Using Thevenin Theorem to solve for unknown values in BJT voltage divider circuit
How do I go about finding the base/collector/emitter currents without knowing the beta value?


You could start by finding a symbolic expression for the base/collector/emitter currents in terms of \$\ \beta_F\$

One simple way to model a BJT circuit is to say that the "apparent" resistance of \$\ R_e\$, when viewed from the base of the transistor, is \$\ r_{e}=(\beta_F+1) R_e\$.

Now you can find the voltage on the base of the transistor (compared to gnd) easily, by modelling the circuit as follows:







simulate this circuit &ndash; Schematic created using CircuitLab

Let's apply KVL and KCL;

\$\ V_{b}-V_{be}-r_e I_{re}=0\implies I_{re}=\frac{V_{b}-V_{be}}{r_e}\$

\$\ \frac{V_{cc}-V_{b}}{R_1}-\frac{V_{b}}{R_2}-I_{re}=0\implies I_{re}=\frac{V_{cc}-V_{b}}{R_1}-\frac{V_{b}}{R_2}\$

\$\ \frac{V_{b}-V_{be}}{r_e}=\frac{V_{cc}-V_{b}}{R_1}-\frac{V_{b}}{R_2}\implies V_b=\frac{R_2 r_e V_{cc} + R_1 R_2 V_{be}}{R_1 r_e + R_2 r_e + R_1 R_2}\$

\$\ I_c=\frac{\beta_F}{\beta_F+1}I_{Re}=\frac{\beta_F (V_b-V_{be})}{(\beta_F+1) R_e}\$

\$\ V_c=V_{cc}-R_c I_c\$


  Assuming this is a DC bias of a voltage-divider type BJT circuit:


I'm not sure I understand what you mean by that, but if you want to model the circuit as two voltage dividers you can, assuming \$\ V_{cc}&gt;&gt;V_{be}\$ you can set \$\ \frac{V_{be}}{V_{cc}}=0\$ and get rid of \$\ V_{be}\$ from the expressions for \$\ V_b\$ and \$\ V_c\$. I will leave this for you to practice your algebra..