Design of a rectifier

Elisabeth_91

1. The problem statement, all variables and given/known data

A classical rectifier is to be designed to provide 5V +/- 1% for a logic circuit, with output power of up to 12W. The input is conventional 220V, 50Hz source.
i) Choose a transformer ratio
ii) Choose a diode configuration
iii) Calculate the capacitor value to meet the requirements
iv) Draw the load voltage, the load current and the source current (secondary side) waveforms for maximum output power (12W).


2. Relevant equations



3. The attempt at a solution

I am a complete beginner in this. I have no clue how to solve. Can you please give me a hint?

NascentOxygen

It's a meaty topic. Start by a google search on: rectifier "filter capacitor"

Elisabeth_91

I need to use a full wave rectifier bridge with a Capacitor parallel to my load. Is this correct?

What I don't understand is, do I put a normal transformer before the bridge?

technician

You are correct. Use a full wave bridge arrangement and you need a transformer to step down 220V to 5V

Elisabeth_91

Would it also be possible to use just a Capacitor Filter, this seems to be the easiest way to solve the problem.
Like shown here: http://www.tpub.com/neets/book7/0249.GIF

What is the advantage of the bridge?

technician

A single diode allows 0ne half of the AC current to flow. Imagine an AC wave which goes + and -. A single diode will cut off the - sections (or the +sections!!). This gives the familiar 'half wave rectification waveform'... can you picture it?
The full wave combination of diodes needs 4 diodes connected in a 'bridge' and this allows all of the AC current to flow in the same direction....it is smoother.

Elisabeth_91

i) transformation ratio

In the end I want a DC Voltage of 5V. Using a full-wave bridge this means
[itex]
V_{dc}=\frac{2 V_{2,max}}{π}
V_{2,max} = \frac{π V_{dc}}{2} = 7.85V
[/itex]


Since I need a transformer that is giving this peak voltage
Transformer ratio =
[itex]
\frac{V_{1,max}}{V_{2,max}} = \frac{V_{1}*\sqrt{2}}{V_{2,max}} = \frac{220V*\sqrt{2}}{7.85V} = 39.6
[/itex]

Can you tell me if this is correct?

Elisabeth_91

ii) diode configuration

Full-Wave-Bridge

iii) capacitor value
http://en.wikipedia.org/wiki/Ripple_...-domain_ripple
Can I use this simplification here?
[itex]
V_{ripple} = \frac{I_{load}}{2fC}
[/itex]

[itex]
P = I_{load}*V_{dc}
[/itex]

technician

The output voltage is specified as 5V +/-1%
This means that the max change in voltage allowed is 0.05V
The capacitor stores electric charge so that current can be maintained between the peaks of the voltage, this is when the voltage is decreasing.
The power that needs to be supplied is 12W .
Can you calculate thew current which must be supplied?
The time between peaks is 0.01s (half a cycle)
Can you calculate the charge that flows in this 0.01s?
This charge comes from the capacitor. If you know the voltage change is 0.05V and also know the charge that must be provided, can you calculate the capacitor value.
Get as far as you can and if you get stuck come back!!!

technician

I put my numbers in my procedure and got C = 0.5F
That formula you have gave 0.48F
Looks like you we on the right track. The formula works and I hope that my steps show how the formula comes about !!!

Elisabeth_91

Thank you very much for your quick reply.

So you mean:
I,load = P / V,dc = 12W / 5V = 2.4 A
Q,c = I,load / (0.5*T) = 2.4 A * 0.01s
C = Q/U = 0.024C / 0.05V = 0.48F

Is this the correct way?
Is it coincidence that is the same result as with my first approach?

Elisabeth_91

What about the transformer ratio, was this thought correct?
Thank you very much!

technician

Yes, you have done more than I would have!
I would just say ratio = Vin/Vout = 220/5 = 44 to 1
One thing to realise that these calculations, in practice, only need to be 'near enough'.
To produce a supply of exactly 5V +/-1% would probably involve using a further electronic circuit.... but that is another matter.
Also the capacitor value we calculated is a minimum value anything bigger than 0.5F would do a better job.
Well done

technician

also...your post #11 is spot on. I think it is better to work through the physics to get the answer, once you can do this then it is OK to use the formula.
well done

gneill

Don't forget to account for the diode voltage drops! The 5V +/-1% specification puts a pretty tight constraint on the allowed peak voltage (Vp), which will follow the peak voltage supplied by the bridge rectifier.

Attached Thumbnails

 

technician

To calculate C I did this:
charge Q = I x t where t is the time for 1/2 cycle (full wave rectification) =1/2f
Q = I/2f
C = Q/V (V is the ripple voltage)
C = 1/2fV

You equation is V = 1/2fC

Both methods are exactly the same

NascentOxygen

I'm guessing that you averaged the full wave rectified waveform to determine this DC value? That analysis only applies where there is no filter capacitor, so is not applicable to your circuit. In your circuit, the big filter capacitor charges to the peak value of the AC and holds this voltage until the next peak. So the DC output will be roughly equal to the peak of the AC (less diode drops).

You calculated 0.5F. That's 500,000 microfarads so is a very large capacitance.