BJTs & amplification

Design an amplifier, and meet a limit of the tool

This capstone is different from the others, and deliberately so. The previous five ended in PCB Studio, and this one cannot — the Studio's curated parts library contains no discrete transistor. That is not an oversight to work around but a design principle to examine, so the capstone has two halves: a complete paper design, and an honest look at why the tool refuses to help you build it.

1. Design a common-emitter stage from scratch: $V_{CC} = 9$ V, target $I_C = 1$ mA, β guaranteed 100–300, and a target voltage gain of at least $-100$ with the emitter bypassed. Choose $V_E$, then $R_E$, then the divider (using the ten-times-stiffness rule), then $R_C$ — and finish with the region verification.
2. Compute the small-signal parameters at your bias point, then both gains (bypassed and unbypassed), $R_{in}$, and $R_{out}$.
3. Size $C_{in}$ for a $50$ Hz low-frequency corner against your computed $R_{in}$. State which CA-6 result you are using.
4. Stress-test the design: recompute $I_C$ assuming β is actually 300 instead of 100, and report the percentage change. If it exceeds about 10%, your divider is not stiff enough — fix it and say what you changed.
5. Now the tool. Open PCB Studio and try to add a transistor. You cannot: /api/parts serves only the fourteen curated parts, and the generator will reference nothing else. Read that constraint against the platform's own architecture — the parts library exists as an anti-hallucination layer, where every part carries a human-verified pin map. Write two or three sentences on what would have to be true before a discrete BJT could join that library, and what could go wrong on a physical board if a part were added without that verification.
6. Build what you CAN build, and compare: place the Pico 2 W with the motor_driver_header, generate, and consider how that header's switched output relates to the amplifier you just designed on paper. One is a switch driven to its rails; the other is a device held carefully in its active region. Same silicon, opposite disciplines — and the difference is entirely in the biasing.