# Dynamic Resistance

Discussion in 'Homework Help' started by xKael, Jun 30, 2010.

1. ### xKael Thread Starter New Member

Jun 30, 2010
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0
I'm studying Electronics and the professor gave us this homework...

As you may know, the formula for dynamic resistance is:

r = resistance
I = current

Now, the question is, where did the "26mV" come from?

Explain why there is a "26mV" there.

Thanks to those who will help...

2. ### retched AAC Fanatic!

Dec 5, 2009
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Its the thermal voltage, at room temperature, of the diode.

3. ### Georacer Moderator

Nov 25, 2009
5,177
1,285
...and is given by the formula
$V_{\small T}=\frac{k \cdot T}{q}$ where
k is the Boltzmann constant k=1.38e^-23 joules/Kelvin
T is the absolut temperature in Kelvin
q is the electron charge q=1.602e^-19 coulomb

This yields approximately a Vt of 25mV @ 20$^{\tiny{o_C}}$ or
26mV @ 25$^{\tiny{o_C}}$

4. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
It is derived from (Dr.) Shockley's Diode Equation and requires some relatively simple differentiation and algebraic manipulation.

It's well known and (if interested) you'll find plenty of derivations of the dynamic resistance on the web.

There's been some recent discussion recently on the forum - so try searching here.

The dynamic resistance is routinely used for BJT small signal amplifier analysis.

5. ### xKael Thread Starter New Member

Jun 30, 2010
24
0
Thanks to all!!!

EDIT:
So, you can derive the Thermal Voltage by differentiating the Shockley Equation right?

Could someone show the detailed differentiation of Shockley's Equation to become the Thermal Voltage Equation...

Last edited: Jun 30, 2010
6. ### xKael Thread Starter New Member

Jun 30, 2010
24
0
Hi, sorry for double posting but, I found this...

The derivation of emitter resistance is as follows: (Google "diode equation" for definitions of k, q, and T)

I=Is(e^(qv/kT)-1)

where kT/q=26mv at T~300 degrees Kelvin

since Is<<I at normal bias currents,

I/Is~e^(V/.026)

V/.026~ln(I/Is)

V~.026(ln(I)-ln(Is))

Recall that R=dV/dI

dV/dI=.026/I QED

Could somebody explain it...

What does "<<" mean?

7. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
Which part is not clear to you?

'Is << I' means 'Is "is very much less than" I'.

8. ### mahdi firouzi_1436825059 New Member

Jul 13, 2015
1
0
whats f mean in If?
it mean forward bias?!!??

9. ### Jony130 AAC Fanatic!

Feb 17, 2009
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I_f = forward current.