Digital Circuits

• Read the question thoroughly.
• Expected to get one guaranteed question on quantum circuits in the first question subsections.
• Practice all the tutorials.

For Exam

• Question 1a:
  • Will generally be cuboidal.
  • Normally in centimeters.

Past Paper Analysis

(!) means its repeated

2023-2024

• Question 1
  • a) Sketch Diagram and find current (semiconductors)
  • b) CMOS to drive LED
  • c) Solve BJT circuit to find load Resistor (!)
  • d) Mosfet question (!)
  • e) CMOS logic to implement boolean function
• Question 2
  • a) BJT to drive LED (buffer circuit) (!)
  • b) Design the circuit (!)
• Question 3
  • a) Find the model of the MOSFET transistor and draw transfer characteristic graph (!)
  • b) Find an expression for Output Voltage (!)
  • c) Calculate Power (!)
• Question 4 (! but different values)
  • a) CMOS inverter, find the transfer characteristic (!)
  • b) Relationship between channel width, steady state current, then find power (!)
  • c) Design a circuit to fit a description (!)

2022-2023

• Question 1
  • a) Doping concentration and doping type (semiconductors)
  • b) Diode model behavior and ratio of saturation currents
  • c) Solve BJT circuit to find load Resistor (!)
  • d) Mosfet question (!)
  • e) CMOS logic to find the boolean function (! but different circuit)
• Question 2
  • a) BJT to drive LED (buffer circuit) (!)
  • b) Design the circuit (!)
• Question 3
  • a) Find the model of the MOSFET transistor and draw transfer characteristic graph (!)
  • b) Find an expression for Output Voltage (!)
  • c) Calculate Power (!)
• Question 4 (! but different values)
  • a) CMOS inverter, find the transfer characteristic (!)
  • b) Relationship between channel width, steady state current, then find power (!)
  • c) Design a circuit to fit a description (!)

2021-2022

• Question 1
  • a) Doping concentration and doping type (semiconductors) (!)
  • b) Diode model behavior and current and doping concentration
  • c) Solve BJT circuit with load capacitor
  • d) Mosfet question (!)
  • e) CMOS logic to find the boolean function (! but different circuit)
• Question 2
  • a) BJT inverter and state
  • b) Calculate the voltage min input High
  • c) Derive the fanout of the transistor
  • d) Calculate base resistance
• Question 3
  • a) BJT, find the voltages
  • b) Calculate Quiescent Current
• Question 4 (! but different circuit)
  • a) CMOS inverter, find the transfer characteristic (!)
  • b) Relationship between channel width, steady state current, then find power (!)
  • c) Design a circuit to fit a description (!)

Question 1a

If in the question electric field is there then the current to calculate is drift current.

Law of Mass Action

nopo = ni2

Where:

• no is the concentration of free electrons.
• po is the concentration of holes.
• ni is the intrinsic carrier concentration.

For intrinsic silicon at room temperature:

• no = po ≈ 1.5 × 1010 cm-3
• ni2 ≈ 2.25 × 1020

Law of Mass Action: N-type

nopo = ni2

For n-type silicon, the concentration of free electrons is much higher than for intrinsic silicon due to doping:

• no = Nd ≫ ni
• po = ni2/Nd ≪ ni

If Nd ≈ 1 × 1013 cm-3 and ni ≈ 1.5 × 1010 cm-3, then po is approximately 700 times smaller than no.

Quantifying the Electron Drift Current

Charge Flux Density (Jdrift)

The average charge flow per unit area in the direction of the field:

Jdriftn = -nqμnE

Where:

• n is the density of electrons.
• q is the charge on the electron (negative).
• μn is the mobility of the electron.
• E is the electric field.

Quantifying the Hole Drift Current

Charge Flux Density (Jdrift)

The average charge flow per unit area in the direction on the field:

For holes:

Jdriftp = pqµpE

• p is the density of holes
• q is the charge on the electron (positive)
• µp is the mobility of the hole
• E is the electric field

Combined Drift Current

The drift current (Idrift) is the charge flux density (Jdrift) integrated over the area A.

The total drift current (Idrift) has two components:

• Net movement of electrons Idriftn
• Net movement of holes Idriftp

Moving in opposite directions:

    Idrift = Idriftn + Idriftp
    = JdriftnA + JdriftpA
    = -n(-q)(µn)EA + p(q)(µp)EA
    = AEq(nµn + pµp)
        

Note: The above statements for drift current and current flux density are only valid for uniform electron density inside a semiconductor.

Different Types

If it is mentioned that it is p-type or n-type, calculate the drift current normally. If it is intrinsic silicon, follow the below:

Intrinsic Silicon

n = p = ni2

If it's not either, then use:

np = ni2