Hi guys! Hope all is well. I just started learning about NPN transistors, which i think are pretty cool. Like all newbies, I have a question about them. In the schematic below, why did the designer of the circuit decide on using a 10K resistor for the base current? What is the math behind it?
The transistor is a 2N3904 NPN Bipolar Junction Transistor.
Thank You for your answers.

 

All calculations rely on Ohm's Law.
First, figure out how much current will be flowing through the LED when the transistor is turned on.
You can make a wild approximation that the current = 9V/1kΩ = 9mA.
If you take into account the voltage drop across the LED is about 2V
a better approximation of the current = 7mA.
This is going to be the collector current Ic.

Next, approximate the base current Ib to be Ic/10 = 0.7mA
A wild guess would put the base resistor at 9V/0.7mA = 13kΩ
If you take the voltage drop across the base-emitter junction to be 0.7V
a better approximation would be 8.3V/0.7mA = 12kΩ

10kΩ is a nice round value.

 

Hmmmm not to discredit MrChips, but I've always been under the impression that base current controls collector current.

So therefore the base current would be the supply voltage minus the base-emitter voltage (probably 0.6 or 0.7 volts) divided by Rbb. The collector current would then be found by multiplying this value by the beta for the transistor.

From there you can apply Ohms law to the resistor to find the volt drop across the resistor, and the voltage across the LED would be given somewhere. The remaining voltage (as per KVL) would be dropped across the emitter-collector junction.

 

Two problems with that approach,
1) it does not tell you how to calculate the value of the base resistor,
2) you don't know what is the transistor current gain beta.

In my example, I simply assume that the transistor is in saturation mode and the current gain is 10.

 

Hmmmm not to discredit MrChips,

Hmmmm, don't worry, you didn't (because he's right).

but I've always been under the impression that base current controls collector current.

In the active region it does -- or at least that is a useful model -- but in this case you are wanting to drive the transistor hard into saturation.

The common rule of thumb is that, for small signal transistors operating well below RF, to do this you want the base current to be about 10% of the collector current. In practice, you will almost always be there if you use 1% since the β is usually a few hundred, so using anything over a few percent should work.

Given this circuit topology, making Rb = 10Rc gives you the 10%, to within the back of an envelope. In actuality it will be a bit over 10%.

 

Mr chips is incorrect on three points.
1. All calculations do not rely on Ohm's law:
I=C(dV/dT), E=MC(squared). etc.

2. For analysis of the circuit, nobody but the designer can tell why he used a 10K base resistor. Anything else is a gross assumption.

3. The collector load determines the collector current if, and only if, the base current is adequate. A reasonable assumption for beta is given in the data sheet as: Ib=1mA, Ic=10mA and Vce<0.2V, so that assumption is validated.

Designing descrete transistor circuits can be very complicated just like designibg op amp circuits, and this is why there is discussion bythe senior members of this community. Don't be led astray by the very experienced people on this site, I am one of them, who use all kinds of approximations based on experience. If I had to design that circuit for low production (less than 100) I would simply use 10K and 1k resistors without doing any calculations. When I was paid to design high volume production circuits I might work on a one or two transistor circuit for several weeks---sounds stupid but when you consider that I could optimize the circuit, improve noise immunity, and save 3 cents on a million volume design ($300,000) it make sense.

 

Mr chips is incorrect on three points.
1. All calculations do not rely on Ohm's law:
I=C(dV/dT), E=MC(squared). etc.

Statements must be taken in the context with which they are made. Trying to pretend the MrChips was claiming that every calculation in the universe relies on Ohm's Law -- which would seem to be what you are implying by bringing in Einstein's equation relating energy and rest mass -- is absurd. He was clearly merely stating that all of the calculations he was about to present for this circuit were based on Ohm's Law.

2. For analysis of the circuit, nobody but the designer can tell why he used a 10K base resistor. Anything else is a gross assumption.

A distinction without meaning. Part of the skills necessary in virtually any professional field is the ability to look at someone else's work and come to reasonable conclusions regarding why that person did what they did or, leaving motivations aside, what the practical impact is of what they did. To say that it is a gross assumption to conclude that the purpose of a resistor that is in series with an LED is to limit the current in the LED to an acceptable level because only the designer can tell us why he used that resistor, even if clinically true, is meaningless.

3. The collector load determines the collector current if, and only if, the base current is adequate. A reasonable assumption for beta is given in the data sheet as: Ib=1mA, Ic=10mA and Vce<0.2V, so that assumption is validated.

First off, the discussion was very much specific to ensuring that this is the the condition that holds. So pointing out the MrChips is somehow wrong because this condition has to apply is, again, rather pointless.

Second, if you were to set up those conditions and lower Ib to 0.9mA you would almost certainly not see any change in Ic. You might well have to lower the base current to under 0.1mA to start seeing any meaningful change in Ic. The whole notion of β (h_FE) is applicable only when the transistor is active and operating in a (largely) linear regime -- it is, after all, a linear two-port parameter It really just doesn't apply or have any meaning when in saturation.

Designing descrete transistor circuits can be very complicated just like designibg op amp circuits, and this is why there is discussion bythe senior members of this community. Don't be led astray by the very experienced people on this site, I am one of them, who use all kinds of approximations based on experience. If I had to design that circuit for low production (less than 100) I would simply use 10K and 1k resistors without doing any calculations. When I was paid to design high volume production circuits I might work on a one or two transistor circuit for several weeks---sounds stupid but when you consider that I could optimize the circuit, improve noise immunity, and save 3 cents on a million volume design ($300,000) it make sense.

So.... if I can figure out a way to save 3 cents each on a million volume design of yours, would you be willing to pay me $50,000 up front for it and you can pocket all the savings as they are realized?

One of the ways that inexperienced people gain some experience (or at least some insight) is by doing exactly what the OP did. Ask experienced people why simple circuits were designed the way they were and what steps they would have taken to come up with the component values to that, or a similar, design. I particularly liked that he specifically asked for the math behind the choices. Now, you can quibble about how describing how we would have picked the values amounts to a "gross assumption" regarding why the original designer chose their values, but that is not really what the OP is asking for; instead, he is asking for some insight into how component values for a circuit like this would be chosen so that he might be able to better choose them himself down the road.

 

I said what I said for the newbie's benefit. I am not interested in your distorted conclusions.

 

"A distinction without meaning. Part of the skills necessary in virtually any professional field is the ability to look at someone else's work and come to reasonable conclusions regarding why that person did what they did or, leaving motivations aside, what the practical impact is of what they did."




I totally agree with that. I've seen a ton of strange things in the Metalworking Trades. Some of the Engineers should have had machining training first, before drawing.

 

In Mr Hale's words, "why did the designer of the circuit decide on using a 10K resistor for the base current?" Mr Hale did not ask for reasonable conclusions or the practical impact of the conclusions; he asked why and MrChips answered a different question. If we are not precise here what are we but a bunch of ego inflaters?

Without any specific reference the statement, "All calculations rely on Ohm's Law." is misleading . This kind of misleading statement can send a newbie down the wrong path, the statement serves no function beside ego inflating on the writer's part.

WBahn-"So.... if I can figure out a way to save 3 cents each on a million volume design of yours, would you be willing to pay me $50,000 up front for it and you can pocket all the savings as they are realized?" You want a sweetheart deal, but Yes I agree, where should I send the origional circuit and specifications, and will you post a similar performance bond?

 

@ramancini8 - You're totally off your rocker!

 

So here is my revised explanation to satisfy Mr Ramancini's criticisms.

1) The formula I will use to determine the value of the base resistance will be Ohm's Law.

2) Since only the original designer can say why he used a 10kΩ base resistor, let me see how I would come up with an appropriate value on my own.

3) The most common resistors I have in my collection are 100Ω, 1kΩ, 10kΩ and 100kΩ with a few values in between.
The maximum specified current for my LED is 20mA. I don't want to stress the LED and I don't mind if the LED is slightly less bright. I will settle for an operating current of 10mA.
A 1kΩ resistor in series with the LED will give about 9V/1kΩ = 9mA. That's close enough. I've got lots of 1kΩ resistors to spare.

I want the NPN driver transistor to present the lowest possible load on the preceding circuit. I can try a 100kΩ base resistance. This will give a base current of about 9V/100kΩ = 90μA. That sounds nice and low. I would need a transistor with a current gain of about 100 to get a collector current of 9mA. That sounds ok.

But what happens if the transistor I end up installing has a gain less than 100?
I've been told that as the transistor reaches saturation mode the gain is reduced.
I'll go on the safe side and increase the base current.
If I use a resistor of 10kΩ, this gives a base current of about 0.9mA.
Hence even if the current gain happens to be as low as 10, I can be guaranteed that the transistor is in saturation mode and I will get the 9mA or there about through my LED.

So I'll stick with the 10kΩ base resistor.

 

MrChips, your inadequacy is no excuse for insults. Excellent explanation; why couldn't you do that without the chicken dancing?

 

MrChips, your inadequacy is no excuse for insults. Excellent explanation; why couldn't you do that without the chicken dancing?

Mr Chips....

Maybe it's the long, bad winter we've been having

Still many inches of snow on the ground "up here"
Someone said spring is coming

 

In Mr Hale's words, "why did the designer of the circuit decide on using a 10K resistor for the base current?" Mr Hale did not ask for reasonable conclusions or the practical impact of the conclusions; he asked why and MrChips answered a different question. If we are not precise here what are we but a bunch of ego inflaters?

It would be interesting for Mr. Hale to state which response better served his objectives.

If you want to pretend you are a robot and can only extract semantics from words by way of strict application of grammar syntax, then by all means be that way. Humans are terribly sloppy communicators in that regard but we have evolved highly sophisticated abilities to extract the proper semantics from very sloppy grammar by using inference and other devices.

I generally find that my customers are much happier with the result when I work to figure out what they really meant and want as opposed to just blindly going by the strict meaning of the sentences in the original specification. Now, it should go without saying but I'm guessing that might not be the case here, I consult with them along the way asking a lot of, "Are you sure you really meant this? I think that will cause these problems, so perhaps you meant this instead."

Without any specific reference the statement, "All calculations rely on Ohm's Law." is misleading . This kind of misleading statement can send a newbie down the wrong path, the statement serves no function beside ego inflating on the writer's part.

The specific reference was the context of the discussion. Within that context it was a quite useful statement.

WBahn-"So.... if I can figure out a way to save 3 cents each on a million volume design of yours, would you be willing to pay me $50,000 up front for it and you can pocket all the savings as they are realized?" You want a sweetheart deal, but Yes I agree, where should I send the origional circuit and specifications, and will you post a similar performance bond?

No need for a performance bond. I stated "IF" I can figure out a way to save 3 cents on the unit cost. I did not guarantee I could do it. And you only have to pay be $50,000 upon successfully doing so. And, I agree, it is a very sweetheart deal because I get $50,000 up front and you won't recover that until you've sold nearly 1.67 million units and won't realize a $300,000 in total savings until you've sold ten million units. Sure you still want to send the original circuit and specs?

 

MrChips, your inadequacy is no excuse for insults. Excellent explanation; why couldn't you do that without the chicken dancing?

Chicken Dance:
http://www.youtube.com/watch?v=6UV3kRV46Zs

To be perfectly accurate... What does this have to do with electronics ?

 

MrChips caught on---my purpose was to improve his communication not fight.

tubeguy and WBahn just want to fight with no good purpose. Gentlemen, I published thousands of pages of electronics copy, all edited, tested and checked, so I can and will help people tell their story in the best possible way. If you think I was hard on MrChips you should have seen my editors work on me.

 

My intent was not to fight, but to lighten the mood a a bit.

The many knowledgeable members on this forum contribute because they enjoy helping others. As far as I know, they don't get paid for this.

Arguing can be a positive thing, to arrive at the best solution. But, it's possible to disagree while still showing well-deserved respect.

 

MrChips; I should have put my comments to you in an email. Then we would have had a profitable conversation without the distractions of other contributers trying to defend you. I apologize for being being rude and using a public forum to transmit a critique. Rest assured that I will not post public comments about another person's work. I thought about how I would have liked it if my EDN editor had made her critiques public, and It was an ugly thought. Please forgive me.

I apologize to the "defenders" for any harm I might have cause them. Please forgive me.

For me; end of topic.

 

I can judge a person's character when they are capable of admitting they made a mistake and apologizes for doing so. Your apologies accepted.