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Key formulas
| Name | Formula | Variables / Notes |
|---|---|---|
| Diode Current (Shockley Equation) | I = I_s * (e^(V / (n * V_T)) - 1) | I: diode current (A); I_s: reverse saturation current (A); V: applied voltage (V); n: ideality factor (1 to 2); V_T: thermal voltage = kT/q ≈ 26 mV at 300 K |
| BJT Collector Current | I_C = β * I_B | I_C: collector current (A); β (h_FE): DC current gain; I_B: base current (A) |
| MOSFET Drain Current (Saturation) | I_D = (μ_n * C_ox / 2) * (W/L) * (V_GS - V_th)^2 | I_D: drain current (A); μ_n: electron mobility (cm²/V·s); C_ox: gate oxide capacitance per unit area (F/cm²); W/L: width-to-length ratio; V_GS: gate-to-source voltage (V); V_th: threshold voltage (V) |
| Voltage Divider Bias (BJT) | V_B = V_CC * R2 / (R1 + R2) | V_B: base voltage (V); V_CC: supply voltage (V); R1, R2: voltage divider resistors (Ω) |
| Small-Signal Transconductance (BJT) | g_m = I_C / V_T | g_m: transconductance (A/V); I_C: quiescent collector current (A); V_T: thermal voltage ≈ 26 mV |
Key concepts
PN Junction Depletion Region
At equilibrium, diffusion of majority carriers creates a charge-depleted region. Built-in potential V_0 ≈ 0.7 V for silicon. Depletion width widens under reverse bias and narrows under forward bias.
BJT Operating Regions
Active: B-E forward biased, B-C reverse biased; used for amplification. Saturation: both junctions forward biased; used as a switch ON. Cutoff: both junctions reverse biased; switch OFF.
MOSFET Channel Formation
Applying V_GS > V_th inverts the semiconductor surface, forming a conducting channel between drain and source. In the linear region, I_D increases with V_DS. In saturation, I_D is nearly constant.
Feedback in Amplifiers
Negative feedback reduces gain but improves bandwidth, linearity, and input/output impedance depending on topology. Gain with feedback: A_f = A / (1 + Aβ), where β is the feedback fraction.
Zener Diode Regulation
Operates in reverse breakdown at a fixed voltage V_Z. Used in shunt regulator circuits. Series resistor R_S limits current: R_S = (V_in - V_Z) / I_Z.
Tables
BJT vs MOSFET Comparison
| Parameter | BJT (NPN) | MOSFET (NMOS) |
|---|---|---|
| Control | Current (I_B) | Voltage (V_GS) |
| Input Impedance | Low (kΩ range) | Very High (GΩ range) |
| Switching Speed | Moderate | Fast |
| Noise | Lower 1/f noise | Higher 1/f noise |
| Biasing | Requires I_B | No gate current needed |
Diode Types and Applications
| Diode Type | Key Property | Typical Use |
|---|---|---|
| Rectifier (1N4007) | V_f ≈ 0.7 V, up to 1 A | AC to DC conversion |
| Zener | Fixed reverse breakdown V_Z | Voltage regulation |
| Schottky | V_f ≈ 0.3 V, fast recovery | High-frequency rectification |
| LED | Emits light at forward bias | Optical indicators |
| Varactor | C_j varies with reverse V | Voltage-controlled tuning |
Quick facts
- Silicon diode forward voltage drop: 0.7 V; Germanium: 0.3 V.
- Thermal voltage V_T = kT/q = 26 mV at room temperature (300 K).
- BJT current gain β typically ranges from 50 to 300 for small-signal transistors.
- MOSFET threshold voltage V_th for typical NMOS processes is 0.5 V to 1.5 V.
- Early voltage V_A for BJTs is typically 50 V to 200 V; accounts for output resistance r_o = V_A / I_C.
- For a CE amplifier: voltage gain A_v = -g_m * R_C (ignoring r_o).
- Depletion width W ∝ sqrt(V_R) for an abrupt PN junction under reverse bias V_R.
Exam shortcuts
- To find Q-point quickly for voltage divider bias: use Thevenin equivalent at the base. V_th = V_CC * R2/(R1+R2), R_th = R1||R2. Then I_B = (V_th - 0.7) / (R_th + (1+β)*R_E). Avoids loop equations entirely.
- For MOSFET saturation vs linear check: if V_DS >= V_GS - V_th, the device is in saturation. State this condition first before computing I_D to avoid region errors.
- g_m shortcut for BJT: g_m = 40 * I_C at room temperature (since 1/V_T = 1/0.025 = 40). For I_C = 1 mA, g_m = 40 mA/V instantly.
- When drawing small-signal model, replace: V_CC with ground, capacitors with short circuit, DC sources with zero. Then write KCL/KVL directly on the simplified circuit.