Creating an Equation for f(t) from the Last Waveform in the Picture

[ACLerok]

http://www.rfcafe.com/references/electrical/images/period5.gif

For the last waveform in the picture above. How would i go about writing an equation for f(t)?

Thanks in advance

 

[OlderDan]

http://www.rfcafe.com/references/electrical/images/period5.gif

For the last waveform in the picture above. How would i go about writing an equation for f(t)?

Thanks in advance

As an absolute value of something, or as a piecewise definition for each of the intervals that has a continuous derivative.

 

[ACLerok]

I'm sorry i do not follow. I understand if it was just a ramp function it would just be (Vm/T) t but i still don't know

 

[OlderDan]

I'm sorry i do not follow. I understand if it was just a ramp function it would just be (Vm/T) t but i still don't know

The last waveform is called a Full-wave rectified sine. It is a sine function with all the negative regions flipped to positive. It is the absolute value of the sine function

$$f(x) = \left| {A\sin 2\pi \frac{t}{T}} \right| = A\left| {\sin 2\pi \frac{t}{T}} \right|$$

or you could write separate functions for the separate intervals with alternating plus and minus signs in front of the sine function.

 

[ACLerok]

i see.. so am i correct to say that the equation for f(x) for the third waveform would be Asin(4pi/T)?

 

[OlderDan]

i see.. so am i correct to say that the equation for f(x) for the third waveform would be Asin(4pi/T)?

No. For one thing you need a variable, t, in the argument of the sine function (T is a constant) and you need to define the function to be zero in the intervals where the waveform is zero. One way to do that would be to take 1/2 times your second waveform and add A/2 so that the square wave is between 0 and A; then use that in place of the A in the sine function you have.

 

[ACLerok]

for the full rectified sine wave, the equation for f(t) from 0 to T/2. can it not have a sin in the equation maybe something like A(1-t^2)? (i know that's incorrect)

 

[ACLerok]

anyone? :(

 

[OlderDan]

for the full rectified sine wave, the equation for f(t) from 0 to T/2. can it not have a sin in the equation maybe something like A(1-t^2)? (i know that's incorrect)

I'm not sure what you are asking. For the full-wave rectified sine the function is a sine function from 0 to T

$$f(x) = A\sin \pi \frac{t}{T}}$$

Between T and 2T it is

$$f(x) = -A\sin \pi \frac{t}{T}}$$

There is no 1-t^2 involved

 

[OlderDan]

The last waveform is called a Full-wave rectified sine. It is a sine function with all the negative regions flipped to positive. It is the absolute value of the sine function

$$f(x) = \left| {A\sin 2\pi \frac{t}{T}} \right| = A\left| {\sin 2\pi \frac{t}{T}} \right|$$

or you could write separate functions for the separate intervals with alternating plus and minus signs in front of the sine function.

CORRECTION!

Sorry, I misinterpreted the T as being the period of the sine function. In fact 2T is the period in the figure. This should have been

$$f(x) = \left| {A\sin \pi \frac{t}{T}} \right| = A\left| {\sin \pi \frac{t}{T}} \right|$$

 

[OlderDan]

i see.. so am i correct to say that the equation for f(x) for the third waveform would be Asin(4pi/T)?

From 0 to T/2 or from nT to (n+1/2)T this should be

$$f(x) = {A\sin 2\pi \frac{t}{T}}$$

From T/2 to T or from (n+1/2)T to (n+1)T f(x) is zero.