a question about the transconductance

Thread Starter

Ghina Bayyat

Joined Mar 11, 2018
135
hello
i have a question about the gm of a bjt
from its defiftion gm = Δic / Δvbe and this is so clear but i don't know how did the equation turn into gm = ic / vt ???
can u please explain
 

MrChips

Joined Oct 2, 2009
23,239
There are two types of resistance, depending on how the resistance is measured.

1) Ohmic, DC, or static resistance
2) AC, or dynamic resistance

DC resistance R = V / I, is a measure of the resistance at a given operating voltage or current.




AC resistance R = ΔV / ΔI is a measure of the rate of change of voltage and current.



Conductance is the reciprocal of resistance.

Hence, conductance G = I / V

Transconductance is gm = ΔI / ΔV

The slope of the blue line in the diagram is equal to the conductance.
The slope of the red line at the given operating point is the transconductance.
 

Thread Starter

Ghina Bayyat

Joined Mar 11, 2018
135
thank u and i understand all of this it's not my question
i ment how is it gm = Δ ic / Δ vbe turned into gm = ic / vt
or where did vt come from and why did vbe disapear ??
 

Jony130

Joined Feb 17, 2009
5,230
For the BJT the collector curtrent is described by the Shockley equation

Ic = Is * exp(Vbe/Vt)

And if we plot this equation we will get this

ZNmXt.png

And the transconductance gm is the slope of the function Ic = f(Vbe). And in math, the slope is a differential quantity dy/dx.
For a given DC collector curremt ( Ic ) the slope of the function Ic = Is * exp(Vbe/Vt) is:

gm = d(Ic)/d(Vbe) = 1/Vt * Ie * exp(Vbe/Vt) = Ic/Vt

Where: Vt is a thermal voltage equal around 26mV

So, the gm = Ic/26mV ≈ 38.5*Ic ≈ 40*Ic

More info here
https://forum.allaboutcircuits.com/blog/fun-with-the-diode-equation.589
https://en.wikipedia.org/wiki/Boltzmann_constant#Role_in_semiconductor_physics:_the_thermal_voltage
 
Last edited:

Thread Starter

Ghina Bayyat

Joined Mar 11, 2018
135
For the BJT the collector curtrent is described by the Shockley equation

Ic = Is * exp(Vbe/Vt)

And if we plot this equation we will get this

View attachment 152721

And the transconductance gm is the slope of the function Ic = f(Vbe). And in math, the slope is a differential quantity dy/dx.
For a given DC collector curremt ( Ic ) the slope of the function Ic = Is * exp(Vbe/Vt) is:

gm = d(Ic)/d(Vbe) = 1/Vt * Ie * exp(Vbe/Vt) = Ic/Vt

Where: Vt is a thermal voltage equal around 26mV

So, the gm = Ic/26mV ≈ 38.5*Ic ≈ 40*Ic

More info here
https://forum.allaboutcircuits.com/blog/fun-with-the-diode-equation.589
https://en.wikipedia.org/wiki/Boltzmann_constant#Role_in_semiconductor_physics:_the_thermal_voltage
Thank u so much the video cleared everything to me
 
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