Semiconductor Electronics — JEE Mains Physics

Formulas (1)

• The p-n junction: barrier, bias and dynamic resistance · Barrier field, energy loss and dynamic resistance
  $$E = \frac{V_b}{d}, \qquad \tfrac{1}{2}mv^{2} = \tfrac{1}{2}mu^{2} - eV_b, \qquad r = \frac{\Delta V}{\Delta I}$$

Reference tables (2)

Watch out for (10)

• Extra electrons do not make a negative crystal
  → Intrinsic, n-type and p-type semiconductors
• The product stays fixed, not the sum
  → Intrinsic, n-type and p-type semiconductors
• Resistivity falls with heat, but never to zero
  → Intrinsic, n-type and p-type semiconductors
• Compare potentials, not signs
  → The p-n junction: barrier, bias and dynamic resistance
• No battery, no current
  → The p-n junction: barrier, bias and dynamic resistance
• The wider layer is on the lightly doped side
  → The p-n junction: barrier, bias and dynamic resistance
• Subtract energy, then take the root
  → The p-n junction: barrier, bias and dynamic resistance
• A photodiode is reverse biased
  → Special-purpose diodes and the bias each one uses
• Use eV with 1240, or joules with hc
  → Special-purpose diodes and the bias each one uses
• A solar cell needs a large area
  → Special-purpose diodes and the bias each one uses

Formulas (3)

• Ideal diodes in resistor networks · A diode as a switch
  $$\text{forward: } R_D = r_f\ \ (0 \text{ if ideal}), \qquad \text{reverse: } R_D \to \infty$$
• Diodes with a fixed forward voltage drop · Current with fixed diode drops
  $$I = \frac{V - \sum V_D}{\sum R}, \qquad V_{\text{LED}} = \frac{P}{I}, \qquad R_S = \frac{V - V_{\text{LED}}}{I}$$
• Rectifiers, filters and clipping · Output frequency and peak
  $$f_{\text{out}} = f\ (\text{half-wave}), \quad 2f\ (\text{full-wave}); \qquad V_{\text{peak}} = V_m - V_D\ \text{per conducting diode}$$

Watch out for (9)

• A blocked branch is gone, resistor and all
  → Ideal diodes in resistor networks
• Read the battery before the diodes
  → Ideal diodes in resistor networks
• Forward resistance goes in series
  → Ideal diodes in resistor networks
• Subtract every conducting diode's drop
  → Diodes with a fixed forward voltage drop
• Germanium and silicon differ
  → Diodes with a fixed forward voltage drop
• Below cut-in there is no current
  → Diodes with a fixed forward voltage drop
• Capacitor across, inductor in series
  → Rectifiers, filters and clipping
• Full-wave doubles the frequency
  → Rectifiers, filters and clipping
• A reversed diode passes the other half
  → Rectifiers, filters and clipping

Formulas (2)

• Currents in a Zener regulator · Regulator currents
  $$I_s = \frac{V_{in} - V_Z}{R_s}, \quad I_L = \frac{V_Z}{R_L}, \quad I_Z = I_s - I_L, \quad P_Z = V_Z I_Z$$
• Choosing the series resistor for a Zener · Safe series resistor
  $$I_{Z,\max} = \frac{P_{\max}}{V_Z}, \qquad R_{s,\min} = \frac{V_{in,\max} - V_Z}{I_{Z,\max}}$$

Watch out for (6)

• Check breakdown before using V_Z
  → Currents in a Zener regulator
• The Zener current is not the series current
  → Currents in a Zener regulator
• Load current comes from V_Z, not the supply
  → Currents in a Zener regulator
• Divide the power by V_Z
  → Choosing the series resistor for a Zener
• Design for the highest input
  → Choosing the series resistor for a Zener
• No load is the worst case
  → Choosing the series resistor for a Zener

Formulas (2)

• Transistor structure, α and β · Transistor currents
  $$I_E = I_B + I_C, \qquad \alpha = \frac{\beta}{1 + \beta}, \qquad \beta = \frac{\alpha}{1 - \alpha}$$
• Gains of a common-emitter amplifier · Common-emitter gains
  $$\beta = \frac{\Delta I_C}{\Delta I_B}, \quad r_i = \frac{\Delta V_{BE}}{\Delta I_B}, \quad A_V = \beta\,\frac{R_L}{r_i}, \quad A_P = \beta A_V$$

Watch out for (6)

• α is below 1, β is large
  → Transistor structure, α and β
• The emitter current is the sum
  → Transistor structure, α and β
• A switch uses cut-off and saturation
  → Transistor structure, α and β
• mA over μA is a factor of a thousand
  → Gains of a common-emitter amplifier
• Power gain has β twice
  → Gains of a common-emitter amplifier
• Use the input resistance, not the base resistor
  → Gains of a common-emitter amplifier

Formulas (2)

• NAND and NOR as universal gates · De Morgan's laws
  $$\overline{A\cdot B} = \overline{A} + \overline{B}, \qquad \overline{A + B} = \overline{A}\cdot\overline{B}$$
• Reducing a gate network with Boolean algebra · Simplifying rules
  $$A + AB = A, \quad A(A + B) = A, \quad A + \overline{A}B = A + B, \quad A \oplus B = A\overline{B} + \overline{A}B$$

Reference tables (1)

Watch out for (9)

• A tied-input NAND is a NOT
  → NAND and NOR as universal gates
• De Morgan flips the operation and every bar
  → NAND and NOR as universal gates
• Look for bubbles on the inputs
  → NAND and NOR as universal gates
• AB already implies A + B
  → Reducing a gate network with Boolean algebra
• A constant answer is allowed
  → Reducing a gate network with Boolean algebra
• XOR and XNOR are complements
  → Reducing a gate network with Boolean algebra
• The diodes' direction decides AND or OR
  → Logic gates built from diodes, transistors and switches
• A transistor stage inverts
  → Logic gates built from diodes, transistors and switches
• Switches across the lamp invert
  → Logic gates built from diodes, transistors and switches

Reference tables (1)

Watch out for (9)

• Check the row order
  → Truth tables of the basic gates
• One row fits several gates
  → Truth tables of the basic gates
• Invert the right input
  → Truth tables of the basic gates
• Trace every wire from each input
  → Finding the inputs that give a required output
• An LED between two outputs needs a difference
  → Finding the inputs that give a required output
• Do not over-constrain a free input
  → Finding the inputs that give a required output
• Mark the edges of both inputs
  → Output waveforms of a gate network
• Reduce first, then read the waveforms
  → Output waveforms of a gate network
• Name the gate from all the intervals
  → Output waveforms of a gate network