How can I calculate R1, R2, RC and RE in the following silicon transistor circuit?

Question

We have 4 unknowns, so we need 4 equations.

If we make the equivalent Thévenin circuit for R1 and R2, and by applying KVL on the input and outputs we get only 2 equations.

Rth=(R1×R2)/(R1+R1)
Vth=(Vcc×R2)(R1+R2)

First equation from KVL on input:

EQ1: Vth-IB×Rth-VBE-IE=0

Second equation from KVL on output:

EQ2: Vcc-ICQ×Rc-VCE-IE×RE=0

We substitute IB=ICQ/β , IE=((β+1)/β)IC so IE approximately equals ICQ. So EQ1: Vth-(5×10^-3)/(100)Rth-0.7-5×10^-3=0

EQ2: 12-(5×10^-3)×RC+6-(5×10^-3)×RE=0

And then:

EQ1: Vth-(5×10^-5)Rth-0.695=0

EQ2: 18-(5×10^-3)×RC-(5×10^-3)×RE=0

How can I get the solution of this problem?

Answer 1

If we make equivalent Thevinin ... only 2 equations.

There is not sufficient information in the problem, as stated, to calculate all four resistor values. As you've stated it, you have four unknowns and two constraints. Either the question gives you the information somewhere else, it's buried in assumptions from the class, or you simply cannot get there from here.

With the problem as stated, you are free to trade off the values of RE and RC, establishing \$\mathrm{V_E}\$ as you see fit. For \$\beta = \infty\$, their sum would be constant but their difference would be a free parameter of your choosing.

Similarly, once you choose RE, \$\mathrm{V_{th}}\$ and \$\mathrm{R_{th}}\$ are interdependent, and you can choose one of these.

So -- two equations, two unknowns, and two free parameters.

Answer 2

The solution is straightforward (no Thévenin transformations necessary):

• Because the current Ic and both voltages Vcc and Vce are given, the resistor values for Rc and Re can be selected with Ic(Re+Rc)=Vcc-Vce (common practice: Re app 0.1*Rc)
• Setting Vbe to app. 0.7 volts you can calculate the required base voltage Vb (against ground).
• Now you are free to select the impedance niveau for the voltage divider R1, R2 for producing Vb. (Remember that Ic=f(Vbe), the base current Ib is only a kind of by-product).
• If you have some information about the factor B=Ic/Ib you can use Ib (through R1) for selecting proper values for the resistors R1 and R2.
• In any case, you should use resistor values which allow a current through the divider which is at least 10 times larger than the expected base current Ib. In this case, we say that the voltage divider produces a sufficiently "stiff" voltage Vb (only a rather small influence of Ib uncertainties).
• If you are unsure because the "vague" assumption of Vbe=0.7 volts, remember that Re creates sufficient voltage feedback which makes the whole circuit relatively unsensitive to the (unknown, estimated) transitor parameters.