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AC/DC BJT transisitor Circuit Analysis

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For the circuit in the image, Beta=120, VCC=5V, Va=100V, and Rb=25kohms. Determine Vbb and RC such that Rpi=5.4kOhms and the Q-point is in the center of the load line.

I have a formula for Rpi=(Vt*Beta)/Icq. From this I found Icq=1.25x10^-4 Amps.

However, is this a correct way to determine Icq? The question said to determine the values such that the Q-point is in the center of the load line. How do I draw the graph to find out the center value if I don't know Vce?

KVL around to ce loop relates RC and VCE: Rc=(5v-Vce)/(1.25x10^-4) if I can use the Icq from earlier.

Diagram is attached.

Please help. What am I missing? Thank you.

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The solution provides aid and guidance to the problem concerning AC/DC BJT tansistor circuit analysis.

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The way you got Icq is fine. But the value looks too small. Please check the unit just in case.
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