Dan Sawyer wrote:
>Thanks Alek,
>
>I will do the math tonight and see if the LC are resonant for the
>frequency. The LC readings are very close for 2 different 50 ohm
>terminators and an antenna that is close to resonant. The frequency was
>7.24 MHz.
>
>
Well here's I done it in Mathematica
http://www.wolfram.com/
for you.
f=1/(2 * pi * sqrt(l c) )
In[4]:= 1 / (2 * Pi Sqrt[ 2 10^-6 2500 10^-12])
You might not follow the formatting, as I doubt it will print properly
in an email, and I can't be bothered to output it in another form and
put on a web page.
5000000 Sqrt[2]
Out[4]= ---------------
Pi
At this point Mathematica has done the computation eexactly (so there is
no rounding errors), but lets put it in a more human readable format, by
asking Mathematica for a numerical value.
In[5]:= N[%]
6
Out[5]= 2.25079 10
But the resonate frequency of the 2uH and 2500pF caps is 2.25 x 10^6 Hz,
or 2.25 MHz.
But it is a pointless computation, as there are an infinite set of L's
and C's which will resonate at any given frequency. Those values
resonate at 2.25MHz, but if you half L (make it 1uH) and double C (make
it 5000pF) it would resonate at exactly the same frequency.
>Is the Z reaking accurate?
>
Z is normally meant to mean impedance, which in general has both a real
(R) and imaginary (X) parts. Since you have not quoted the X part, you
have not stated an impedance, only a resistance. But for a perfect dummy
load, one would expect R=50, X=0, so it has indicated the resistive part
right, but you can't say it has given you the correct impedance, since
you have not quoted one.
>Dan
>
BTW, you might want to take a look at Mathematica
http://www.wolfram.com/
Whilst it's an expensive program (~$1800 on Windoze), there was at one
point (probably still is) a free download that will compute anything,
but does not allow you to save the results.
Mathematica is useful if you want to play around with some text books on
this sort of thing, as unlike calculators, you don't need to put numbers
in, but can leave equations in the form of unknown R's, L's, C's etc.
(In Mathematica, you should use lower case variables).
If you wanted to find the solution of a quadratic
ax^2 + bx + c == 0
which you might recall from school days, you don't need to know what a,
b, and c are.
In[8]:= Solve[ a x^2 + bx + c == 0,x]
again the result does not print too well, but it shows the two solutions.
Sqrt[-bx - c] Sqrt[-bx - c]
Out[8]= {{x -> -(-------------)}, {x -> -------------}}
Sqrt[a] Sqrt[a]
You could write a simple function to compute the resonance frequency of
any inductance and capacitance. I'll force it to print the the result
numerically this time, but using '1.0' rather than '1' in the formula.
In[16]:= f[l_,c_]=1.0/ (2 Pi Sqrt[l c])
0.159155
Out[16]= ---------
Sqrt[c l]
In[17]:= f[2 10^-6, 2500 10^-12]
6
Out[17]= 2.25079 10
It's well worth looking at for learning. And if you want to learn about
complex numbers (i.e. those with an imaginary part), which you need to
understand impedance properly, Mathematica can calculate with them just
as easily as real numbers.
First try a calculation.
In[18]:= (3 - 20 I) / (4 + 9 I)
Mathematica produces an exact result, which might not be what you want.
168 107 I
Out[18]= -(---) - -----
97 97
So you ask it for a numerical approximation.
In[19]:= N[%]
Out[19]= -1.73196 - 1.10309 I
And so we have divided two complex numbers, and get a complex result.
Good luck.
--
Dr. David Kirkby,
G8WRB
Please check out http://www.g8wrb.org/
of if you live in Essex http://www.southminster-branch-line.org.uk/
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