Questions about biasing an NPN transistor

[Heidi]

Suddenly I think of one thing - the strike voltage itself at 28°C might be changing as well - among different devices or even devices of the same type.

Did I interpret the graph correctly?

Graphs of this kind may carry much more information I believe, but sometimes for learners it might be confusing too, such as the semilog plots, until now I still don't quite understand what its power or value really is, or why they have such power. However, I think it's just a matter of time, I will ultimately get a better understanding - hopefully : )

 

[MrAl]

Hi,

Oh yes, i see where you are coming from now. It takes a little experience with these kinds of things, where the one thing is relative to another thing rather than just one set value.

For example, although the strike voltage may change between the same exact part numbers made by the same manufacturer, they will not show that data the same way, but will use a statistical plot instead that gives us an idea how many pieces can be expected to deviate from the mean where the mean is like how "most" of the units behave. For example, out of 100 units maybe 90 will fit close to the mean by some error margin, while 80 will fit within a larger error margin. They dont always show that data though in the data sheet itself, you have to look on the manufacturer's site to see if they publish this data.
When you read the main data sheet, you assume they are talking about the mean. Later when you do the design, you may want to refer to the statistical data in order to ascertain the risk associated with going by the mean and perhaps make adjustments to the circuit.

As far as a semi log plot, they use that when one variable is better shown on a linear scale and the other varies widely. For the linear plot the data is usually of interest over the entire range without too much difference in significance between points, while the log axis is used to show a lot of range but without showing every single data point. For example, the linear scale may run from 0 to 10 in steps of 1, while the log scale may run 1,10,100,1000,10000, etc. That's because the difference between 10 and 11 on the log scale is not as interesting as the difference between say 10 and 20 or 10 and 100. This could be frequency for example, where if we know what the amplifier does at 10 Hertz we more or less know what it does at 11Hz (so we dont need 11 Hertz plotted with as much resolution), but we still want to know what it does at 20Hertz or 100 Hertz.
So the log plots are used when the significance between data points is not as great as between larger groups of points (like 10 and 100) and this helps to cover a much wider range of data. For example, if we had to plot the response for frequencies from 1Hz to 1Mhz we'd have to plot a million points, and even more significant is the fact that the response does not change that much between points like 999998 to 999999 Hertz, but it does change significantly between points 100000 and 1000000 Hertz or maybe even between 100000 and 200000 Hertz. So instead of having a plot that includes every single point we just use 1,10,100,1000,10000,100000,1000000.
Note that we can plot between 1 and 10 without too much difficulty:
1,2,3,4,5,6,7,8,9,10
But when it comes to doing 1 to 100 we'd be there forever, and if we shorten it to decades (linear):
10,20,30,40,50,60,70,80,90,100
which is not too bad, but then we run into the same problem when we try to do the same for 10 to 1000.
Using the log scale means we only have to show a few points per decade to get the main idea of what is going on across.

One of the things you can do to help understand this kind of thing is you can work through several examples of a design, trying to make it work the way it should, then try to figure out what is important by comparing designs. Try to figure out what can go wrong and how you can make it better.
I know it's not as easy as having a drawn out procedure, but sometimes that's the way it goes

 

[Heidi]

Thank you, MrAl.

Another problem about the semi-log plot that has been confusing me is:
Why is the distance between 1 and 2, or between 10 and 20, or between 100 and 200 etc largest? For example, the following plot shows that the distances between points are not the same, what is the advantage?

I noticed that log2 is located at about 3/10 of one unit, log3 is about 1/2 of one unit etc, what profit can we get by doing this?

 

[Heidi]

My question is: Why do we use the scale A instead of the scale B shown below? What's the advantage scale A is over scale B?

I mean if the X-axis indicates frequency, we can make not only 1Hz, 10Hz, 100Hz, 1000Hz ... equally spaced, but also make 1Hz, 2Hz, 3Hz ... 10Hz, 20Hz, 30Hz ... 100Hz ... equally spaced. Why don't we adopt this simpler scheme?

Thank you!

 

[MrAl]

Thank you, MrAl.

Another problem about the semi-log plot that has been confusing me is:
Why is the distance between 1 and 2, or between 10 and 20, or between 100 and 200 etc largest? For example, the following plot shows that the distances between points are not the same, what is the advantage?
View attachment 86754
I noticed that log2 is located at about 3/10 of one unit, log3 is about 1/2 of one unit etc, what profit can we get by doing this?

Hi again,

I am replying with two posts for the separate questions to keep things a little more clear hopefully.

That's just how the log function works, it compresses some ranges and allows other ranges to be wider. It helps us because of the way some things respond in nature, or how they relate to reality.
For example, the 'difference' between 1 and 2 is the same as the 'difference' between 9 and 10, yet these two ranges do not appear to take up the same spacial span. Subtracting, 2-1=1, and 10-9=1, so they 'should' be the same. However, if we look at the ratios we see a whole different story:
2/1=2.00
10/9=1.11

Now we see something different, jumping from 1 to 2 we have to jump by 100 percent, while jumping from 9 to 10 we only have to jump by 11 percent. That's quite a 'difference' now, and now the jump from 9 to 10 does not look as important as the jump from 1 to 2 anymore.

This is actually quite significant too, because often our devices do not change in response that much for incremental changes that are small relative to the initial value (like 9 to 10) while the response change can be much more significant for small changes that are large relative to the initial value (like 1 to 2).

A good example of this is the open loop frequency response of an op amp. If we look at the data sheet for an LM358, we see a graph of voltage gain vs frequency. The frequency points on the x axis of the graph shown are:
1,10,100,1k,10k,100k,1M,10M
This means that the change between 9Hz and 10Hz has about the same significance to a design as the change from 90 to 100, and also about the same as the change from 900 to 1000, and 9k to 10k, etc.
So in the end, the change from 9Hz to 10Hz has about the same significance as the change from 900kHz to 1000kHz, even though they are very different frequencies and between 9 and 10 we only have 1Hz while between 900kHz and 1000kHz we have 100kHz, which is a hundred thousand times greater.

 

[MrAl]

My question is: Why do we use the scale A instead of the scale B shown below? What's the advantage scale A is over scale B?
View attachment 86764
I mean if the X-axis indicates frequency, we can make not only 1Hz, 10Hz, 100Hz, 1000Hz ... equally spaced, but also make 1Hz, 2Hz, 3Hz ... 10Hz, 20Hz, 30Hz ... 100Hz ... equally spaced. Why don't we adopt this simpler scheme?

Thank you!

Hi,

This is one of those cases where you should sit down, roll up your sleeves, and dont be afraid to get your hands dirty. Sit down and try to graph the plot of voltage gain vs frequency for the LM358 and see what happens.

Also, there are two ways of interpreting your question. The first way means we keep the same spacing for every frequency, the second way means we keep the same spacing only between one such group like from 1 to 10 or from 10 to 100, but still allow variable spacing. So we would see 1,2,3,4,5...10 for the first group, and 10,20,30,40,50..100 for the second group.
For the first interpretation we would have far too many points to plot.
For the second we would see a graph which is very wavy rather than have a straight line, because things in nature do not usually follow that kind of rule. So we'd see a graph that had many droops in it or many bumps in it, when doing it the other way we'd see a nice smooth curve even though we use the log scale.

If you sit down and try to graph a curve like that of the op amp frequency response you quickly get a feel for this. That's what i was trying to get at in my other previous post about two posts back. Trying things out ie testing the ideas that you have can get you going a long way. If you think something is better another way, then try it and see what happens. Once in a while it may turn out that it makes it better for you yourself alone and so you may still find it useful even if others dont like it, but sometimes it could turn out that it could make it better for others too.
Your apparent interesting in these subjects tells me that you are one of the few who are willing to take this last step and find things out by experiment. Also, as you learn to design your own experiments, you get better and better at this so you progress faster and faster.

 

[Heidi]

Hello, MrAl

Thanks for the encouragement and reminding me of the value of 'just do it'.
I'll do it.

Many thanks!