Help whit BJT calculation

[jony130]

Hi,
I got this little circuit (bjt in saturation)

And I can write down this:
Ie=Ib+Ic
Rb*Ib+Ube+Ie*Re=Et
Rc*Ic+Uce+Ie*Re=Ecc
Can anyone show me step by step how to calculate Ib

 

[LvW]

As you have no information about the input characteristic Ib=f(Ube) it is common practice to set Ube=0.65...0,7 volts.

Than, you have 3 equations and 4 unknown parameters (Ic, Ie, Ib, Uce).
Therefore, you need a 4th equation for this system: Ic=h21*Ib (with h21= β)
That meens that the current gain of the BJT must be known.

Now you have 4 equations and 4 unknown parameters. This system can be solved very easily with standard methods.

 

[jony130]

But I now that transistor is in saturation, and Uce(sat)=0.1V; Ube=0.7V .

(ET-Ube)=Rb*Ib+Re*Ie
(Ecc-Uce(sat))=Rc*Ic+Re*Ie
And I don't know what next ?
I'm not to good whit mathematics.

 

[LvW]

No, Uce is an unknown parameter (it should have several volts, normally).

With 4 equations it is always possible to find the 4 unknown values I´ve mentioned.
Simply use the "put-in"-method. For example, replace Ic in each equation by Ib*h21.
Now, you have only three unknown values....and so on.
You really should try it - and, as a result, you have learned something. Try it !!!

 

[jony130]

In this circuit
Ecc=15V; β=100
and
Icmax=Ecc/(Rc+Re)=5mA.

Ic=[β*(Et-Ube)]/(Rb+(β+1)*Re)= 5.7mA
Uc=4.13V
Ue=5.7V
Uce=-1.57V
So transistor is in saturation.
And now from KCL
Ib=(Et-(Ube+Ue))/Rb
Ic=(Ecc-(Uce(sat)+Ue))/Rc
Ie=Ue/Re
Ib+Ic=Ie
so I solve the equation:

Gb*Et-Gb*Ube-Gb*Ue+Gc*Ecc-Gc*Uce-Gc*Ue-Ge*Ue=0

Ue=[(Et-Ube)*Gb+(Ecc-Uce)*Gc]/(Gb+Gc+Ge)) \[=(\frac{Et-Ube}{Rb}+\frac{Ecc-Uce}{Rc})*(Rg||Rc||Re)=5.16V\]

Ie=5.16mA
Ic=4.88mA
Ib=290uA
Where
G=1/R

But I can't solve the equation whit KVL
(ET-Ube)=Rb*Ib+Re*Ie
(Ecc-Uce(sat))=Rc*Ic+Re*Ie
Ib+Ic=Ie
What's next ?

 

[LvW]

The solution is easy if you would follow my recommendation as mentioned in my reply.
Reference: Three equations below your circuit diagram.

1.) In the first equation: Substitute Ie=Ic(1+β)/β and Ib=Ic/β
2.) In the second equ.: Substitute Ie and Ib as above; you can solve for Ic.
3.) In the third equ.: Substitute Ie by Ic and you can solve for Uce.
Thats all.

 

[jony130]

But when BJT is in saturation the Ic=hfe*Ib don't hold any more

 

[LvW]

Yes, you are right. I´ve overlooked your comment in your first contribution "BJT in saturation ". Sorry.
Of course, my comments apply only to the active region.
In your case with pure switching application the calculation of Ib isn´t so simple.
I would propose, instead, to simulate the circuit.

 

[trapoe]

If you know Ucesat (Uce in saturation) and Ubesat (Ube in saturation) then in the first group of equations

Ie=Ib+Ic
Rb*Ib+Ube+Ie*Re=Et
Rc*Ic+Uce+Ie*Re=Ecc

you have only three unknown (Ie, Ic, Ib) and you can solve the system.
You can start substituting the first equation in the following two and obatining

Rb*Ib+Ube+(Ib+Ic)*Re=Et
Rc*Ic+Uce+(Ib+Ic)*Re=Ecc

if you continue in few steps you will find Ib.