Find Max VB for BJT Active Region in Fig. P5.69

[Kurokari]

Homework Statement

V_BE=0.7V

The transistor in the circuit of Fig. P5.69 has a very
high 0. Find the highest value of VB for which the transistor
still operates in the active mode.

Homework Equations

V_C>V_B

I_C=I_E (since I_B is approximated to zero due to high beta)

EDIT: I_E= [V_E-0]/1k (VB - VE = VBE = 0.7V ---> VE = VB-0.7V)

The Attempt at a Solution

This question is taken from sedra/smith 5th edition, there's some worked solution floating around the internet, however the solution provided is confusing. The condition given is that V_C-V_B=-0.4V

I can't agree with the solution given because that equation would mean that the voltage at base is higher than that of the voltage of the collector since the potential difference is negative.

What I was thinking is that V_C - V_B = 0.

Am I correct, or did I missed anything?

 

[rude man]

I think you're correct. Saturation is defined as Vc < Vb by any amount. Which is when the b-c junction becomes forward-biased.

However, fact remains that saturation voltages well below Vb are typically attained. Well below 0.3V which would roughly correspond to their answer. But you don't have the information you need to determine that level.

 

[NascentOxygen]

This question is taken from sedra/smith 5th edition, there's some worked solution floating around the internet, however the solution provided is confusing. The condition given is that V_C-V_B=-0.4V

I can't agree with the solution given because that equation would mean that the voltage at base is higher than that of the voltage of the collector since the potential difference is negative.

What I was thinking is that V_C - V_B = 0.

The textbook is correct in making that reasonable assumption. For very low collector currents, V_CE can go down to 0.1V or less for some transistors, so this means that (for NPN) the base can be at higher potential than the collector. Take a look at the data sheet for some common small signal transistors.

Saturation occurs when the base current loses control of the collector current, i.e., when an increase in I_B fails to elicit a corresponding increase in I_C. Under these conditions, I_C is being controlled by the external collector/emitter circuit, and not by the base.