Formula Sheet — Tutorial 12: Semiconductors & Electronics
1. Diode Circuits
Forward Bias Voltage Drops
| Diode Type | Forward Voltage Drop ($V_D$) |
|---|---|
| Silicon (Si) | $0.7 \text{ V}$ |
| Germanium (Ge) | $0.3 \text{ V}$ |
Ohm's Law for Diode Circuits
$$I = \frac{V_{supply} - V_D}{R}$$
| Variable | Meaning | Units |
|---|---|---|
| $I$ | Current through circuit | A |
| $V_{supply}$ | Supply voltage | V |
| $V_D$ | Total forward voltage drop across diodes | V |
| $R$ | Resistance | $\Omega$ |
Note: For multiple diodes in series, subtract the sum of all forward voltage drops from the supply voltage.
Voltage Across a Resistor
$$V_R = IR$$
2. Rectifiers
Half-Wave Rectifier — Peak Output Voltage
$$V_o = V_{peak} - V_D$$
| Variable | Meaning | Units |
|---|---|---|
| $V_o$ | Peak output voltage | V |
| $V_{peak}$ | Peak AC source voltage | V |
| $V_D$ | Diode forward voltage drop | V |
Half-Wave Rectifier — Average DC Output Voltage
$$V_{DC} = \frac{V_o}{\pi}$$
| Variable | Meaning | Units |
|---|---|---|
| $V_{DC}$ | Average DC output voltage | V |
| $V_o$ | Peak output voltage | V |
Full-Wave Rectifier — Average DC Output Voltage
$$V_{DC} = \frac{2V_o}{\pi}$$
3. Bipolar Junction Transistor (BJT) — Basic Relationships
Current Relationship
$$I_E = I_C + I_B$$
| Variable | Meaning | Units |
|---|---|---|
| $I_E$ | Emitter current | A |
| $I_C$ | Collector current | A |
| $I_B$ | Base current | A |
DC Current Gain ($\beta$)
$$\beta = \frac{I_C}{I_B}$$
| Variable | Meaning | Units |
|---|---|---|
| $\beta$ | DC current gain | unitless |
Collector Current in Active Region
$$I_C = \beta I_B$$
Emitter Current
$$I_E = (\beta + 1) I_B$$
4. BJT Fixed-Bias Configuration
Base Current
$$I_B = \frac{V_{CC} - V_{BE}}{R_B}$$
| Variable | Meaning | Units |
|---|---|---|
| $V_{CC}$ | Collector supply voltage | V |
| $V_{BE}$ | Base-emitter voltage ($\approx 0.7 \text{ V}$ for Si) | V |
| $R_B$ | Base resistor | $\Omega$ |
Collector-Emitter Voltage
$$V_{CE} = V_{CC} - I_C R_C$$
| Variable | Meaning | Units |
|---|---|---|
| $V_{CE}$ | Collector-emitter voltage | V |
| $R_C$ | Collector resistor | $\Omega$ |
Saturation Collector Current
$$I_{C(sat)} = \frac{V_{CC}}{R_C}$$
5. BJT Voltage-Divider Bias (Approximate Analysis)
Condition for Approximate Analysis
$$\beta R_E \geq 10 R_B$$
Base Voltage
$$V_B = \frac{R_2}{R_1 + R_2} V_{CC}$$
Emitter Voltage
$$V_E = V_B - V_{BE}$$
Emitter Current
$$I_E = \frac{V_E}{R_E} \approx I_C$$
Collector-Emitter Voltage
$$V_{CE} = V_{CC} - I_C(R_C + R_E)$$
| Variable | Meaning | Units |
|---|---|---|
| $R_1, R_2$ | Voltage divider resistors | $\Omega$ |
| $R_E$ | Emitter resistor | $\Omega$ |
| $V_B$ | Base voltage | V |
| $V_E$ | Emitter voltage | V |
6. Summary Table of Key Parameters
| Parameter | Symbol | Typical Value |
|---|---|---|
| Si diode forward voltage | $V_D$ | $0.7 \text{ V}$ |
| Ge diode forward voltage | $V_D$ | $0.3 \text{ V}$ |
| Si BJT base-emitter voltage | $V_{BE}$ | $0.7 \text{ V}$ |