FAD1022: Rapid-Fire Drill Pack — Transistors & Op-Amps

Objective: Master mechanical execution of BJT biasing and op-amp gain calculations without hesitation.
Target: 90 seconds per problem. If you stall >2 minutes, skip and mark it.
Total problems: 48
Estimated time: 75–90 minutes

Cheat Sheet (Memorize First)

BJT Current Relationships

Formula Description
$I_E = I_B + I_C$ KCL at transistor node
$\beta = \frac{I_C}{I_B}$ Current gain
$I_C = \beta I_B$ Collector current (active region)
$I_E = (\beta + 1)I_B$ Emitter current
$V_{BE} \approx 0.7$ V Silicon base-emitter voltage

BJT Operating Regions

Region E-B Junction C-B Junction Behavior
Active Forward Reverse Amplifier: $I_C = \beta I_B$
Saturation Forward Forward Closed switch: $V_{CE} \approx 0$
Cutoff Reverse Reverse Open switch: $I_C = 0$

BJT Biasing Configurations

Fixed Bias: $$I_B = \frac{V_{CC} - V_{BE}}{R_B}, \quad I_C = \beta I_B, \quad V_{CE} = V_{CC} - I_C R_C$$ $$I_{C(sat)} = \frac{V_{CC}}{R_C}$$

Emitter-Stabilized Bias: $$I_B = \frac{V_{CC} - V_{BE}}{R_B + (\beta + 1)R_E}$$ $$V_{CE} = V_{CC} - I_C(R_C + R_E), \quad I_{C(sat)} = \frac{V_{CC}}{R_C + R_E}$$

Voltage Divider Bias (Approximate): $$V_B = \frac{R_{B2} V_{CC}}{R_{B1} + R_{B2}}, \quad V_E = V_B - V_{BE}$$ $$I_C \approx I_E = \frac{V_E}{R_E}, \quad V_{CE} = V_{CC} - I_C(R_C + R_E)$$

Condition for approximate: $\beta R_E \geq 10 R_{B2}$

Op-Amp Golden Rules

  1. No current into inputs — input impedance is infinite
  2. Virtual short: $V_+ = V_-$ (with negative feedback)

Op-Amp Configurations

Configuration Gain Formula Phase Shift
Inverting $V_{out} = -\frac{R_f}{R_1}V_{in}$ 180°
Non-inverting $V_{out} = \left(1 + \frac{R_f}{R_1}\right)V_{in}$ 0°

Quick Identification

  • Inverting: Input goes to $(-)$ pin, $(+)$ grounded → negative gain
  • Non-inverting: Input goes to $(+)$ pin → gain > 1, positive
  • Fixed bias: No $R_E$ resistor
  • Emitter-stabilized: Has $R_E$ to ground, single base resistor
  • Voltage divider: Two base resistors ($R_{B1}$, $R_{B2}$) forming divider

Part A: BJT Current Relationships

Target: 60 seconds per problem.

Set A1 — Basic Current Calculations (6 problems)

Instructions: Use $I_E = I_B + I_C$ and $\beta = I_C/I_B$ relationships.

  1. Given $I_B = 40$ μA and $\beta = 100$, find $I_C$ and $I_E$.

  2. Given $I_C = 5$ mA and $\beta = 125$, find $I_B$ and $I_E$.

  3. Given $I_E = 3$ mA and $\beta = 80$, find $I_B$ and $I_C$.

  4. Given $I_B = 25$ μA and $I_E = 2.025$ mA, find $\beta$ and $I_C$.

  5. Given $I_C = 8$ mA and $I_E = 8.1$ mA, find $I_B$ and $\beta$.

  6. Given $\beta = 150$ and $I_E = 4.525$ mA, find $I_B$ and $I_C$.

Score: ___/6

Part B: Fixed-Bias DC Analysis

Target: 90 seconds per problem.

Set B1 — Fixed-Bias Standard Problems (6 problems)

Instructions: Calculate $I_B$, $I_C$, $V_{CE}$, and $I_{C(sat)}$. Assume $V_{BE} = 0.7$ V.

  1. Given: $V_{CC} = 15$ V, $R_B = 300$ kΩ, $R_C = 2$ kΩ, $\beta = 75$. Find $I_C$.

  2. Given: $V_{CC} = 20$ V, $R_B = 450$ kΩ, $R_C = 4$ kΩ, $\beta = 100$. Find $V_{CE}$.

  3. Given: $V_{CC} = 12$ V, $R_B = 200$ kΩ, $R_C = 1.5$ kΩ, $\beta = 60$. Find $I_{C(sat)}$.

  4. Given: $V_{CC} = 24$ V, $R_B = 600$ kΩ, $R_C = 3$ kΩ, $\beta = 120$, and measured $V_{CE} = 6$ V. Find actual $\beta$ of the transistor.

  5. Given: $V_{CC} = 18$ V, $R_B = 350$ kΩ, $R_C = 2.5$ kΩ, $\beta = 90$. Find $V_C$ (collector voltage to ground).

  6. Given: $V_{CC} = 30$ V, $R_B = 500$ kΩ, $R_C = 5$ kΩ, $\beta = 50$. Find the Q-point $(I_{CQ}, V_{CEQ})$.

Score: ___/6

Part C: Emitter-Stabilized Bias

Target: 120 seconds per problem.

Set C1 — Emitter-Stabilized Standard Problems (6 problems)

Instructions: Calculate specified values. Assume $V_{BE} = 0.7$ V.

  1. Given: $V_{CC} = 20$ V, $R_B = 400$ kΩ, $R_C = 2$ kΩ, $R_E = 1$ kΩ, $\beta = 80$. Find $I_C$.

  2. Given: $V_{CC} = 25$ V, $R_B = 500$ kΩ, $R_C = 3$ kΩ, $R_E = 2$ kΩ, $\beta = 100$. Find $V_{CE}$.

  3. Given: $V_{CC} = 16$ V, $R_B = 320$ kΩ, $R_C = 2.5$ kΩ, $R_E = 1.5$ kΩ, $\beta = 60$. Find $I_{C(sat)}$.

  4. Given: $V_{CC} = 22$ V, $R_B = 440$ kΩ, $R_C = 4$ kΩ, $R_E = 2$ kΩ, $\beta = 120$, and $I_C = 3$ mA. Verify consistency and find actual $V_{CE}$.

  5. Given: $V_{CC} = 12$ V, $R_B = 250$ kΩ, $R_C = 2$ kΩ, $R_E = 0.5$ kΩ, $\beta = 50$. Find $V_E$.

  6. Given: $V_{CC} = 28$ V, $R_B = 550$ kΩ, $R_C = 3.5$ kΩ, $R_E = 1.5$ kΩ, $\beta = 150$. Check if $(\beta + 1)R_E \geq 10R_B$ is satisfied.

Score: ___/6

Part D: Voltage Divider Bias

Target: 120 seconds per problem.

Set D1 — Voltage Divider Standard Problems (6 problems)

Instructions: Use approximate analysis. Check condition first. Assume $V_{BE} = 0.7$ V.

  1. Given: $V_{CC} = 20$ V, $R_{B1} = 40$ kΩ, $R_{B2} = 10$ kΩ, $R_C = 2$ kΩ, $R_E = 1$ kΩ, $\beta = 100$. Find $V_B$ and $I_C$.

  2. Given: $V_{CC} = 16$ V, $R_{B1} = 60$ kΩ, $R_{B2} = 20$ kΩ, $R_C = 3$ kΩ, $R_E = 2$ kΩ, $\beta = 80$. Find $V_{CE}$.

  3. Given: $V_{CC} = 24$ V, $R_{B1} = 80$ kΩ, $R_{B2} = 16$ kΩ, $R_C = 4$ kΩ, $R_E = 2$ kΩ, $\beta = 120$. Verify approximation condition, then find $I_C$.

  4. Given: $V_{CC} = 18$ V, $R_{B1} = 36$ kΩ, $R_{B2} = 12$ kΩ, $R_C = 2.5$ kΩ, $R_E = 1.5$ kΩ, $\beta = 90$. Find $V_C$.

  5. Given: $V_{CC} = 12$ V, $R_{B1} = 50$ kΩ, $R_{B2} = 10$ kΩ, $R_C = 1.8$ kΩ, $R_E = 0.9$ kΩ, $\beta = 50$, find $I_E$.

  6. Given: $V_{CC} = 30$ V, $R_{B1} = 100$ kΩ, $R_{B2} = 25$ kΩ, $R_C = 5$ kΩ, $R_E = 3$ kΩ, $\beta = 150$. Find $V_E$.

Score: ___/6

Part E: Op-Amp Inverting Amplifier

Target: 60 seconds per problem.

Set E1 — Inverting Amplifier Standard Problems (6 problems)

Instructions: Use $V_{out} = -\frac{R_f}{R_1}V_{in}$. Note the negative sign!

  1. Given: $R_1 = 10$ kΩ, $R_f = 100$ kΩ, $V_{in} = 0.5$ V. Find $V_{out}$.

  2. Given: $R_1 = 20$ kΩ, $R_f = 80$ kΩ, $V_{in} = 1.2$ V. Find voltage gain $A_v$.

  3. Given: $R_f = 200$ kΩ, $R_1 = 50$ kΩ, $V_{out} = -8$ V. Find $V_{in}$.

  4. Given: $R_1 = 25$ kΩ, $V_{in} = 0.8$ V, desired $V_{out} = -4$ V. Find required $R_f$.

  5. Given: $R_f = 150$ kΩ, $R_1 = 30$ kΩ, $V_{in} = 0.6$ V. Find current through $R_f$.

  6. Given: $V_{in} = 2$ V, $V_{out} = -10$ V, $R_1 = 40$ kΩ. Find $R_f$ and the gain.

Score: ___/6

Part F: Op-Amp Non-Inverting Amplifier

Target: 60 seconds per problem.

Set F1 — Non-Inverting Amplifier Standard Problems (6 problems)

Instructions: Use $V_{out} = \left(1 + \frac{R_f}{R_1}\right)V_{in}$.

  1. Given: $R_1 = 10$ kΩ, $R_f = 90$ kΩ, $V_{in} = 0.4$ V. Find $V_{out}$.

  2. Given: $R_1 = 25$ kΩ, $R_f = 75$ kΩ, $V_{in} = 1.5$ V. Find voltage gain $A_v$.

  3. Given: $R_f = 180$ kΩ, $R_1 = 20$ kΩ, $V_{out} = 10$ V. Find $V_{in}$.

  4. Given: $R_1 = 50$ kΩ, $V_{in} = 0.5$ V, desired $V_{out} = 3$ V. Find required $R_f$.

  5. Given: $R_f = 300$ kΩ, $R_1 = 60$ kΩ, $V_{in} = 2.9$ V. Find $V_{out}$.

  6. Given: $V_{in} = 1.7$ V, $V_{out} = 10.2$ V, $R_1 = 20$ kΩ. Find $R_f$ and the gain.

Score: ___/6

Part G: Circuit Identification & Mixed Problems

Target: 90 seconds per problem.

Set G1 — Identify and Calculate (6 problems)

Instructions: Identify the circuit type first, then calculate.

  1. Circuit has input to $(-)$ pin, $(+)$ grounded, $R_1 = 15$ kΩ, $R_f = 120$ kΩ, $V_{in} = 0.9$ V. Identify and find $V_{out}$.

  2. Circuit has input to $(+)$ pin, feedback to $(-)$ pin, $R_1 = 40$ kΩ, $R_f = 200$ kΩ, $V_{in} = 2.5$ V. Identify and find $V_{out}$.

  3. Transistor circuit has $V_{CC} = 18$ V, single $R_B = 360$ kΩ, $R_C = 2$ kΩ, no $R_E$, $\beta = 90$. Identify bias type and find $V_{CE}$.

  4. Transistor circuit has $V_{CC} = 20$ V, $R_B = 400$ kΩ, $R_C = 2.5$ kΩ, $R_E = 1$ kΩ, $\beta = 100$. Identify bias type and find $I_C$.

  5. Given: $V_{in} = 3$ V, $V_{out} = -15$ V, circuit is inverting. $R_1 = 50$ kΩ. Find $R_f$.

  6. Given: $V_{in} = 2$ V, $V_{out} = 12$ V, circuit is non-inverting. $R_1 = 20$ kΩ. Find $R_f$.

Score: ___/6

Part H: Exam Traps & Reverse Problems

Target: 120 seconds per problem.

Set H1 — Common Traps (6 problems)

Instructions: Watch for traps: sign errors, swapped formulas, hidden conditions.

  1. Fixed-bias: $V_{CC} = 12$ V, $R_B = 200$ kΩ, $R_C = 2$ kΩ, $\beta = 100$. Find $I_{C(sat)}$ — NOT the operating $I_C$.

  2. Emitter-stabilized: $V_{CC} = 16$ V, $R_B = 320$ kΩ, $R_C = 2$ kΩ, $R_E = 1$ kΩ, $\beta = 100$, measured $V_{CE} = 4$ V. Is the transistor in active or saturation region?

  3. Voltage divider: $V_{CC} = 20$ V, $R_{B1} = 100$ kΩ, $R_{B2} = 10$ kΩ, $\beta = 50$, $R_E = 1$ kΩ. Check if approximate analysis is valid before proceeding.

  4. Inverting op-amp: Given $V_{in} = 0.5$ V, desired $\vert V_{out} \vert = 5$ V, but you need POSITIVE output. What gain magnitude is needed and which configuration should you use instead?

  5. Non-inverting op-amp: $R_1 = 10$ kΩ, $R_f = 50$ kΩ. Someone calculates gain as $-\frac{R_f}{R_1}$ and gets confused about the negative result. What is the correct gain?

  6. Voltage divider bias: Given $V_B = 2$ V, $V_{CC} = 12$ V, $R_{B1} + R_{B2} = 60$ kΩ. Find $R_{B1}$ and $R_{B2}$ individually.

Score: ___/6

Final Scorecard

Part Sets Problems Raw Score
A — Current Relationships A1 6 ___/6
B — Fixed-Bias B1 6 ___/6
C — Emitter-Stabilized C1 6 ___/6
D — Voltage Divider D1 6 ___/6
E — Op-Amp Inverting E1 6 ___/6
F — Op-Amp Non-Inverting F1 6 ___/6
G — Identification & Mixed G1 6 ___/6
H — Exam Traps H1 6 ___/6
TOTAL 48 ___/48

Proficiency Benchmarks

  • 34/48 (71%) — Proficient. You can handle standard exam problems.
  • 41/48 (85%) — Solid. Fast and accurate.
  • 45/48 (94%) — Exam-ready. Any mistake is a careless slip.

Speed Benchmarks

  • <60 minutes: Excellent mechanical fluency.
  • 60–75 minutes: Good. Review missed patterns.
  • >90 minutes: Drill the specific sets you scored lowest on again tomorrow.

Error Log Template

After grading, list every wrong problem number with a one-word reason:

Problem Reason
e.g. 4 forgot IE formula

Re-solve all wrong problems immediately with notes, then again in 24 hours without notes.

Answer Key

Set A1 — Current Relationships

  1. $I_C = 4$ mA, $I_E = 4.04$ mA
  2. $I_B = 40$ μA, $I_E = 5.04$ mA
  3. $I_B = 37.04$ μA, $I_C = 2.963$ mA
  4. $\beta = 80$, $I_C = 2$ mA
  5. $I_B = 0.1$ mA, $\beta = 80$
  6. $I_B = 30$ μA, $I_C = 4.5$ mA

Set B1 — Fixed-Bias 7. $I_C = 3.575$ mA 8. $V_{CE} = 10.6$ V 9. $I_{C(sat)} = 8$ mA 10. $\beta = 240$ 11. $V_C = 9.975$ V 12. $(2.93$ mA, $15.35$ V)

Set C1 — Emitter-Stabilized 13. $I_C = 2.236$ mA 14. $V_{CE} = 12.91$ V 15. $I_{C(sat)} = 4$ mA 16. $V_{CE} = 4$ V (consistent) 17. $V_E = 1.147$ V 18. No, $228 \text{ kΩ} < 5.5 \text{ MΩ}$

Set D1 — Voltage Divider 19. $V_B = 4$ V, $I_C = 3.3$ mA 20. $V_{CE} = 8.05$ V 21. Yes, condition satisfied, $I_C = 2.3$ mA 22. $V_C = 13.125$ V 23. $I_E = 2.556$ mA 24. $V_E = 1.94$ V

Set E1 — Op-Amp Inverting 25. $V_{out} = -5$ V 26. $A_v = -4$ 27. $V_{in} = 2$ V 28. $R_f = 125$ kΩ 29. $I = 40$ μA 30. $R_f = 200$ kΩ, gain = $-5$

Set F1 — Op-Amp Non-Inverting 31. $V_{out} = 4$ V 32. $A_v = 4$ 33. $V_{in} = 1$ V 34. $R_f = 250$ kΩ 35. $V_{out} = 17.4$ V 36. $R_f = 100$ kΩ, gain = $6$

Set G1 — Identification & Mixed 37. Inverting, $V_{out} = -7.2$ V 38. Non-inverting, $V_{out} = 15$ V 39. Fixed-bias, $V_{CE} = 9.35$ V 40. Emitter-stabilized, $I_C = 2.405$ mA 41. $R_f = 250$ kΩ 42. $R_f = 100$ kΩ

Set H1 — Exam Traps 43. $I_{C(sat)} = 6$ mA 44. Active (calculated $V_{CE} = 4.785$ V vs saturation $\approx 0$ V) 45. No, $\beta R_E = 50$ kΩ, $10R_{B2} = 100$ kΩ 46. Need gain of 10, use non-inverting instead 47. Gain = $6$ (positive!) 48. $R_{B1} = 50$ kΩ, $R_{B2} = 10$ kΩ

Related Resources