TINA_Advanced_Topics.pdf

Frequencyhz 000 250g 500g 750g 1000g amplitude vs 000

Info icon This preview shows pages 61–65. Sign up to view the full content.

View Full Document Right Arrow Icon
Frequency[Hz] 0.00 2.50G 5.00G 7.50G 10.00G Amplitude [Vs] 0.00 250.00p 500.00p 750.00p 1.00n Amplitude spectrum generated by Tina's Interpreter You can easily check, that the above spectrum provided by the closed formula and the spectrum provided by Tina’s Fourier Spectrum command are exactly the same. It’s rather easy to compare these curves using the clipboard. First select the curve which was generated by the Interpreter, then copy this curve onto the clipboard then in the diagram window go back to the previous page and paste the curve back. The curves will be identical, so we do not show here both.
Image of page 61

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Example : Transform of a sine wave (fourex4.sch) The Fourier transform of a sine wave results in a Dirac-delta function, that is an infinitely high spike of zero width at the frequency of a sine wave. We can not reproduce that with DFT. We can actually examine sine waves of finite length. The longer the sine wave is, the taller and narrower the spectrum becomes. Let us first examine a 3ms long sine wave with 1kHz frequency. Time [s] 0.00 1.00m 2.00m 3.00m Voltage [V] -1.00 -500.00m 0.00 500.00m 1.00 T=3m If you run Fourier spectrum on this curve you will get the following result. Frequency [Hz] 0 1k 2k 3k 4k 5k Amplitude [Vs] 0.00 500.00u 1.00m 1.50m 2.00m T 2 =1.5m
Image of page 62
Although the peak value of this spectrum is correct the shape of the spectrum is quite rough. To get a better spectrum change the simulation time to 21ms and carry out the analysis again. At FFT the frequency resolution is inversely proportional to the duration of the signal. Time [s] 0.00 1.00m 2.00m 3.00m 4.00m 5.00m Voltage [V] -1.00 -500.00m 0.00 500.00m 1.00 Note that the actual simulation time in this example was 21ms to get a better spectrum. (Not shown on the figure.) Frequency [Hz] 0 1k 2k 3k 4k 5k Amplitude [Vs] 0.00 500.00u 1.00m 1.50m 2.00m
Image of page 63

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Let us check this result using the theory of Fourier transform: F } sin ) ( { 0 t t d ω , where > < = = t 0 if , 1 T or t 0 t if , 0 ) ( ) ( ) ( T T t t t d ε ε = = = = + T t j T t j t j t j t j T t j T dt e dt e j dt e j e e t d dt te t d j F 0 ) ( 0 ) ( 0 0 0 0 0 2 1 2 ) ( sin ) ( ) ( ω ω ω ω ω ω ω ω ω ω ) ( 2 ) sin( ) ( 2 ) sin( 0 0 2 ) ( 0 0 2 ) ( 0 0 ω ω ω ω ω ω ω ω ω ω ω ω + + + j T e j T e T j T j Note, that the main amplitude of the spectrum at 0 ω ω = and at 0 ω ω = is 2 T . Let us draw this function with Tina’s Interpreter (fourex3.ipr). In this example we will use a simplified expression, because this part is significant only regarding the amplitude of the spectrum. The following simplified function calculates the amplitude spectrum. Function SinusAmplSpe(f); Begin w := 2 * pi * f; w0 := 2 * pi * 1k; T := 3m; SinusAmplSpe := Abs(Sin((w - w0) * T / 2) / (w - w0) – Sin((w + w0) * T / 2) / (w + w0)); End; Draw(SinusAmplSpe(Frequency), AmplSpe) To try out the above example invoke the Interpreter from the Tools menu, type in the above text or read in fourex3.ipr by selecting the Open command from the File menu. If you press the Run button after a short time the following function appears Frequency[Hz] 0.00 1.00k 2.00k 3.00k 4.00k 5.00k Amplitude [Vs] 0.00 500.00u 1.00m 1.50m 2.00m Amplitude spectrum calculated by Tina's Interpreter
Image of page 64
Image of page 65
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern