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Deriving Data and Plotting

asked 2012-08-14 09:15:56 -0500

gjm gravatar image

updated 2012-08-14 14:08:26 -0500

calc314 gravatar image

In the following x means multiply.

Let

z1=2 x pi x 650 x 10^6
p1=2 x pi x 1.9 x 10^9
p2=2 x pi x 5 x 10^9
adc=.667
deltaF=.2 x 10^9

In the following j is the imaginary representation Now let N=(adc x p1 x p2)/z1 and

M=(-2 x j x pi x freq x z1)/((-2 x j x pi x freq+p1) x (-2 x j x pi x freq+p2))

The base formula is abs(20 x log(N x M,10)) or the absolute value of 20 log(N x M) where the log base is base 10. Within the base formula is freq (the value of the frequency) which will be swept from 10^8 to 10^11 in steps of deltaF (.2 x 10^9)

The vertical range is from -25 to 5 (linear scale) and the horizontal range is from 10^8 to 10^11 (log scale)

The horizontal axis as stated is a Log scale as opposed to Linear.

How do I set this up in Sage to plot per the above? Thanks.

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answered 2012-08-14 15:50:51 -0500

calc314 gravatar image

I'm not getting the vertical range that you are specifying, but here is what I've got. Note that the log plot only works in the latest release (5.2) of Sage.

z1=2 * pi * 650 * 10^6
p1=2 * pi * 1.9 * 10^9
p2=2 * pi * 5 * 10^9
adc=.667
deltaF=.2 * 10^9

N=(adc * p1 * p2)/z1
M(freq)=(-2 * i * pi * freq * z1)/((-2 * i * pi * freq+p1) * (-2 * i * pi * freq+p2))

g(frq)=20*abs(log(N*M(frq),10))

pts=[(frq,g(frq).n()) for frq in srange(10^8,10^11,deltaF)]

list_plot(pts, scale='semilogx')
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answered 2012-08-15 08:18:15 -0500

gjm gravatar image

Thanks for the answer. I actually needed to have the absolute value of N x M(freq) and that should give me the right range.

What is the correct syntax? I have tried log(abs(N x M(freq)),10)) and that does not seem to work and I get an error.

Also, is there a reason for the change from freq to frq? Thanks!

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answered 2012-08-15 08:34:28 -0500

gjm gravatar image

It's okay, I got it to work with the abs defined where I wanted it and had one minor change to the equation to get the correct range. Now I need to find out how to get Sage 5.2.

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Asked: 2012-08-14 09:15:56 -0500

Seen: 141 times

Last updated: Aug 15 '12