Operating point of a transistor circuit

Question

I need to find the operating point of this circuit (Ic and Vce). There is an NPN transistor and Ec=15V, Vbe=0.65V, Rb1=120Ω, Rb2=60Ω, Rc=6Ω, Re=6Ω an β=150. As far as I know, Ic=β*Ib and Vce should be Ec-Ic*Rc-Ie*Re, in this case. My problem is that I don't know how to determine Ib.

What are the equations for determining Ib and is
Vce = Ec - Ic * Rc - Ie * Re?

Answer 1

(Corrected answer):

I propose to use the superposition principle for finding - as the first step - the base potential Vb=Vb1+Vb2. The two voltage sources contributing to Vb are the supply voltage Vs (for Vb1) and the base-emitter voltage Vbe (for Vb2), which will be treated as a constant DC voltage source Vbe=0.65...0.7 volts.

• This method requires nothing else than to use twice the voltage divider principle.

1.) For Vb1 (simple voltage divider) we set Vbe=0 and find the voltage at the parallel connection of Rb2 and the reflected emitter resistor Re" (which must be transferred to the base side): Re"=(1+B*Re).

2.) For Vb2 we set the supply voltage Vs to zero and calculate the voltage at the base node - driven by Vbe (again, a simple voltage divider).

3.) Now we have Vb=Vb1+Vb2 and Ve=IeRe=Vb-Vbe.

4.) As the last step we can find Ie (via Ve) and Ic.

5.) Comment: As you can see, it was NOT necessary to find the base current Ib. This is not surprising because the current Ie is controlled by the voltage Vbe - and Ib is nothing else than an (unwanted) by-product. Of course, if you wish you can calculate Ib as the last step: Ib=Ic/β.

Answer 2

Steps:

1. Convert the circuit at the base of T1 (Ec, Rb1 & Rb2) to its Thevinan equivalent (voltage with series resistance). This now sets the voltage at the T1 base for Ib = 0.
2. Calculate V at T1 emitter (Ve) for Ib = 0.
3. Calculate Ie: Ie = Ve / Re.
4. Calculate Ib: Ib = Ie / (β + 1).
5. Re-calculate the new value for V at T1 emitter using the value of Ib obtained at step 4. This will change due to the new value of base current causing a voltage drop in the series resistance of the Thevinan equivalent of step 1.
6. Re-calculate new value for Ie (same formula as step 3).
7. Re-calculate new value for Ib (same formula as step 4).
8. Repeat steps 5, 6, 7 for as many times as required for the accuracy needed. For your example here I suggest doing this 2 or 3 times at most.
9. Once you are happy with accuracy, calculate Ic: Ic = Ie - Ib.
10. Calculate V at T1 collector: Vc = Ec - (Ic * Rc).