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Let start analyzing Analog microelectronics: Bandgap Reference

Offline blackfin

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Let start analyzing Analog microelectronics: Bandgap Reference
« on: September 14, 2009, 04:49:52 PM »
Hopefully this will roll along. Let's start analyzing the Bandgap voltage reference. For a voltage reference, it should be insensitive to changes in power supply and temperature and the Bandgap volatge reference is one of them. There are many variation for this and I am posting a simple Brokaw cell. Care to know how it operates? (without cheat) ;)

Offline TinTopHack

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Re: Let start analyzing Analog microelectronics: Bandgap Reference
« Reply #1 on: September 14, 2009, 06:11:02 PM »
NS has a good write up about this. Please visit: http://www.national.com/rap/Application/0,1570,24,00.html
The world, as everybody knows, is analog; unless, of course, it's digitized.

Offline blackfin

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Re: Let start analyzing Analog microelectronics: Bandgap Reference
« Reply #2 on: September 14, 2009, 07:27:39 PM »
Care to know how to identify the function of each element? With the knowledge from the write-up, how is the bandgap voltage generated from the simple brokaw cell?

Offline TinTopHack

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Re: Let start analyzing Analog microelectronics: Bandgap Reference
« Reply #3 on: September 16, 2009, 10:20:46 AM »
Pre,
This will need some time because it needs some review. If you can start the discussion, please start.  Dagdagan ko na lang.
The world, as everybody knows, is analog; unless, of course, it's digitized.

Offline blackfin

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Re: Let start analyzing Analog microelectronics: Bandgap Reference
« Reply #4 on: September 18, 2009, 10:18:46 PM »
Ok. let's start with some basic formulas first. Then I will expound on the principles later.

Review of bipolar transistor base-emitter voltage formula as simplified Vbe = Vt*ln(Ic/Is) where
Vt = kT/q is the thermal voltage at specific temperature
k is Boltzmann's constant ~ 1.38x10e-23 J/degK
T is temperature at deg Kelvin
q is electron charge ~ 1.6x10e-19 Coulombs

We learned from college that the temperature coefficient of Vbe is approximately -2mV/degC and for simplicity sake let's just accept it.
How about the temperature coefficient of Vt, well it is k/q if you differentiate Vt with respect to temperature. Approximately 86.25uV/degC.

Now for some principles:
Most likely the most important characteristics of a voltage reference and even current reference are:
1) It should be stable against any supply voltage variation
2) It should be stable against any temperature variation

So why are we reviewing Vbe and Vt equations? Because these two terms when added together can satisfy the voltage reference characteristics
1) Vbe or Vt doesn't have supply volatge in their equations
2) With Vbe having a negative tempco and Vt having a positive tempco, adding them together would yield almost zero tempco. But the magnitude of Vt needs to be multiplied because its tempco is smaller. Calculating this magnitude is merely dividing the absolute value of Vbe tempco by the Vt tempco which is about 23.

So if we add Vbe and approximately 23 times of Vt, we will get a voltage which would yield almost zero tempco and supply variation independent.

This is the simplest as I could present the bandgap voltage reference.

Next will discuss how to generate magnified Vt and present with the circuit above.

Offline blackfin

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Re: Let start analyzing Analog microelectronics: Bandgap Reference
« Reply #5 on: September 26, 2009, 07:31:03 PM »
Now let's start discussing the circuit.
Let's concentrate on Q3, Q2, Q1, R1 and R2.
Q3 is split collector type transistor and is actually a current mirror, meaning the reference current which is also the emitter current going to Q2 is 'mirrored' (maybe equal or multiple/fraction) as collector current of Q1. Let's term this as Iref.
Now looking at Q2, the 10 actually refers to the number of emitters. It is as if there are 10 parallel transistors comprising Q2.
Now the Iref will be divided equally by 10 as collector current of each of 10 parallel transistor of Q2, so Ic2 = Iref/10.
Now Q3 as we say is current mirror and is 1:1 mirror so Ic3=Iref.
Now we calculate the Vbe of Q2 and Q1 as
Vbe2 = Vt*ln(Ic2/Is) = Vt*ln((Iref/10)/Is)
Vbe1 = Vt*ln(Ic1/Is) = Vt*ln(Iref/Is)
I forgot to mention that Is is the saturation current and is the same for both type of monolithic transistor on the same process.
Let's KVL on the bases of Q2, Q1 and R1:
Vbe2 + Vr1 = Vbe1
Vbe1 - Vbe2 = Vr1 : the delta of Vbe is across R1
Vt*ln(Iref/Is) - Vt*ln((Iref/10)/Is)  = Vr1
Remembering logarithmic properties that ln(a/b) = ln(a) - ln(b)
Vr1 = Vt*ln (10)

How do we calculate K:
Ir1 = Vr1 / R1 is actually the same current on Ic1 because of the current mirror Q3
Ir2 = Ir1 + Ic1 = Ir1 + Ir1 = 2Ir1 = 2Vt*ln(10)/R1

Now how do we get Vref:
Vref = Vbe1 + KVt
Vref = Vbe1 + Ir2*R2 = Vbe1 + R2*2Vt*ln(10)/R1
Vref = Vbe1 + (2R2/R1*ln(10))*Vt
so K = 2R2/R1*ln(10)

So we now have bandgap reference voltage.

Q4 is for current boost. How about R3,Q5,Q6 and Q7? What is the purpose of these?
Next time we'll discuss about it.

Hope you like it :)

Offline TinTopHack

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Re: Let start analyzing Analog microelectronics: Bandgap Reference
« Reply #6 on: September 26, 2009, 09:44:29 PM »
Keep going Bro.
The world, as everybody knows, is analog; unless, of course, it's digitized.

Offline ネ㑟㑯㑠

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Re: Let start analyzing Analog microelectronics: Bandgap Reference
« Reply #7 on: September 26, 2009, 09:51:31 PM »
nice tutorial bro....

ito ba yong gamit ng TL431 na voltage ref ic?  hanga kasi ako dito kahit painitin ko ng soldering iron tip wala paring pagbabago sa ref ko.

Offline blackfin

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Re: Let start analyzing Analog microelectronics: Bandgap Reference
« Reply #8 on: September 27, 2009, 09:38:03 PM »
nice tutorial bro....

ito ba yong gamit ng TL431 na voltage ref ic?  hanga kasi ako dito kahit painitin ko ng soldering iron tip wala paring pagbabago sa ref ko.

Check ko yung schematic nya, bandgap reference din sya although wala pa ako exact calculations. Meron kasi delta Vbe generator.

Offline ネ㑟㑯㑠

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Re: Let start analyzing Analog microelectronics: Bandgap Reference
« Reply #9 on: September 27, 2009, 09:40:37 PM »
 ^^^ aa okay....

ganda ng tutorial nyo :)

Offline blackfin

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Re: Let start analyzing Analog microelectronics: Bandgap Reference
« Reply #10 on: September 27, 2009, 10:06:16 PM »
Continuing this one. Consider taking out R3,Q7,Q5,Q6 first.
Since the bandgap core of Q1,Q2,R1.R2 needs biasing current especially base currents for Q1 and Q2, what if there's no base current whatsoever? And specially at very cold conditions where even thermal effects couldn't trickle some base current. Your bandgap core may not start and Vref could be stuck at zero.

This is where R3,Q7,Q5 and Q6 comes into play. It is a start-up circuit.
Let's picture the moment we apply voltage to VCC and Vref is at zero with no base current to your core. Q5 and Q6 (acts as diodes)  will pull current through R3 and will kick start also Q7. When Q7 turns on, it will start supplying base current to Q1 and Q2. Once there's base current on Q1 and Q2, the core will ramp up to its programmed Vref. Once Vref is attained approximately 1.25V, Q7 will be cut-off since the base of Q7 is about 1.4V ( 2 diode drop) and the emitter is 1.25V. This is critical to start-up circuits, once the programmed voltage is attained, it should stop supplying the base current so as not to mess up the core.
Also the R3, Q5 and Q6 branch should consume less current. Notice R3 value which is large resistance.

Hope you like it  :)

Offline blackfin

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Re: Let start analyzing Analog microelectronics: Bandgap Reference
« Reply #11 on: September 27, 2009, 10:18:57 PM »
Pasensya na kung ganun ko present yung explanation. Medyo mahaba kasi kaya divide and conquer style. Saka para di maumay yung bumabasa.