Art of Electronics Third Edition Exercise 2.24 - transistor current source

[StevieOnlyR]

Hi all, forum newbie here

This question is directed to fellow AoE 3 owners. I won't include a picture as I am concerned with copyright

My question is about (b) in Exercise 2.24 (page 125): a transistor current source with a voltage divider at the base to provide DC bias and an emitter resistor to "set" the current.
The authors write that as the transistor's β varies from 50 to 100 over the full compliance voltage range, the output current will vary, which is caused by two effects.

The first effect should be the β variation changing the load on the voltage divider at the transistor's base. Now I reckon the second effect is the Early effect (V_BE varies with V_CE edit: at constant I_C). What confuses me though is that they specifically ask how the Early effect influences the output current in (c). It doesn't really make sense to me to ask for something in one question and have the answer for it right there in the next question.

Am I missing something here?

[LvW]

At first, in my version of AoE (second edition) there is no exercise 2.24.
nevertheless, I think I can give some comments:
1) In case of a voltage divider at the base (which provides the DC base bias) it is our intention to make this divider as low-resistive as possible. In this case, there will be only a minor change in VB caused by a varying DC base current (as a result of beta tolerances). It is common practice to select resistors so that the current through the divider is approximately 10 times the nominal base current (or even larger).
In this case, we say that we provide a (nearly) "stiff" base voltage Vb.
However, the divider chain must not be too low-resistive with respect to (a) power consumption and (b)  signal input resistance.
Hence, a trade-off is necessary between two conflicting effects - this is quite normal in electronics; we always face the problem that improving one parameter will adversely influence another system parameter.

2.) This has nothing to do with the well-known Early-effect. 

Quote:" VBE varies with VCE"

This statement is quite misleading - in fact it is wrong! VBE does NOT vary.
What happens is the following: When we increase VCE the collector current Ic increases as well (caused by shrinking of the depletion area).
Now - if we want to bring the current Ic back to the previous value the voltage VBE must be externally reduced.
In short: VBE does not vary (automatically), but we must reduce VBE in order to keep Ic constant (for increasing VCE).
_______
I hope I could express myself clear enough.

[StevieOnlyR]

At first, in my version of AoE (second edition) there is no exercise 2.24.
nevertheless, I think I can give some comments:
1) In case of a voltage divider at the base (which provides the DC base bias) it is our intention to make this divider as low-resistive as possible. In this case, there will be only a minor change in VB caused by a varying DC base current (as a result of beta tolerances). It is common practice to select resistors so that the current through the divider is approximately 10 times the nominal base current (or even larger).
In this case, we say that we provide a (nearly) "stiff" base voltage Vb.
However, the divider chain must not be too low-resistive with respect to (a) power consumption and (b)  signal input resistance.
Hence, a trade-off is necessary between two conflicting effects - this is quite normal in electronics; we always face the problem that improving one parameter will adversely influence another system parameter.

Thank you for the elaboration, I understand that we want to provide a stiff base voltage to minimize the effect of base current variation.


Quote: "2.) This has nothing to do with the well-known Early-effect."

I know that the Early effect doesn't have anything to do with providing the DC bias. However, in the case of a transistor current source I guess it has an effect on output current: If V_CE increases and we want constant I_C we have to reduce V_BE. Therefore we have a bigger voltage drop across the emitter resistor, which increases I_C.

Concerning my "(V_BE varies with V_CE)" statement: you provided the technically accurate description of the Early effect. I should have included "at constant I_C" from the beginning.

[LvW]

Quote: If VCE increases and we want constant IC we have to reduce VBE. Therefore we have a bigger voltage drop across the emitter resistor, which increases IC.

If you want to describe the effect of an emitter resistor Re, you should realize that an increase in Ic will also increase the voltage across this resistor RE and thus reduce VBE, which will decrease (bring back) Ic (nearly) to its previous value. This is the classical negative feedback effect.which stabilizes Ic against temperature variations.

[StevieOnlyR]

Of course, negative feedback plays a role too.
In my view, the following happens: The voltage at the base is held constant by the input resistor divider. Therefore, a reduction in Vbe (as a result of an increase in Vce at constant Ic) will increase the voltage across RE and hence the current flowing through it. Now, the increased Ic will in turn increase Vbe. This increase in Vbe, however, is not even close to compensating the reduction caused by the Early effect (for most cases - this of course depends on bias conditions / resistor values).

Feel free to correct me if this is complete BS

Vcc=10V
R1=8.2k
R2=1.6k
RE= 1.5k

[bd139]

Have a read through "Learning the Art of Electronics" (AoE companion book) section 5S.2. This contains a walk through of the early effect.

Don't have the book? Well conveniently it's in the free sample here as linked from the official web site: https://www.book2look.com/vbook.aspx?id=9780521177238

Page 222 onwards.

The explanation in there is very good and there are examples and scenarios for it.

[StevieOnlyR]

Have a read through "Learning the Art of Electronics" (AoE companion book) section 5S.2. This contains a walk through of the early effect.

Don't have the book? Well conveniently it's in the free sample here as linked from the official web site: https://www.book2look.com/vbook.aspx?id=9780521177238

Page 222 onwards.

The explanation in there is very good and there are examples and scenarios for it.

Thanks, I'll take a look