# How accurately does Vbe determine collector current?

#### dsharp02

Joined Aug 8, 2015
17
Page 91 of Art of Electronics Third Edition has a passage that reads in part: "For transistors it is important to realize that the collector current is accurately determined by the base-emitter voltage, rather than by the base current (the base current is then roughly determined by beta) and that this exponential law is accurate over an enormous range of currents, typically from nanoamps to milliamps." I've breaded-boarded up the following circuit and tested it with a number of different 2N3904 and it seems like the collector current is varies from around 10mA to as high as 16mA. Is this spread normal? I would have thought the term "accurately" would have the different transistors with a few percent of each other. How do you know what the Is(T) value is?

Thanks,
Dave

#### WBahn

Joined Mar 31, 2012
26,062
You are comparing apples and oranges. The claim is that Vbe accurately determines Ic in a given transistor. What you are doing is looking at the differences between different transistors (which is known as "matching"). Discrete transistors generally display poor matching characteristics.

The claim they are making (which ignores the effect of the Early voltage, or perhaps is assuming a constant Vce for the sake of the claim) is that if you measure the beta of the transistor at one current and then try to use that to predict the collector current by measuring the base current as the base current is varied you will not get very good results because the beta itself is a fairly strong function of current. If, instead, you determine Is at one current and then predict the collector current as Vbe is varied you will get a much more accurate prediction.

#### hp1729

Joined Nov 23, 2015
2,304
Page 91 of Art of Electronics Third Edition has a passage that reads in part: "For transistors it is important to realize that the collector current is accurately determined by the base-emitter voltage, rather than by the base current (the base current is then roughly determined by beta) and that this exponential law is accurate over an enormous range of currents, typically from nanoamps to milliamps." I've breaded-boarded up the following circuit and tested it with a number of different 2N3904 and it seems like the collector current is varies from around 10mA to as high as 16mA. Is this spread normal? I would have thought the term "accurately" would have the different transistors with a few percent of each other. How do you know what the Is(T) value is?

Thanks,
Dave
View attachment 99376
Accurately? Like a precise base voltage is going to determine collector current? I would say no. Base voltage is determined by base current. Collector current is determined by the load. The description in the book must fit other text in the book, but I would say it is a bad way to describe things.
You can't measure base voltage and determine collector current, can you?

#### dannyf

Joined Sep 13, 2015
2,197
"collector current is accurately determined by the base-emitter voltage, rather than by the base current (the base current is then roughly determined by beta) "

He is essentially saying that a bjt is a voltage controlled device, and I think he is in the minority on that and that description isn't consistent with the physical essense of the device. Hopefully he articulated in the book why he thinks so and why others are wrong.

As to the word "accurately", it depends on what he meant by it. Probably " deterministically" is a better word.

#### joeyd999

Joined Jun 6, 2011
4,425
AOE is referring to Eber-Molls. I agree with Horowitz and Hill 100% regarding Ic vs. Vbe.

If this weren't the case, things like current mirrors and logarithmic amplifiers would be impossible.

#### kubeek

Joined Sep 20, 2005
5,731
... Base voltage is determined by base current...
Base voltage is determined by base current, and base current is determined by base voltage. Just like in a resistor or diode or whatever.
I hope we are not getting into the typical flamewar of which of these views is truer.

#### Bordodynov

Joined May 20, 2015
2,643
The Scatter of the voltage base-emitter for one producer and one type transistor +/-50 mV. This gives the sevenfold scatter a current. I.e. 0.14 - 7 from nominal value.
At scatter 10 mV --> 0.68-1.47 nom.
At scatter 3 mV --> 0.89-1.12 nom.
At scatter 2 mV --> 0.93-1.08 nom.
BCM847BV; BCM847BS; BCM847DS -->
VBE1-VBE2 VBE matching 2mV.

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#### hp1729

Joined Nov 23, 2015
2,304
AOE is referring to Eber-Molls. I agree with Horowitz and Hill 100% regarding Ic vs. Vbe.

If this weren't the case, things like current mirrors and logarithmic amplifiers would be impossible.
Interesting. You couldn't describe the operation of a CURRENT mirror by current operations instead of voltage?

#### hp1729

Joined Nov 23, 2015
2,304
The Scatter of the voltage base-emitter for one producer and one type transistor +/-50 mV. This gives the sevenfold scatter a current. I.e. 0.14 - 7 from nominal value.
At scatter 10 mV --> 0.68-1.47 nom.
At scatter 3 mV --> 0.89-1.12 nom.
At scatter 3 mV --> 0.93-1.08 nom.
BCM847BV; BCM847BS; BCM847DS -->
VBE1-VBE2 VBE matching 2mV.
Accurate? 0.68 to 1.47 is accurate? I must be missing what you are saying.

#### hp1729

Joined Nov 23, 2015
2,304
Base voltage is determined by base current, and base current is determined by base voltage. Just like in a resistor or diode or whatever.
I hope we are not getting into the typical flamewar of which of these views is truer.
When I pull a current through the base the voltage changes as a result. Collector current depends on the collector load, not the base current or voltage. If I remove the collector load completely the base voltage and current still change but collector current does not change at all. So how can we say base voltage "accurately" influences collector current?

#### Jony130

Joined Feb 17, 2009
5,180
hp1729 are you trying to say that the Vbe has no influance on collector current ?
Interesting. You couldn't describe the operation of a CURRENT mirror by current operations instead of voltage?
How can you explain the working principle of a BJT current mirror without involving Vbe then? We can ask the same question about differential amplifier.

#### joeyd999

Joined Jun 6, 2011
4,425
Interesting. You couldn't describe the operation of a CURRENT mirror by current operations instead of voltage?
Be my guest:

#### joeyd999

Joined Jun 6, 2011
4,425
hp1729 are you trying to say that the Vbe has no influance on collector current ?

How can you explain the working principle of a BJT current mirror without involving Vbe then? We can ask the same question about differential amplifier.
You beat me to it by 2 minutes.

#### WBahn

Joined Mar 31, 2012
26,062
When I pull a current through the base the voltage changes as a result. Collector current depends on the collector load, not the base current or voltage. If I remove the collector load completely the base voltage and current still change but collector current does not change at all. So how can we say base voltage "accurately" influences collector current?
Seriously? The claim is only applicable in the active region. Not cutoff and not saturation.

#### kubeek

Joined Sep 20, 2005
5,731
When I pull a current through the base the voltage changes as a result.
Also when I apply voltage to base, the current changes as a result. Your point being?

#### dannyf

Joined Sep 13, 2015
2,197
How can you explain the working principle of a BJT current mirror without involving Vbe then?
Current mirrors work if the two devices are identical.

Whether they are current controlled or voltage controlled is irrelevant. Ie. You can build a current mirror with current controlled devices as well, as long as they are identical.

#### dannyf

Joined Sep 13, 2015
2,197
When I pull a current through the base the voltage changes as a result. C
The reverse can be argued that if you apply a voltage on the be junction current flows through it.

That is not the primary consideration as to whether a device is current or voltage controlled.

#### dannyf

Joined Sep 13, 2015
2,197
Collector current depends on the collector load, not the base current or voltage. I
Within reason, collector current is unrelated to collector load.

#### WBahn

Joined Mar 31, 2012
26,062
Current mirrors work if the two devices are identical.

Whether they are current controlled or voltage controlled is irrelevant. Ie. You can build a current mirror with current controlled devices as well, as long as they are identical.
Yet current mirrors work even when the devices are not identical -- they just aren't perfect mirrors. But they are still well behaved.

You claim that you can build a current mirror with a current controlled device. So replace the transistors in the basic mirror with the basic current controlled current source model of a BJT having a fixed Vbe and then try to explain it's operation.

#### WBahn

Joined Mar 31, 2012
26,062
Let's not lose sight of the TS's question -- which parameter, Ib or Vbe, more accurately predicts Ic (in the linear region). Note specifically that the TSdid not ask whether a BJT is voltage-controlled or current-controlled.

To predict something we need a prediction equation. We really only have two available:

$$i_c \; = \; \beta i_b$$

or

$$i_c \; = \; I_s \( e^{\frac{v_{be}}{\eta V_{th}}} \; - \; 1$$
\)

We all know that beta is not a constant and that it varies with collector current (among other things, such as temperature which we are assuming is being held constant). The variation with current, however, is more than enough to render it suspect if we are relying on it being constant in order to predict the current. The other option involves two parameters neither of which is significantly affected by current.

So if you were to take a real transistor (even though we are leaving out the Early voltage) and use these two equations to predict the collector current within the linear region, which would give you the more accurate prediction. Answer -- the second.