I'm reading "Practical Electronics" by Ralph Morrison. On p.99, he shows an Emitter-Follower circuit. See attached image for my rendition of it -- both voltage sources are 25V; the resistors are 10k and 2.7k; the transistor has Beta=100. The resistor is supposed to be a 2N3904 (NPN) transistor, although I used the simulator's default NPN transistor. (The graph shows the output voltage, according to the simulator. The "V=-862.05mV" refers to the simulator's calculation of voltage at Base of the transistor.)

Here is what he says: "Assume there is no input signal connected. The emitter current is about 10mA. It is determined by the emitter resistor and the minus power supply voltage. If the Beta of the transistor is 100, the base current is 100uA. This current flows in the 10kOhm resistor and the base voltage rises to 1V. This means that the emitter voltage is actually about 0.4V."

I do not understand why "the base voltage rises to 1V". By my calculations, it should be about -0.860V, which is reasonably close to the -0.862V that I found with the simulator. Specifically,
(0-v_Base)/10k = i_Base = (1/101)*[(v_Base - 0.7)-(-25)]/2.7k
This gives v_Base = -24.3/28.27 = -0.860V

What am I missing? (Is it possible that the author mistakenly concluded that the Base goes to 1V rather than -1V?)

 

I think the math works more like this:

25v/2.7k=9.593mA

9.593mA/100(beta)=92.593uA

92.593uA*10k=.92593V

But, I believe you're correct regarding the sign. Just switch the probes on the meter around and you'll have -v

 

I think the math works more like this:

25v/2.7k=9.593mA

9.593mA/100(beta)=92.593uA

92.593uA*10k=.92593V

But, I believe you're correct regarding the sign. Just switch the probes on the meter around and you'll have -v

Actually, his math is correct. Yours is approximate.

 

I'm a student, so I'm trying to get this straight. I still can't see how I was off so much. I just realized I used 100 instead of 101, but that still doesn't lead me to .8. I've attached my solution using the original math. I still come up with roughly my original answer. Any help would be great.

Vb/10k=1/101*([(Vb-0.7)-(-25)])/2.7k

Vb/10k=((Vb+24.3))/272.7k

272.2kVb=10kVb+243K

262.2kVb=243K

Vb=0.92677

 

I'm a student, so I'm trying to get this straight. I still can't see how I was off so much. I just realized I used 100 instead of 101, but that still doesn't lead me to .8. I've attached my solution using the original math. I still come up with roughly my original answer. Any help would be great.

Vb/10k=1/101*([(Vb-0.7)-(-25)])/2.7k

Vb/10k=((Vb+24.3))/272.7k

272.2kVb=10kVb+243K

262.2kVb=243K

Vb=0.92677

You missed a minus sign:

Ib= - Vb/10k

 

Why do you have a negative Vb on one side and not the other?

 

Why do you have a negative Vb on one side and not the other?

On the left side:
Base current is defined as flowing into the base.
Ib=(0-Vb)/Rb

On the right side:
Ie=(Ve-(-25V))/Re
Ve=Vb-0.7
Ib=Ie/101
Therefore,
Ib=(Vb-0.7-(-25))/(101*Re)

We have 2 equations for Ib. Setting them equal to each other,

-Vb/Rb=(Vb+24.3)/(101*Re)
cross-multiplying,
-101VbRe=VbRb+24.3Rb
Vb(Rb+101Re)=-24.3Rb
Vb=-24.3Rb/(Rb+101Re)
Rb=10k, Re=2.7k
Vb=-860mV

 

Got it...I forgot about the 0-Vb. Thanks!