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Digital Circuits

  • Read the question thoroughly
  • Expected to get one guranteed quesiton on quantum circuits in the first question subsections
  • Practise all the tutorials

For exam:

  • Question 1a:
    • Will generally be cuboidal
    • Normally in centimeter

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 implment 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 experission for Output Voltage (!)
    • c) Calculate Power (!)

  • Question 4 (! but different values)

    • a) CMOS inverter, find the transfer characteristic (!)
    • b) Relationship between channel width, then 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 behvaiour 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 experission for Output Voltage (!)
    • c) Calculate Power (!)

  • Question 4 (! but different values)

    • a) CMOS inverter, find the transfer characteristic (!)
    • b) Relationship between channel width, then 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 behvaiour 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, then 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

$n_{o}$$p_{o}$ = $n_{i}^{2}$

where:

  • $n_{o}$ is the concentration of free electrons
  • $p_{o}$ is the concentration of holes
  • $n_{i}$ is the intrinsic carrier concentration

For intrinsic silicon at room temperature:

  • $n_{o}$ = $p_{o}$ ~ 1.5 x $10^{10}$ $cm^{-3}$
  • $n_{i}^{2}$ ~ 2.25 x $10^{20}$

Law of Mass Action: N-type

The law of mass action still applies

$n_{o}$$p_{o}$ = $n_{i}^{2}$

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

$n_{o}$ = $N_{d}$ >> $n_{i}$

$p_{o}$ = $n_{i}^{2}$/$N_{d}$ << $n_{i}$

if $N_{d}$ ~ 1 x $10^{13}$ $cm^{-3}$ and $n_{i}$ ~ 1.5 x $10^{10}$ $cm^{-3}$, $p_{o}$ is approximately 700 times smaller than $n_{o}$.

Law of Mass Action: P-type

The law of mass action still applies

$n_{o}$$p_{o}$ = $n_{i}^{2}$

For p-type, the concentration of holes is much higher than for intrinsic silicon due to doping, hence:

$p_{o}$ = $N_{a}$ >> $n_{i}$

$n_{o}$ = $n_{i}^{2}$/$N_{a}$ << $n_{i}$

if $N_{a}$ ~ 1 x $10^{13}$ $cm^{-3}$ and $n_{i}$ ~ 1.5 x $10^{10}$ $cm^{-3}$, $n_{o}$ is approximately 700 times smaller than $p_{o}$.

Quantifying the Electron Drift Current

Charge flux Density ($J^{drift}$)

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

For electrons: $J^{drift}{n}$ = -nq$\mu{n}$E

where:

  • n is the density of electrons
  • q is the charge on the electron(negative)
  • $\mu_{n}$ is the mobility of the electron
  • E is the electric field.

Note: The sign of the carrier is already present so just need to put the value of q in. Not sure yet

Quantifying the Hole Drift Current

Charge flux Density ($J^{drift}$)

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

For electrons: $J^{drift}{p}$ = pq$\mu{p}$E

where:

  • p is the density of holes
  • q is the charge on the electron(positive)
  • $\mu_{n}$ is the mobility of the hole
  • E is the electric field.

Note: The sign of the carrier is already present so just need to put the value of q in. Not sure yet

Combined Drift Current

THe drift current ($I^{drift}$) is the charge flux density ($J^{drift}$) integrated over the area A.

The total drift current ($I^{drift}$) has two components:

  • Net movement of electrons $I^{drift}_{n}$
  • Net movement of holes $I^{drift}_{p}$

moving in opposite directions

$$I^{drift} = I^{drift}_n + I^{drift}_p \\\ = J^{drift}_nA + J^{drift}_pA \\\ = -n(-q)(\mu_n)EA + p(q)(\mu_p)EA \\\ = AEq(n\mu_n + p\mu_p)$$

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

Different types

if it is mentioned that it is p type or n type do normally by finding drift current.

If it is intrinsic Silicon do the below

Intrinsic Silicon

n = p = $n_{i}^{2}$

If its not either then just do

np = $n_{i}^{2}$