Semiconductors Formulas
Semiconductor formulas describe the behaviour of diodes, transistors, and their biasing networks. These calculators help you set operating points and predict device currents and voltages. They underpin amplifier, switch, and logic-level interface design.
Semiconductors Formula Calculators
- MOSFET Conduction Loss P = I² × Rds(on) Drain Current 2 mA, Rds(on) 0.1 mΩ → Power = 4 × 10⁻⁴ µW
- MOSFET Switching Loss P = ½ × V × I × (tr + tf) × f Drain-Source Voltage 0.33 V, Drain Current 2 mA, Rise Time 100 ps, Fall Time 0.22 ns, Switching Frequency 100 Hz → P = 1.06 × 10⁻¹¹ W
- BJT Total Dissipation P = VCE × IC + VBE × IB VCE 0.33 V, IC 2 mA, VBE 0.726 V, IB 100 µA → P = 7.33 × 10⁻⁴ W
- Diode Power Loss P = Vf × If Forward Voltage 0.33 V, Forward Current 2 mA → Power = 0.66 mW
- Zener Regulation Resistor R = (Vin − Vz) / (Iz + Iload) Input Voltage 3.3 V, Zener Voltage 1.55 V, Zener Current 1 mA, Load Current 0.47 mA → Resistance = 1.19 kΩ
- Transistor Current Gain (β) β = IC / IB Collector Current 100 µA, Base Current 100 nA → Current Gain = 1000
- MOSFET Gate Drive Power Pd = Qg × Vgs × f Total Gate Charge 100 pC, Gate-Source Voltage 0.33 V, Switching Frequency 100 Hz → Gate Drive Power = 0.0033 µW
- MOSFET Rds(on) vs Temperature RDS(T) = RDS_ref × (1 + tc × ΔT) Rds(on) Reference 0.22 mΩ, Temp Coefficient 0.025, Temperature Change 2.5 °C → Rds(on) at Temp = 0.2338 mΩ
- Op-Amp Slew Rate Limit fmax = SR / (2π × Vpk) Slew Rate 0.1 V/µs, Peak Output Voltage 0.33 V → Max Frequency = 48.23 kHz
- BJT Vbe vs Temperature Vbe(T) = Vbe_ref − 0.002 × ΔT Vbe Reference 22 mV, Temperature Change 2.5 °C → Vbe at Temp = 17 V
- Diode Vf vs Temperature Vf(T) = Vf_ref − 0.002 × ΔT Vf Reference 22 mV, Temperature Change 2.5 °C → Vf at Temp = 17 V
- Op-Amp Input Offset Error Vos_total = Vos + drift × ΔT Initial Offset 2.2 µV, Offset Drift 0.1 µV/°C, Temperature Change 2.5 °C → Total Offset = 2.45 V
- MOSFET Gate Drive Headroom Vmargin = Vgs − Vth Gate-Source Voltage 0.726 V, Threshold Voltage 1.55 V → Gate Headroom = -0.824 V
- BJT Emitter Bias Current Ic ≈ (VB − 0.7) / RE Base Voltage 0.33 V, Emitter Resistor 1 Ω → Collector Current = -0.37 A
- Shockley Diode Equation I = Is × (e^(V/(n×Vt)) − 1) Diode Voltage 10 mV, Saturation Current 100 pA, Ideality Factor 0.025 → I = 5.25 × 10⁻⁴
- IGBT Total Loss P = Vce × Ic × D + Esw × f Collector-Emitter Voltage 0.33 V, Collector Current 2 mA, Duty Cycle 2.5 %, Switching Energy (Eon+Eoff) 100 µJ, Switching Frequency 100 Hz → P = 0.01002
- MOSFET Body Diode Loss P = Vf × If × (1 − D) Diode Forward Voltage 0.33 V, Diode Current 2 mA, Duty Cycle 2.5 % → Body Diode Loss = 0.6435 mW
- MOSFET Avalanche Energy Eas = 0.5 × L × I² × Vbr/(Vbr − Vcc) Inductance 100 nH, Current at Turn-Off 2 mA, Breakdown Voltage 0.33 V, Supply Voltage 0.726 V → Eas = -1.67 × 10⁻¹³
- Varactor Diode Capacitance C = Cj0 / (1 + V/Vbi)^m Zero-Bias Capacitance 1 pF, Reverse Bias Voltage 0.33 V, Built-in Potential 0.726 V, Grading Coefficient 0.025 → C = 9.91 × 10⁻¹³
- Gate-Driver Peak Current Ipk = Vdrive / (Rdrv + Rg) Drive Voltage 0.33 V, Driver Resistance 1 Ω, Gate Resistance 2.2 Ω → Peak Gate Current = 103.1 mA
- Bootstrap Capacitor Cboot = Qg / ΔV Gate Charge 100 pC, Allowed Droop 10 mV → Bootstrap Capacitance = 10 nF
- MOSFET Output Capacitance Loss P = ½ · Coss · Vds² · fsw Output Capacitance 1 pF, Drain-Source Voltage 0.33 V, Switching Frequency 100 Hz → Power Loss = 5.45 × 10⁻⁶ µW
- Diode Reverse-Recovery Loss P = Qrr · Vin · fsw Recovery Charge 100 pC, Switching Voltage 0.33 V, Switching Frequency 100 Hz → Power Loss = 0.0033 µW
Worked result for every Semiconductors formula
| Formula | Expression | Worked result |
|---|---|---|
| MOSFET Conduction Loss | P = I² × Rds(on) | Drain Current 2 mA, Rds(on) 0.1 mΩ → Power = 4 × 10⁻⁴ µW |
| MOSFET Switching Loss | P = ½ × V × I × (tr + tf) × f | Drain-Source Voltage 0.33 V, Drain Current 2 mA, Rise Time 100 ps, Fall Time 0.22 ns, Switching Frequency 100 Hz → P = 1.06 × 10⁻¹¹ W |
| BJT Total Dissipation | P = VCE × IC + VBE × IB | VCE 0.33 V, IC 2 mA, VBE 0.726 V, IB 100 µA → P = 7.33 × 10⁻⁴ W |
| Diode Power Loss | P = Vf × If | Forward Voltage 0.33 V, Forward Current 2 mA → Power = 0.66 mW |
| Zener Regulation Resistor | R = (Vin − Vz) / (Iz + Iload) | Input Voltage 3.3 V, Zener Voltage 1.55 V, Zener Current 1 mA, Load Current 0.47 mA → Resistance = 1.19 kΩ |
| Transistor Current Gain (β) | β = IC / IB | Collector Current 100 µA, Base Current 100 nA → Current Gain = 1000 |
| MOSFET Gate Drive Power | Pd = Qg × Vgs × f | Total Gate Charge 100 pC, Gate-Source Voltage 0.33 V, Switching Frequency 100 Hz → Gate Drive Power = 0.0033 µW |
| MOSFET Rds(on) vs Temperature | RDS(T) = RDS_ref × (1 + tc × ΔT) | Rds(on) Reference 0.22 mΩ, Temp Coefficient 0.025, Temperature Change 2.5 °C → Rds(on) at Temp = 0.2338 mΩ |
| Op-Amp Slew Rate Limit | fmax = SR / (2π × Vpk) | Slew Rate 0.1 V/µs, Peak Output Voltage 0.33 V → Max Frequency = 48.23 kHz |
| BJT Vbe vs Temperature | Vbe(T) = Vbe_ref − 0.002 × ΔT | Vbe Reference 22 mV, Temperature Change 2.5 °C → Vbe at Temp = 17 V |
| Diode Vf vs Temperature | Vf(T) = Vf_ref − 0.002 × ΔT | Vf Reference 22 mV, Temperature Change 2.5 °C → Vf at Temp = 17 V |
| Op-Amp Input Offset Error | Vos_total = Vos + drift × ΔT | Initial Offset 2.2 µV, Offset Drift 0.1 µV/°C, Temperature Change 2.5 °C → Total Offset = 2.45 V |
| MOSFET Gate Drive Headroom | Vmargin = Vgs − Vth | Gate-Source Voltage 0.726 V, Threshold Voltage 1.55 V → Gate Headroom = -0.824 V |
| BJT Emitter Bias Current | Ic ≈ (VB − 0.7) / RE | Base Voltage 0.33 V, Emitter Resistor 1 Ω → Collector Current = -0.37 A |
| Shockley Diode Equation | I = Is × (e^(V/(n×Vt)) − 1) | Diode Voltage 10 mV, Saturation Current 100 pA, Ideality Factor 0.025 → I = 5.25 × 10⁻⁴ |
| IGBT Total Loss | P = Vce × Ic × D + Esw × f | Collector-Emitter Voltage 0.33 V, Collector Current 2 mA, Duty Cycle 2.5 %, Switching Energy (Eon+Eoff) 100 µJ, Switching Frequency 100 Hz → P = 0.01002 |
| MOSFET Body Diode Loss | P = Vf × If × (1 − D) | Diode Forward Voltage 0.33 V, Diode Current 2 mA, Duty Cycle 2.5 % → Body Diode Loss = 0.6435 mW |
| MOSFET Avalanche Energy | Eas = 0.5 × L × I² × Vbr/(Vbr − Vcc) | Inductance 100 nH, Current at Turn-Off 2 mA, Breakdown Voltage 0.33 V, Supply Voltage 0.726 V → Eas = -1.67 × 10⁻¹³ |
| Varactor Diode Capacitance | C = Cj0 / (1 + V/Vbi)^m | Zero-Bias Capacitance 1 pF, Reverse Bias Voltage 0.33 V, Built-in Potential 0.726 V, Grading Coefficient 0.025 → C = 9.91 × 10⁻¹³ |
| Gate-Driver Peak Current | Ipk = Vdrive / (Rdrv + Rg) | Drive Voltage 0.33 V, Driver Resistance 1 Ω, Gate Resistance 2.2 Ω → Peak Gate Current = 103.1 mA |
| Bootstrap Capacitor | Cboot = Qg / ΔV | Gate Charge 100 pC, Allowed Droop 10 mV → Bootstrap Capacitance = 10 nF |
| MOSFET Output Capacitance Loss | P = ½ · Coss · Vds² · fsw | Output Capacitance 1 pF, Drain-Source Voltage 0.33 V, Switching Frequency 100 Hz → Power Loss = 5.45 × 10⁻⁶ µW |
| Diode Reverse-Recovery Loss | P = Qrr · Vin · fsw | Recovery Charge 100 pC, Switching Voltage 0.33 V, Switching Frequency 100 Hz → Power Loss = 0.0033 µW |
Variables used across Semiconductors formulas
- P — Conduction power loss (W)
- I — Drain current (A)
- Rds(on) — On-state drain-source resistance (Ω)
- V — Drain-source voltage being switched (V)
- tr — Turn-on rise time (s)
- tf — Turn-off fall time (s)
- f — Switching frequency (Hz)
- VCE — Collector-emitter voltage (V)
- IC — Collector current (A)
- VBE — Base-emitter voltage (V)
- IB — Base current (A)
- Vf — Forward voltage drop (V)
- If — Forward current (A)
- R — Series resistor value (Ω)
- Vin — Input supply voltage (V)
- Vz — Zener breakdown voltage (V)
- Iz — Minimum Zener current for regulation (A)
- Iload — Maximum expected load current (A)
- β — DC current gain (dimensionless)
- Pd — Average gate drive power loss (W)
- Qg — Total gate charge per switching cycle (C)
- Vgs — Gate drive voltage (V)
- RDS — Rds(on) at operating temperature (Ω)
- RDS_ref — Rds(on) at reference temperature, usually 25°C (Ω)
- tc — Temperature coefficient (typically 0.004 to 0.008 per °C for Si)
- ΔT — Temperature rise from reference (°C)
- fmax — Maximum undistorted frequency (Hz)
- SR — Op-amp slew rate (V/s)
- Vpk — Peak output voltage amplitude (V)
- Vbe — Base-emitter voltage at operating temperature (V)
- Vbe_ref — Vbe at reference temperature (V)
- Vf_ref — Forward voltage at reference temperature (V)
- Vos_total — Total input offset voltage (V)
- Vos — Initial offset at room temperature (V)
- drift — Offset temperature drift (V/°C)
- V_margin — Gate drive headroom above threshold (V)
- V_gs — Applied gate-to-source voltage (V)
- V_th — Gate threshold voltage (V)
- Ic — Collector current (A)
- V_B — Base voltage from voltage divider (V)
- R_E — Emitter resistor (Ω)
- Is — Reverse saturation current (A)
- n — Ideality factor (1-2, dimensionless)
- V_ce — Collector-emitter saturation voltage (V)
- I_c — Collector current (A)
- D — Duty cycle (0 to 1)
- E_sw — Total switching energy per cycle, Eon + Eoff (J)
- V_f — Body diode forward voltage (V)
- I_f — Current through the body diode (A)
- L — Parasitic or load inductance (H)
- V_br — MOSFET avalanche breakdown voltage (V)
- V_cc — Supply voltage (V)
- C_j0 — Zero-bias junction capacitance (F)
- V_bi — Built-in junction potential (V, typically 0.6-0.8 for Si)
- m — Grading coefficient (0.3-2, dimensionless)
- Ipk — Peak gate-drive current (A)
- Vdrive — Gate drive voltage (V)
- Rdrv — Driver internal output resistance (Ω)
- Rg — External gate resistor (Ω)
- Cboot — Bootstrap capacitance (F)
- ΔV — Allowed bootstrap voltage droop (V)
- Coss — Effective output capacitance (F)
- Vds — Drain-source voltage at turn-on (V)
- fsw — Switching frequency (Hz)
- Qrr — Reverse-recovery charge (C)
Questions people ask about Semiconductors
- Mosfet conduction loss i squared rds on formula — MOSFET Conduction Loss
- Mosfet conduction loss formula — MOSFET Conduction Loss
- Fall time in mosfet formula — MOSFET Switching Loss
- What is the current gain beta of a transistor — Transistor Current Gain (β)
- Β bipolar transistor how calculate — Transistor Current Gain (β)
- Calculate maximum undistorted frequency from slew rate — Op-Amp Slew Rate Limit
- Vbe temp coefficient — BJT Vbe vs Temperature
- Calculate voltage headroom — MOSFET Gate Drive Headroom
- How to calculate body-diode forward current of mosfet — MOSFET Body Diode Loss
- Mosfet avalanche calculation — MOSFET Avalanche Energy
- Avalanche energy calculate — MOSFET Avalanche Energy
- Gate driver peak current — Gate-Driver Peak Current
- Diode reverse recovery loss calculation — Diode Reverse-Recovery Loss
- Reverse recovery charge calculation — Diode Reverse-Recovery Loss
Related Formula Categories
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