Level 2 — Recall

Transistors - BJT & FET

⏱ 30 minutes40 marksprintable — key stays hidden on paper

Level: 2 (Recall / Standard textbook problems) Time limit: 30 minutes Total marks: 40

Q1. Define the three operating regions of a BJT and state the junction bias conditions (base-emitter and base-collector) for each. (6 marks)

Q2. For a BJT, the current gain $\beta = 100$ . (a) Compute $\alpha$ . (2 marks) (b) If the base current $I_B = 20\ \mu\text{A}$ , find the collector current $I_C$ and emitter current $I_E$ . (3 marks)

Q3. An NPN transistor is used as a switch driving an LED. $V_{CC} = 5\text{ V}$ , collector resistor $R_C = 220\ \Omega$ . When saturated, $V_{CE(sat)} = 0.2\text{ V}$ . (a) Find the collector (saturation) current $I_{C(sat)}$ . (2 marks) (b) If $\beta = 100$ , find the minimum base current needed. Using an overdrive factor of 3, find the design base current. (3 marks)

Q4. State two differences between a JFET and a MOSFET regarding gate construction and gate current. (4 marks)

Q5. Distinguish between enhancement-mode and depletion-mode MOSFETs in terms of the channel at $V_{GS}=0$ . (4 marks)

Q6. An NMOS transistor has $V_{th} = 1\text{ V}$ , $k_n = \tfrac{1}{2}\mu_n C_{ox}\frac{W}{L} = 0.5\ \text{mA/V}^2$ . It operates with $V_{GS} = 3\text{ V}$ in saturation. (a) State the saturation-region current equation. (1 mark) (b) Compute the drain current $I_D$ (ignore channel-length modulation). (3 marks)

Q7. Define transconductance $g_m$ of a MOSFET and, for the transistor in Q6, compute $g_m$ using $g_m = 2k_n(V_{GS}-V_{th})$ . (4 marks)

Q8. State the condition (in terms of $V_{GS}$ , $V_{DS}$ , $V_{th}$ ) that separates the triode and saturation regions of an NMOS. (3 marks)

Q9. Briefly explain the body effect in a MOSFET and its impact on threshold voltage. (3 marks)

Q10. Define subthreshold leakage current and state why it becomes important in modern short-channel devices. (2 marks)

Answer keyMark scheme & solutions

Q1. (6 marks) — 2 marks each region.

Cutoff: BE junction reverse (or below-on) biased, BC reverse biased → transistor OFF, $I_C \approx 0$ .
Active: BE forward biased, BC reverse biased → $I_C = \beta I_B$ ; used for amplification.
Saturation: BE forward biased, BC forward biased → transistor fully ON, $V_{CE}$ small, $I_C < \beta I_B$ ; used as closed switch.

Q2. (5 marks) (a) $\alpha = \dfrac{\beta}{\beta+1} = \dfrac{100}{101} = 0.9901$ . (2) (b) $I_C = \beta I_B = 100 \times 20\ \mu A = 2\text{ mA}$ . (1.5) $I_E = I_C + I_B = 2\text{ mA} + 0.02\text{ mA} = 2.02\text{ mA}$ . (1.5)

Q3. (5 marks) (a) $I_{C(sat)} = \dfrac{V_{CC}-V_{CE(sat)}}{R_C} = \dfrac{5-0.2}{220} = \dfrac{4.8}{220} = 21.8\text{ mA}$ . (2) (b) $I_{B(min)} = \dfrac{I_{C(sat)}}{\beta} = \dfrac{21.8\text{ mA}}{100} = 0.218\text{ mA}$ . (1.5) With overdrive factor 3: $I_B = 3 \times 0.218 = 0.654\text{ mA}$ . (1.5)

Q4. (4 marks) — 2 marks each.

Gate construction: JFET gate is a reverse-biased pn junction (no insulator); MOSFET gate is a metal/poly electrode separated from channel by an oxide insulator.
Gate current: JFET has tiny reverse leakage current; MOSFET gate is DC-isolated by oxide → essentially zero (only capacitive) gate current.

Q5. (4 marks) — 2 marks each.

Enhancement-mode: no conducting channel exists at $V_{GS}=0$ (normally OFF); a channel must be induced by applying $|V_{GS}| > |V_{th}|$ .
Depletion-mode: a channel exists at $V_{GS}=0$ (normally ON); gate voltage is used to deplete/reduce the channel to turn it off.

Q6. (4 marks) (a) $I_D = k_n (V_{GS}-V_{th})^2$ (with $k_n = \tfrac12 \mu_n C_{ox} W/L$ ). (1) (b) $V_{GS}-V_{th} = 3-1 = 2\text{ V}$ ; $I_D = 0.5\times(2)^2 = 0.5\times4 = 2\text{ mA}$ . (3)

Q7. (4 marks) Definition: $g_m = \dfrac{\partial I_D}{\partial V_{GS}}$ — change in drain current per unit change in gate-source voltage (small-signal gain of the transistor). (2) Computation: $g_m = 2k_n(V_{GS}-V_{th}) = 2\times0.5\times2 = 2\text{ mA/V}$ . (2)

Q8. (3 marks) Assume $V_{GS} > V_{th}$ (device ON).

Triode: $V_{DS} < V_{GS}-V_{th}$ (i.e. $V_{DS} < V_{ov}$ ). (1.5)
Saturation: $V_{DS} \ge V_{GS}-V_{th}$ . (1.5)

Q9. (3 marks) Body effect: when the source-to-body voltage $V_{SB}$ is non-zero (reverse), the depletion region widens, requiring more gate charge and thus increasing the threshold voltage: $V_{th} = V_{th0} + \gamma(\sqrt{2\phi_F + V_{SB}} - \sqrt{2\phi_F})$ . Effect: $V_{th}$ rises with increasing $V_{SB}$ .

Q10. (2 marks) Subthreshold leakage: the small drain current that flows when $V_{GS} < V_{th}$ (weak inversion), varying exponentially with $V_{GS}$ . Important in short-channel/low- $V_{th}$ devices because it causes static power dissipation and grows as devices scale down.

[
  {"claim":"alpha for beta=100 is 100/101","code":"beta=100; alpha=beta/(beta+1); result = abs(alpha-0.990099)<1e-5"},
  {"claim":"IC=2mA and IE=2.02mA for IB=20uA","code":"IB=20e-6; IC=100*IB; IE=IC+IB; result = abs(IC-2e-3)<1e-9 and abs(IE-2.02e-3)<1e-9"},
  {"claim":"IC_sat = 4.8/220 A approx 21.8mA","code":"Ic=(5-0.2)/220; result = abs(Ic-0.021818)<1e-5"},
  {"claim":"ID=2mA for kn=0.5mA/V2, Vov=2V","code":"kn=0.5e-3; ID=kn*(3-1)**2; result = abs(ID-2e-3)<1e-9"},
  {"claim":"gm=2mA/V","code":"kn=0.5e-3; gm=2*kn*(3-1); result = abs(gm-2e-3)<1e-9"}
]