpoint of -j10 or 10 ohms. the total load impedance under these conditions is approximately 36.401 ohms, making the point that load impedance consists of resistance and any reactances present at the feedpoint.
i'm assuming that we all know that any generator (or transmitter) delivers all available developed power when it sees an input impedance at the source end that matches its own.
that given, the premise is this. every length of line is a matching transformer when Zl (the load) is something other than the Zc of the line and in this case reflection is present. it is this very condition that makes all of the following possible.
assuming a line with a velocity factor of .78 % and an operating frequency of 27 mhz., we would like to determine at what points along the line (and the associated shift in phase angles) that would produce an input impedance looking into the transmitter end of the line approximating 50 ohms so that the transmitter will still produce all available developed power regardless of the mismatch present at the load.
there will not be just one spot in the line where this will occur, there will be several depending on the length of the line.
before we get to that, let's test the program that we are about to use for calibration purposes using a tuned 1/2 wave line to check for the mirroring aspect and properties of such a line. ignore the 160M band indication as this setting is not being used. the frequency is 27 mhz.
http://www.firecommunications.com/ScreenHunter_087.gif
as you can see, the tuned half wave line is mirroring the values almost exactly at the transmitter input, with slight variances due to negligible values of cable and swr losses.
now we will attempt to adjust the line length so that the standing waves on the line and the attendant phase shifts producing the variable values of impedance along the line coincide at the transmitter input to a value more closely matching the Zs or source impedance at the transmitter, namely 50 ohms.
http://www.firecommunications.com/ScreenHunter_088.gif
now the load impedance at the transmitter is exactly 50 ohms. we do however have an inductive value of reactance on the order of approximately +j18.935 ohms, preventing a more normalized input resistance but 46.276 ohms ain't that bad. the remaining inductive reactance can be cancelled easily using an open length of the same feedline in conjunction with a t-connector, the feedline input and the transmitter output to exactly cancel the remaining inductive reactance and restoring a purely resistive, non-reactive match between the input of the feedline and the transmitter. approximately 9 inches of RG-8X from T-plug to open end almost perfectly cancels the inductive reactance present at the transmitter. RG-8X exhibits roughly 25.3 pf. of capacitance for every foot (12 inches) of length. this works out to approximately 2.10833/RPT pf. per inch.
did the swr change? one might argue that the swr at the transmitter did, we'll come back to that later. what did change here is the reduction in transmitter power output created by the reflection mismatch at the load and back up the line. as you can see in the example of the tuned 1/2 wave line, the mismatch at the load is almost exactly duplicated at the transmitter. by altering the length of the line we have restored the match at the transmitter so that the reduction in transmitter power no longer exists. this doesn't happen with random lengths of line.
let's look at one more example. let's shorten the line this time. let's shorten it considerably.
http://www.firecommunications.com/ScreenHunter_089.gif
look familiar? and no hot spot problems either. if you don't like this we can try some series matching techniques using 2 feedline lengths of dissimilar impedances and we can elegantly match not only the load to the transmitter but cancel or null all reactance in the system as well in one fell swoop. these are some of the ways we deal with these situations when there's nothing else at the antenna to adjust. it can be a lot easier than you think. this is just one small example of what "the coax length thing" is all about. and before anyone mentions the fact that a 1.5:1 swr isn't that big of a deal to begin with let me add this. these and other techniques are well able to deal with much larger degrees of mismatch than the the sample presented here. fyi.
every length of feedline is a matching transformer....Cebik.
HUH?
