Calculating base current without knowing current amplification

So I'm currently doing an assignment where I'm meant to design my own common emitter. I'm supposed to choose the Q-point of my collector current and choose my own signal amplification (Av). During this design, I'm assuming (I_C=I_E, if I_B << I_C) and (I_R1=I_R2, if I_B << I_R1)

I'm using the hybrid-pi model.

I got the following value:

• Vcc = 22V
• Voltage over R_C: 11V
• Collector resistance: 3.7k ohm
• I_CQ (Q-point of collector): 3mA
• Small signal amp: Av = 6 times.
• Emitter resistance: R_E = -(R_C/|Av|) = 615 ohm
• Voltage across emitter resistance V_Re: 1.85V
• Voltage at base V_B = Vbe + V_Re = 0.7 + 1.85 = 2.55V
• I_R1 = I_R2 = I_C/10 = 3mA/10 = 0.3mA
• V_R2 = 2.55V (Same as V_B)
• R_2 = 8.5k ohm
• V_R1 = 19.45V
• R_1 = 65k ohm
• My voltage (V_CE) across the transistor is 9.15 V

When I'm going over to small-signal analysis, to calculate R_in and R_out. I need to know the base current I_b or current amplification beta/hfe, however, I know neither with makes me get stuck.

• r_pi = beta/gm

Circuit diagram in LTSpice:

• Can't we calculate Ic and Ie, and from that get Ib? Oct 5, 2020 at 1:21
• When you assumed $I_C=I_E$ you already made an assumption about $\beta$. Oct 5, 2020 at 2:05
• The Photon, you're correct. I apparently did make an assumption without acknowledging it. In the assignment, I'm supposed to choose my own current amplification Beta. Oct 5, 2020 at 10:14