Level 1 — Recognition

Transistors - BJT & FET

⏱ 20 minutes30 marksprintable — key stays hidden on paper

Chapter: 2.4 Transistors: BJT & FET Level: 1 — Recognition (MCQ + Matching + True/False with justification) Time Limit: 20 minutes Total Marks: 30

Section A — Multiple Choice (1 mark each) — 10 marks

Q1. In an NPN BJT operating in the active region, which junction states are correct?

A) Base–emitter forward biased, base–collector reverse biased
B) Both junctions forward biased
C) Both junctions reverse biased
D) Base–emitter reverse biased, base–collector forward biased

Q2. The relationship between $\alpha$ and $\beta$ of a BJT is:

A) $\beta = \dfrac{\alpha}{1+\alpha}$
B) $\alpha = \dfrac{\beta}{1+\beta}$
C) $\alpha = \dfrac{\beta}{\beta-1}$
D) $\beta = 1 - \alpha$

Q3. For a BJT used as a switch in the ON state, the transistor operates in the:

A) Cutoff region
B) Active region
C) Saturation region
D) Breakdown region

Q4. An enhancement-mode NMOS transistor conducts when:

A) $V_{GS} < V_{th}$
B) $V_{GS} > V_{th}$ (with $V_{th} > 0$ )
C) $V_{GS} = 0$ always
D) $V_{GS} < 0$ only

Q5. In the saturation region of a MOSFET, the drain current is approximately:

A) Linearly proportional to $V_{DS}$
B) Independent of $V_{GS}$
C) Proportional to $(V_{GS} - V_{th})^2$
D) Proportional to $\sqrt{V_{GS}}$

Q6. The transconductance $g_m$ of a MOSFET is defined as:

A) $\dfrac{\partial V_{GS}}{\partial I_D}$ at constant $V_{DS}$
B) $\dfrac{\partial I_D}{\partial V_{GS}}$ at constant $V_{DS}$
C) $\dfrac{\partial I_D}{\partial V_{DS}}$ at constant $V_{GS}$
D) $\dfrac{V_{DS}}{I_D}$

Q7. A depletion-mode MOSFET differs from an enhancement-mode MOSFET in that it:

A) Has no gate terminal
B) Conducts with zero gate-source voltage (channel exists at $V_{GS}=0$ )
C) Cannot be turned off
D) Uses no oxide layer

Q8. Subthreshold leakage current in a MOSFET flows when:

A) $V_{GS}$ is well above $V_{th}$
B) $V_{GS}$ is slightly below $V_{th}$
C) The device is in deep saturation
D) The drain is grounded

Q9. The body effect in a MOSFET causes the threshold voltage to:

A) Decrease as source-to-body voltage increases
B) Increase as source-to-body reverse bias increases
C) Remain constant
D) Become negative

Q10. In a common-emitter amplifier, the output signal at the collector is:

A) In phase with the input
B) 180° out of phase (inverted) relative to the input
C) 90° out of phase
D) Attenuated to zero

Section B — Matching (1 mark each) — 8 marks

Q11. Match each term in Column X to its correct description in Column Y.

Column X	Column Y
(a) JFET	(1) Voltage that must be exceeded for channel to form
(b) Threshold voltage $V_{th}$	(2) Field-effect device controlled by a reverse-biased pn junction gate
(c) Triode (linear) region	(3) MOSFET acts like a voltage-controlled resistor
(d) Cutoff region (BJT)	(4) Both junctions reverse biased; negligible collector current

Q12. Match each device/effect to its property.

Column X	Column Y
(a) PMOS	(1) Conducts with $V_{GS} < V_{th}$ (negative $V_{th}$ )
(b) Short-channel effect	(2) Reduced control of gate over channel as $L$ shrinks
(c) $\beta$ (hFE)	(3) Ratio $I_C/I_B$
(d) Saturation (MOSFET)	(4) Current nearly constant with $V_{DS}$

Section C — True/False WITH Justification (2 marks each: 1 for T/F, 1 for reason) — 12 marks

Q13. "In a PNP transistor, the emitter is more negative than the base during normal active operation." True or False? Justify.

Q14. "For a MOSFET, increasing the channel length $L$ tends to reduce short-channel effects." True or False? Justify.

Q15. "A BJT with $\beta = 99$ has an $\alpha$ of approximately 0.99." True or False? Justify with calculation.

Q16. "An ideal MOSFET switch in the ON (triode, $V_{DS}\approx 0$ ) state dissipates large static power because current flows through it." True or False? Justify.

Q17. "In the MOSFET saturation region, drain current is independent of $V_{DS}$ in the ideal (long-channel) model." True or False? Justify.

Q18. "Fixed-base (single resistor) biasing of a BJT provides a stable Q-point against variations in $\beta$ ." True or False? Justify.

Answer keyMark scheme & solutions

Section A (1 mark each)

Q1 — A. In active mode the BE junction is forward biased (injects carriers) and the BC junction is reverse biased (collects them). (1)

Q2 — B. By definition $\alpha = \beta/(1+\beta)$ ; derived from $I_E = I_C + I_B$ . (1)

Q3 — C. A closed (ON) switch means low $V_{CE}$ with both junctions forward biased → saturation. (1)

Q4 — B. Enhancement NMOS needs $V_{GS} > V_{th}$ (with positive $V_{th}$ ) to invert the channel. (1)

Q5 — C. Saturation current $I_D = \tfrac{1}{2}k(V_{GS}-V_{th})^2$ (ignoring $\lambda$ ). (1)

Q6 — B. $g_m \equiv \partial I_D/\partial V_{GS}$ at fixed $V_{DS}$ . (1)

Q7 — B. Depletion-mode has a built-in channel and conducts at $V_{GS}=0$ . (1)

Q8 — B. Subthreshold conduction occurs just below $V_{th}$ (weak inversion), exponential in $V_{GS}$ . (1)

Q9 — B. Reverse source-body bias widens depletion region, raising $|V_{th}|$ . (1)

Q10 — B. CE amplifier inverts: rising input increases $I_C$ , dropping collector voltage → 180° phase shift. (1)

Section B (1 mark each)

Q11: (a)→(2), (b)→(1), (c)→(3), (d)→(4). (1 each = 4)

Q12: (a)→(1), (b)→(2), (c)→(3), (d)→(4). (1 each = 4)

Q13 — False. (1) In a PNP the emitter is at a higher (more positive) potential than the base so the EB junction is forward biased for a p-emitter (current flows emitter→collector). (1 reason)

Q14 — True. (1) Longer $L$ increases gate control over the channel and reduces drain-induced barrier lowering and other short-channel effects. (1 reason)

Q15 — True. (1) $\alpha = \beta/(1+\beta) = 99/100 = 0.99$ . (1 calculation)

Q16 — False. (1) In triode with $V_{DS}\approx 0$ the voltage across the ON switch is nearly zero, so $P = V_{DS}I_D \approx 0$ ; static dissipation is small (ideally zero). (1 reason)

Q17 — True. (1) In the long-channel ideal model, once pinched off, $I_D=\tfrac12 k(V_{GS}-V_{th})^2$ is independent of $V_{DS}$ (flat curve; channel-length modulation neglected). (1 reason)

Q18 — False. (1) Fixed-base bias makes $I_C = \beta I_B$ directly proportional to $\beta$ , so Q-point shifts strongly with $\beta$ variation and temperature — it is the least stable scheme. (1 reason)

[
  {"claim":"alpha = beta/(1+beta) gives 0.99 for beta=99","code":"beta=99; alpha=beta/(1+beta); result = abs(alpha-0.99)<1e-9"},
  {"claim":"beta from alpha=0.99 is 99","code":"alpha=Rational(99,100); beta=alpha/(1-alpha); result = beta==99"},
  {"claim":"Saturation drain current scales as (Vgs-Vth)^2","code":"k,Vgs,Vth=symbols('k Vgs Vth',positive=True); Id=Rational(1,2)*k*(Vgs-Vth)**2; result = simplify(diff(Id,Vgs) - k*(Vgs-Vth))==0"},
  {"claim":"ON switch power ~0 when Vds->0","code":"Vds,Id=symbols('Vds Id'); P=Vds*Id; result = P.subs(Vds,0)==0"}
]

Section A — Multiple Choice (1 mark each) — 10 marks

Section B — Matching (1 mark each) — 8 marks

Section C — True/False WITH Justification (2 marks each: 1 for T/F, 1 for reason) — 12 marks

Section A (1 mark each)

Section B (1 mark each)

Section C (2 marks each)