Ebers Moll model art of electronics

[Ray242]

Hi, I've been learning the book 'the Art of Electronics' and I came across a few problems with the Ebers Moll equation described in page 92 3rd (2.3.2).

Ic = Is(T)exp(Vbe/Vt), where Vt = kT/q = 25.3mV at room temperature and Is is the saturation current.

The author says if we take the derivative of Vbe with respect to Ic, we get re = 25/Ic ohms. How did he get this?

For the temperature dependence, the author considered Ic at constant Vbe and Vbe at constant Ic. How do we take that into account in real design? For example, if Vbe was initially 0.6V and Ic 10uA, how do they change if temperature is incresed by 10 degrees?

How can I understand the early effect equation Ic = Ico(1 + Vce/Va)? For example, if Vce increases, Ic increases and therefore the voltage drop across the collector resistor should increase, so Vc decreases and therefore Vce decreases. It doesn't make sense to me.


Thanks very much in advance.

 

[Ratch]

Hi, I've been learning the book 'the Art of Electronics' and I came across a few problems with the Ebers Moll equation described in page 92 3rd (2.3.2).

Ic = Is(T)exp(Vbe/Vt), where Vt = kT/q = 25.3mV at room temperature and Is is the saturation current.

The author says if we take the derivative of Vbe with respect to Ic, we get re = 25/Ic ohms. How did he get this?

A simple differentiation.

For the temperature dependence, the author considered Ic at constant Vbe and Vbe at constant Ic. How do we take that into account in real design? For example, if Vbe was initially 0.6V and Ic 10uA, how do they change if temperature is incresed by 10 degrees?

Temperature is in kelvin units.

How can I understand the early effect equation Ic = Ico(1 + Vce/Va)? For example, if Vce increases, Ic increases and therefore the voltage drop across the collector resistor should increase, so Vc decreases and therefore Vce decreases. It doesn't make sense to me..

The Early effect is modeled by a resistor between the collector and base. Some of the current is shunted by that resistor. Read another source for a different or better explanation.

Ratch