Trying to answer a successive approximation question

[Femme_physics]

The following component is connected to a reference voltage of Vref = 6V. The component is given the value (2C)₁₆ to convert. Calculate Vout.

http://img69.imageshack.us/img69/7396/figuringout.jpg

Basically I treated this supposedly successive approximation converter like any other converter is this calculation..hope it's valid?

 

[I like Serena]

Looks good to me.

 

[Femme_physics]

Thank you!

 

[NascentOxygen]

One tiny error...

 

[Femme_physics]

One tiny error...

What? :uhh: What could that be?

 

[NascentOxygen]

What could that be?

What we're discussing in your other thread. :uhh:

 

[Femme_physics]

Which? I made way too many heh...

 

[NascentOxygen]

Which? I made way too many heh...

I've suggested they create another sub-forum, Femmes_Forum. ☺

 

[Femme_physics]

Lol ;)

 

[Femme_physics]

Did I actually made a tiny error? Can you please point it out, I can't see it.

 

[Femme_physics]

I need to provide an explanation of how this A/D converter with 8 bits work based on successive approximation...but I'm still not sure I understand how successive approximation works. According to my notebook,
"
In this type of converter there is a logic system that's comprised of a shift register. The logic system provides a logic '1' to DAC from the MSB till the LSB, although if the comparator outputs '0' the logic system reboots the bit and this way you get binary digit that gets closer to the final number in each period. And Vout gets closer to Vin.
"

...But if the logic system REBOOTS the bit how come we get a binary number closer to the final number?

If I reboot my computer it just reboots my computer, it doesn't get me closer to any value.

 

[I like Serena]

For starters, it's a DAC and not an A/D converter.

"Rebooting" the bit only means that it sets the bit to zero.
It's similar to rebooting your computer, which sets ALL bits to zero. ;)

 

[Femme_physics]

For starters, it's a DAC and not an A/D converter.

Well they've made a mistake in the question...don't look at me.

"Rebooting" the bit only means that it sets the bit to zero.
It's similar to rebooting your computer, which sets ALL bits to zero. ;)

Yes, but Successive Approximation graph is like this:

http://img85.imageshack.us/img85/7590/sasan.jpg

How...does...it do it?

The explanation doesn't let me know that

 

[I like Serena]

Well they've made a mistake in the question...don't look at me.

I am looking at you. :)
Your problem statement shows a DAC, but a successive approximation converter is an ADC...

Yes, but Successive Approximation graph is like this:
http://img85.imageshack.us/img85/7590/sasan.jpg

How...does...it do it?

The explanation doesn't let me know that

So we are talking about an ADC now.

It starts with the most significant bit, which corresponds to the number 128.
In your case the input has a higher voltage, so this bit is set, and we move on the the second bit.

The second bit corresponds to the value 64, for a total of 128+64=172.
In your case the input has a lower voltage, so this bit is reset (or "rebooted" if you will).
So we remain at 128 and try the 3rd bit next (corresponding to 32, for a total of 128+32=160).

And so on...

 

[Femme_physics]

So it's basically doing guesswork based on constant numbers?

I don't see how could it be necessarily faster than the continuous method?

I am looking at you. :)
Your problem statement shows a DAC, but a successive approximation converter is an ADC...

Ah..you're right, the question is not about the pic I posted

 

[I like Serena]

So it's basically doing guesswork based on constant numbers?

I don't see how could it be necessarily faster than the continuous method?

Not guess work, but successive measurements which determine each bit.

In 8 steps the analog input signal is converted into the 8-bit number 175.The alternative method that counts from 0 up, would need 175 steps to count up to 175.Now I'd say that 8 steps is a marked improvement over 175 steps.
(It's a gem in electronic engineering. ;)

 

[Femme_physics]

Why do we even use the continuous one if it's so crappy? A matter of cost?

 

[I like Serena]

I think it's a matter of exercise and education.

If they'd give you the schematic of a direct conversion ADC, that'd be pretty overwhelming.
But the principle given by a count-from-zero circuit makes the material understandable.
And ultimately it does the same thing, just slower.

 

[Femme_physics]

Ah...understood. :) Perfectly... I like it. Thanks. Do you know what made Nascent Oxygen say my calculation was wrong?

 

[I like Serena]

I believe NascentO₂ meant there should be (2⁸-1) in the denominator instead of 2⁸.
As far as I'm concerned both would be okay.

Since your teacher gave you 2⁸ in the denominator, I'd say there was no error.

 

[Femme_physics]

I am looking at you. :)
Your problem statement shows a DAC, but a successive approximation converter is an ADC...So we are talking about an ADC now.

It starts with the most significant bit, which corresponds to the number 128.
In your case the input has a higher voltage, so this bit is set, and we move on the the second bit.

The second bit corresponds to the value 64, for a total of 128+64=172.
In your case the input has a lower voltage, so this bit is reset (or "rebooted" if you will).
So we remain at 128 and try the 3rd bit next (corresponding to 32, for a total of 128+32=160).

And so on...

Just to clarify,

8 bits =256

10 bits = 1024etc etc...?

I believe NascentO₂ meant there should be (2⁸-1) in the denominator instead of 2⁸.
As far as I'm concerned both are okay.

Since your teacher gave you 2⁸ in the denominator, I'd say there was no error.

Gotcha :)

PS how fast am I?

 

[I like Serena]

Just to clarify,

8 bits =256

10 bits = 1024


etc etc...?

Yes.

Gotcha :)

PS how fast am I?

Wheeeeeeeeeeeeeeeeeeee! :D

 

[Femme_physics]

hehe..you rock!

When I say:8 bits =256

10 bits = 1024I know the left side is called bits...what do you call the right side? Number of values?

 

[I like Serena]

Yes.

8 bits means that the number of possible values is 256.

Furthermore the most significant bit represents the value 128.
And the least significant bit represents the value 1.

 

[Femme_physics]

Thanks for the clarification...ohh a big blog update is coming up soon :)

 

[I like Serena]

You seem to be enthusiastic about electronics now! :)
So are you going to electrify cardboard men any time soon?

I'll be waiting for your blog update!

 

[Femme_physics]

Oh yea, I'm always super enthusiastic before an external test. Truth is we got 3 more months but we haven't covered "power systems" good enough (translating that term from Hebrew). Worst of all, we were given a notebook without final answers written out, and our teacher seems to be neglecting a lot of material and letting us figure a lot for ourselves. (he's a good teacher in terms of explaining the material, just negligent in terms of scope of material since it's his first year teaching).

I made it a personal mission to help my classmates (and myself) get to the answers and be able to explain it. I plan to volunteer my time in explaining electronics to struggling classmates. I solved nearly all of the exercise books in terms of the stuff we were taught so far. It's passover break so I was finally able to get a lot of work done!

Thanks a lot to you all. Yea, really enthusiastic about electronics indeed! :) NascentOxygen wasn't joking when he said they ought to open a femme_physics subforum :P

I'm getting my 1st year mechanics groove back on!

Thanks to you all...really...

 

[I like Serena]

Volunteering time to help classmates?
Where did you get that from?

 

[I like Serena]

I just checked your blog... but... where are the solutions to the electronic exercises?