No Vbe is not a constant. The Vbe varies with Ib current.Hi Jony,
As i understand, you are trying to find Vbe of a transistor by solving the equation using iterative method. I thought that Vbe for a trans is always constant regardless of β value.
I measure Vbe Vs Ib for BC337-40 for Vcc = 10V
RB = 680kΩ....Vbe = 0.614V....Ib = 13.8µA
RB = 470kΩ....Vbe = 0.616V....Ib = 20µA
RB = 220kΩ....Vbe = 0.624V....Ib = 42.61µA
RB = 100kΩ....Vbe = 0.639V....Ib = 93.61µA
RB = 50kΩ......Vbe = 0.659V....Ib = 187µA
RB = 10kΩ......Vbe = 0.719V....Ib = 928µA
RB = 5kΩ........Vbe = 0.748V....Ib = 1.85mA
RB = 2kΩ........Vbe = 0.787V....Ib = 4.6mA
RB = 1kΩ........Vbe = 0.819V....Ib = 9.18mA
RB = 500Ω......Vbe = 0.856V....Ib = 18.29mA
RB = 200Ω......Vbe = 0.989V....Ib = 45mA
As you can see the base current change 45mA/13.8μA = 3260 times. But Vbe change only by 375mV. This very small change in Vbe compared with the huge changes in the base current can be ignored in some cases. And this is why we use Vbe= 0.6...0.7V in hand calculations.
The first method is to simply assume that the Vbe is in range between 0.6V...0.7V.Jony, i don't see the second method that you mentioned. Can you show the other method to figure out Vbe?
And next find the base current
Ib = (Vcc - Vbe)/Rb and Ic = β * Ib (current control method)
And the second method (voltage control method) is to use Shockley equation (Ic=Is*(e^(Vbe/VT)-1)) and iterative method to solve for Ib, Vbe and Ic.