Determine: The r.m.s. ripple voltage

[ifan davies]

An aircraft electrical system operates at 115 volts at 400 hertz. It is to supply an average d.c. voltage of 28 volts and an average current of 20 A at a ripple factor of 0.005.

Determine: The r.m.s. ripple voltage

Here is my attempt.

Vc= Vs-2Vd
=28-2(0.7)
= 26.6 Volts

Vr= (1/2 x fs x C x Rl )(Vc)

R=V/I 28/20= 1.4

(1/2x400x1.4)(26.6)
= 0.023

Vrms= Vr/2sqrt3 Vrms = 0.0063

Now there's a good chance I'm way of here...Thanks for any help!

 

[gneill]

Hi ifan davies, Welcome to Physics Forums.

Different authors define the ripple factor slightly differently. In most cases it's considered to be equal to the ratio of the RMS ripple voltage to the DC component of the power supply output. Others use ratio of the peak to peak value of the ripple voltage to the DC component. Still others convert the result to a percentage ("percent ripple") by multiplying the ratio by 100.

What definition is being used in your textbook or course?

 

[ifan davies]

Hey hey, its the first one you mentioned where it's considered to be equal to the ratio of the RMS ripple voltage to the DC component of the power supply output.

 

[gneill]

Hey hey, its the first one you mentioned where it's considered to be equal to the ratio of the RMS ripple voltage to the DC component of the power supply output.

Okay, so write it out as an equation and plug in your givens. Solve for what you want.

 

[ifan davies]

right let's start again...

Vrms= Vripple/2sqrt3

Vripple= I(load)/2fc

Vripple= 2/(2x400)

= 0.0025

Vrms= 0.0025/(2sqrt3)

vrms= 0.00072

this seems low..

 

[gneill]

You're making it much more complicated than it needs to be. Work with the definition of the ripple factor. What terms in that defining equation are you given in the problem statement?

 

[ifan davies]

Vpk= Vaverage x (pi/2)

Vpk = 28 x (pi/2)

Vpk= 43.98v

Vrms= Vpk/sqrt(3)

Vrms = 43.98/ sqrt(3)

Vrms= 25.39

 

[gneill]

Again, you're all over the map. Write out the defining equation for the ripple factor. It's one equation.

 

[ifan davies]

Kv= rms value of the a.c. voltage component/ average value of the load

 

[gneill]

What specifically do you mean by "average value of the load"?

Hint: See your own post #3.

 

[ifan davies]

its the average load voltage according to my notes? Thanks for sticking with me!

 

[gneill]

Okay, it's the average DC component of the load voltage. So the equation is:

$K_r = \frac{V_{rms}}{V_{DC}}$

where $K_r$ is the ripple factor, $V_{rms}$ is the RMS ripple voltage, and $V_{DC}$ is the average DC voltage.

Which values do you know from the given information?

 

[ifan davies]

Vrms = 115/sqrt2

Vdc= 28

Kr= 81.3/28

Kr = 2.9

Please be right

 

[gneill]

You're given the ripple factor ($K_r = 0.005$) and the DC voltage ($V_{DC} = 28~V$). You want to find the $V_{rms}$.

 

[ifan davies]

this has to be it ...

Kr x Vdc = Vrms

0.005 x 28 = 0.14

 

[gneill]

Yup.

Be sure to include units on your answer.

 

[ifan davies]

When you put it like that its easy! Your awesome!

Now to calculate a suitable value of smoothing capacitor

C= i load / frequency x V

20/ (400x0.14)

0.357 F

 

[gneill]

I'm not sure about your capacitor calculation. For a full-wave rectifier you should have something like

$V_{pp} = \frac{I}{2 f C}$

where $V_{pp} = 2 \sqrt{3} V_{rms}$ is the peak-to-peak ripple voltage assuming a sawtooth waveform.

That would yield a somewhat smaller value for the capacitor.

 

[ifan davies]

0.48= 200/2x400x C

0.00024= 2x 400 x C

0.0012= 400 x C

C= 3 uF

 

[gneill]

What does the "200" value represent? The load current was given as 20 Amps.

 

[ifan davies]

30 uF it is my bad! Thanks for the help, think il go and attempt some other questions now.

 

[gneill]

I think you should recheck your calculation. The capacitance should be much larger than 30 μF .

 

[ifan davies]

0.48 = 20/ 2 x 400 x C

0.48/20 = 2 x 400 x C

0.024 = 2x 400 x C

0.024/2= 400 x C

0.012= 400 x C

C = 0.00003 F or 30 uF

Not correct?

 

[gneill]

0.48 = 20/ 2 x 400 x C

0.48/20 = 1/(2 x 400 x C)

Or,

20/0.48 = 2 x 400 x C
... etc.

 

[ifan davies]

Or that yea lol

0.05 F

 

[gneill]

That looks better.

If the marker is a stickler for significant figures be sure to carry sufficient digits through all calculations and only round values accordingly at the end for presentation of final values.

 

[ifan davies]

I will keep that in mind. Thank you