Test
Prompt
You are acting as an independent final scientific-admission judge for an undergraduate Electronics I question bank. Your job is NOT to agree with the supplied solution. Independently solve the problem first, then audit every material claim in the candidate solution. Use rigorous circuit analysis. Do not use the web. Do not assume that a textbook approximation is acceptable unless you quantitatively justify it. Problem An NPN BJT common-emitter amplifier has: * VCC = 12 V * R1 = 100 kΩ from VCC to base * R2 = 20 kΩ from base to ground * RC = 2.7 kΩ * RE = 1.0 kΩ * β = 100 * VBE = 0.70 V * Early effect neglected, so ro → ∞ * VT = 25 mV The signal source has: * source resistance Rs = 600 Ω * coupling capacitors are ideal shorts at midband The emitter bypass capacitor is an ideal AC short at midband. A load RL = 10 kΩ is connected to the collector through an ideal coupling capacitor. Find the midband voltage gain Av = vo / vs where vs is the Thevenin source voltage before Rs and vo is the AC voltage across RL. Assume the transistor operates in forward-active region unless your calculation proves otherwise. ⸻ Candidate solution submitted for admission “The base-voltage divider is stiff, so base current can be ignored. VB = 12 × 20/(100+20) = 2.00 V VE = 2.00 − 0.70 = 1.30 V IE = 1.30 mA IC ≈ IE = 1.30 mA gm = IC/VT = 1.30 mA / 25 mV = 0.052 S rπ = β/gm = 1.923 kΩ The AC collector resistance is RC || RL = 2.7 kΩ || 10 kΩ = 2.126 kΩ The small-signal input resistance seen at the base is Rin = rπ || R1 || R2 = 1.923 kΩ || 100 kΩ || 20 kΩ ≈ 1.724 kΩ Therefore vb/vs = Rin/(Rs + Rin) = 1.724/(0.600 + 1.724) = 0.742 and vo/vb = −gm(RC || RL) = −0.052(2126) = −110.55 Hence Av = vo/vs = (−110.55)(0.742) ≈ −82.0 V/V FINAL ANSWER: Av ≈ −82 V/V.” ⸻ Your required audit Perform the following in this exact order. 1. Independent solution Solve the DC bias exactly enough to determine: * Thevenin equivalent of the base divider * IB * IC * IE * VB * VE * VC * VCE Explicitly verify whether the transistor is in forward-active operation. Then calculate the midband small-signal gain vo/vs using: * gm * rπ * the loading of R1 and R2 * Rs * RC || RL Do not copy intermediate values from the candidate solution. 2. Approximation audit Quantitatively determine whether neglecting base-current loading of the divider is justified. Do not merely say “the divider is/not stiff.” Give at least one numerical stiffness/loading metric and explain what it implies. 3. Candidate-solution defect audit For every material defect you find, classify it as exactly one of: * FATAL — invalidates the answer or scientific admission * MAJOR — materially changes the result or reasoning * MINOR — real but does not materially alter the conclusion * NONE Distinguish between: * incorrect physics/circuit reasoning * unjustified approximation * arithmetic error * notation/presentation issue Do not invent defects. 4. Correct final answer Give your best numerical value for Av = vo/vs. Also report the percentage error of the candidate answer relative to your independently calculated result. 5. Admission verdict Return exactly one of: PASS PASS_WITH_MINOR_CORRECTION FAIL_MAJOR_REPAIR_REQUIRED FAIL_FATAL A numerically plausible answer is not sufficient for PASS if the reasoning contains a materially unjustified approximation. 6. Adversarial self-check Before finalizing, actively try to falsify your own result. Check at minimum: * whether IC ≈ IE was used where an exact β relation materially matters * whether R1 and R2 are AC-grounded correctly * whether the bypassed emitter changes the small-signal input resistance * whether Rs has been included in vo/vs rather than merely vo/vb * whether the output load is correctly combined with RC * whether the transistor’s DC operating point is physically consistent If this self-check changes your conclusion, explicitly say so. ⸻ Required output format INDEPENDENT RESULT [calculations] APPROXIMATION AUDIT [quantitative assessment] DEFECT LEDGER ID Candidate claim Classification Explanation CORRECTED ANSWER Av = … Candidate percentage error = … % FINAL ADMISSION VERDICT [one allowed verdict only] CONFIDENCE 0–100% SELF-CHECK [brief adversarial verification]
