On Mon, 9 Feb 2004 13:37:29 +0100, "Massi"
wrote:

|Hi to everybody,
|I got the VSWR of an antenna from a Vector Analyzer and I'd like to know
|(and how) if is possible to calculate the Quality Factor from it.
|Thanks,
|Massimo

Do you have the R +jX data, or only VSWR?
|

Do you have the R +jX data, or only VSWR?
|


I have also the Smith Chart and the R+jX data for every frequency (I'm
working about between 10 MHz and 15 MHz)

On Mon, 9 Feb 2004 17:22:28 +0100, "Massi"
wrote:

|
| Do you have the R +jX data, or only VSWR?
| |
|
|
|I have also the Smith Chart and the R+jX data for every frequency (I'm
|working about between 10 MHz and 15 MHz)

For simple resonant antennas, (dipole for example) you can evaluate
the slope of reactance v. frequency and calculate Q.

Consider that the antenna has the properties of a series RLC circuit
with L and C as unknowns and R known. The antenna has a constant L and
C and the reactance you measure at any frequency is determined by
their sum.

By picking two frequencies, preferably spaced equally about the
resonant frequency, and setting up two equations with two unknowns you
can solve for L and C and then using the reactance of either,
calculate Q as X/R. You can use Excel's solver, Mathcad or brute force
to solve the equations.

Another related method is to use the following:

Let

t1 = deltaX / deltaF

t2 = t1 / (4 * pi)

Q = t2 * omega / R

Whe

deltaX = the reactance difference at two frequencies

and

deltaF = the difference between the two frequencies

omega = 2 * pi * Fres

In another posting on a different subject, Steve Best offered this:

Begin Quote

Near the antenna's resonance, a different method must be used to
determine antenna Q. One method is to determine Q from the antenna's
1/2 power impedance bandwidth as follows:

Q = 2 / BW

where BW is the bandwidth determined from the 1/2 power SWR points
where the ZO used to determine SWR is the antenna's feedpoint
resistance. The 1/2 power SWR is equal to 5.828.

Another method is to determine Q directly as follows:

Q = A (B + C)

where A = w / (2 R), w = 2 pi F

B = dX/dw

C = |X|/w

End Quote.

So contrary to other posts, VSWR and Q *are* related and you have all
of the data you need to make the calculation.

Wes Stewart N7WS


|