# Small Diode Emitter Resistance,RE

Discussion in 'General Electronics Chat' started by seikoemill89, Sep 21, 2011.

1. ### seikoemill89 Thread Starter New Member

Sep 21, 2011
3
0
hi everyone,here i would like to ask on how to prove this below equation
IE=Is(qVBE/e kT -1) until we get this equation:re=26mV/IE..
this is from the topic of BJT Biasing...hopefully someone can help me to solve this...TQ

2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
For a diode with voltage drop Vd & current Id.

By Shockley's equation

$I_d=I_s(e^{\frac{\normalsize{q} V_d}{kT}}-1)$

$(e^{\frac{\normalsize{q} V_d}{kT}}-1)=\frac{I_d}{I_s}$

$e^{\frac{\normalsize{q} V_d}{kT}}=\frac{I_d}{I_s}+1$

Taking the natural logarithm of both sides gives

$\frac{\normalsize{q} V_d}{kT}=ln(\frac{I_d}{I_s}+1)$

$V_d=\frac{kT}{\normalsize{q}}ln(\frac{I_d}{I_s}+1)$

Differentiating wrt Id gives

$\frac{d(V_d)}{dI_d}=\frac{kT}{\normalsize{q}} \frac{\frac{1}{\normalsize{I_s}}}{(\frac{ \normalsize {I_d}}{ \normalsize {I_s}}+1)}$

$\frac{d(V_d)}{dI_d}=\frac{kT}{\normalsize{q}}\frac{1}{\normalsize{I_d}+\normalsize{I_s}}$

Normally Id>>Is

So to a good approximation

$\frac{d(V_d)}{dI_d}=\frac{\frac{kT}{\normalsize{q}}}{\normalsize{I_d}}$

typically at room temp

$\frac{kT}{\normalsize{q}}=0.026 \ volt$

and

$\frac{d(V_d)}{dI_d}=\frac{0.026}{\normalsize{I_d}}$

If the term

$\frac{d(V_d)}{dI_d}$

is recognized as effectively a small signal dynamic resistance rd

then

$r_d=\frac{0.026}{\normalsize{I_d}} \ ohms$

For the BJT emitter region diode junction we can state (by a similar process) the equivalent dynamic emitter resistance for a quiescent emitter current IE

$r_e=\frac{0.026}{\normalsize{I_E}} \ ohms$

Or if IE is expressed in mA

$r_e=\frac{26}{\normalsize{I_E[mA]}} \ ohms$

Last edited: Sep 21, 2011
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3. ### seikoemill89 Thread Starter New Member

Sep 21, 2011
3
0
thank you so much for t_n_k...the answer is so meaningful for me because i am a fresh degree student,so i have forgotten what i have study before in diploma...a lot of thanks for you...peace!