Calculate the ratio of effective resistance to DC resistance Reff/Rdc in a copper foil of thickness d carrying the pulsed current waveform shown in Figure 6.12.

Question

Calculate the ratio of effective resistance to DC resistance [latex] R_{eff}/R_{dc}[/latex] in a copper foil of thickness d carrying the pulsed current waveform shown in Figure 6.12.

Accepted Answer

This waveform is a more realistic version of the waveform in Example 6.1, with a rise and fall time along with a slower characteristic at the start and end of the rising and falling fronts. The derivative is also shown. This waveform is typical of the input in a forward converter. Find the optimum value of D for six layers and [latex]t_{r}/T= [/latex] 4%.

This waveform has a Fourier series:

[latex]i(t)= I_{0}\left( \frac{1}{2}-\frac{t_{r}}{T} \right) +\sum\limits_{n= 1}^{\infty }{\frac{4I_{0}}{n^{3}\pi ^{3}\left(\frac{t_{r}}{T} \right)^{2} } } \left[ 1-cos\left( \frac{n\pi t_{r}}{T} \right) \right] \sin\left( n\pi \left( \frac{1}{2}-\frac{t_{r}}{T} \right) \right) \cos\left(n \left(\omega t-\frac{\pi }{2} \right) \right) [/latex]

The rms value of i(t) is:

[latex] I_{rms} = I_{0}\sqrt{0.5-\frac{37t_{r}}{30T} }[/latex]

Following the procedure outlined in Example 6.1, [latex] R_{eff}/R_{dc}[/latex] is plotted in Figure 6.13 for p = 6 and [latex]t_{r}/T= [/latex] 4%. The optimum value of D is 0.418.
The MATLAB program for this example is listed at the end of the chapter.

Question 6.2: Calculate the ratio of effective resistance to DC resistance...

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