Discrete Amplifiers Formulas
Discrete Amplifiers formulas cover Thermal Voltage, Small-Signal Emitter Resistance, Transistor Transconductance and more. These calculators let you solve for any unknown by entering the values you already know. Use them for quick design checks, study, and verifying real circuits.
Discrete Amplifiers Formula Calculators
- Thermal Voltage VT = k · T / q Temperature 7.7 K → Thermal Voltage = 0.6635 mV
- Small-Signal Emitter Resistance re = VT / Ie Thermal Voltage 10 mV, Emitter Current 100 µA → Emitter Resistance = 100 Ω
- Transistor Transconductance gm = Ic / VT Collector Current 100 µA, Thermal Voltage 10 mV → Transconductance = 10 mS
- Diode Dynamic Resistance rd = VT / Id Thermal Voltage 10 mV, Diode Current 100 µA → Dynamic Resistance = 100 Ω
- Common-Emitter Voltage Gain Av = −Rc / re Collector Resistor 100 Ω, Emitter Resistance 1 Ω → Voltage Gain = -100
- BJT Alpha–Beta Relationship α = β/(β+1), β = α/(1−α) Common-Emitter Gain β 0.055 → Common-Base Gain α = 0.05213
- Darlington Pair Current Gain βtotal = β1 · β2 Gain β1 0.055, Gain β2 0.118 → Total Gain = 0.00649
- Emitter-Follower Input Impedance Zin ≈ β · RE Current Gain β 0.025, Emitter Resistor 0.22 kΩ → Input Impedance = 5.5 Ω
- Cascaded Amplifier Gain Av = Av1 · Av2 · Av3 Stage 1 Gain 0.055, Stage 2 Gain 0.118, Stage 3 Gain 0.0118 → Total Gain = 7.66 × 10⁻⁵
- JFET Drain Current (Shockley) Id = Idss · (1 − Vgs/Vp)² Idss 0.22 mA, Gate-Source Voltage 0.33 V, Pinch-off Voltage 0.726 V → Drain Current = 65.45 µA
- MOSFET Drain Current (Saturation) Id = K · (Vgs − Vth)² Conduction Parameter 100 µA/V², Gate-Source Voltage 0.33 V, Threshold Voltage 0.726 V → Drain Current = 15.68 µA
- Transistor Switch Base Resistor Rb = (Vin − Vbe) · β / Ic Drive Voltage 0.33 V, Base-Emitter Voltage 0.726 V, Current Gain β 0.025, Collector Current 100 µA → Base Resistor = -99 Ω
- Amplifier Power Gain Ap = Av · Ai Voltage Gain 0.055, Current Gain 0.118 → Power Gain = 0.00649
- BJT Emitter-Bias Current Ic ≈ (Vb − Vbe) / Re Base Voltage 0.33 V, Base-Emitter Voltage 0.726 V, Emitter Resistor 100 Ω → Collector Current = -3.96 mA
- Common-Source JFET Gain Av = −gm · Rd Transconductance 100 µS, Drain Resistor 100 Ω → Voltage Gain = -0.01
- Common-Collector Current Gain Ai = β + 1 Current Gain β 0.055 → Current Gain = 1.055
Worked result for every Discrete Amplifiers formula
| Formula | Expression | Worked result |
|---|---|---|
| Thermal Voltage | VT = k · T / q | Temperature 7.7 K → Thermal Voltage = 0.6635 mV |
| Small-Signal Emitter Resistance | re = VT / Ie | Thermal Voltage 10 mV, Emitter Current 100 µA → Emitter Resistance = 100 Ω |
| Transistor Transconductance | gm = Ic / VT | Collector Current 100 µA, Thermal Voltage 10 mV → Transconductance = 10 mS |
| Diode Dynamic Resistance | rd = VT / Id | Thermal Voltage 10 mV, Diode Current 100 µA → Dynamic Resistance = 100 Ω |
| Common-Emitter Voltage Gain | Av = −Rc / re | Collector Resistor 100 Ω, Emitter Resistance 1 Ω → Voltage Gain = -100 |
| BJT Alpha–Beta Relationship | α = β/(β+1), β = α/(1−α) | Common-Emitter Gain β 0.055 → Common-Base Gain α = 0.05213 |
| Darlington Pair Current Gain | βtotal = β1 · β2 | Gain β1 0.055, Gain β2 0.118 → Total Gain = 0.00649 |
| Emitter-Follower Input Impedance | Zin ≈ β · RE | Current Gain β 0.025, Emitter Resistor 0.22 kΩ → Input Impedance = 5.5 Ω |
| Cascaded Amplifier Gain | Av = Av1 · Av2 · Av3 | Stage 1 Gain 0.055, Stage 2 Gain 0.118, Stage 3 Gain 0.0118 → Total Gain = 7.66 × 10⁻⁵ |
| JFET Drain Current (Shockley) | Id = Idss · (1 − Vgs/Vp)² | Idss 0.22 mA, Gate-Source Voltage 0.33 V, Pinch-off Voltage 0.726 V → Drain Current = 65.45 µA |
| MOSFET Drain Current (Saturation) | Id = K · (Vgs − Vth)² | Conduction Parameter 100 µA/V², Gate-Source Voltage 0.33 V, Threshold Voltage 0.726 V → Drain Current = 15.68 µA |
| Transistor Switch Base Resistor | Rb = (Vin − Vbe) · β / Ic | Drive Voltage 0.33 V, Base-Emitter Voltage 0.726 V, Current Gain β 0.025, Collector Current 100 µA → Base Resistor = -99 Ω |
| Amplifier Power Gain | Ap = Av · Ai | Voltage Gain 0.055, Current Gain 0.118 → Power Gain = 0.00649 |
| BJT Emitter-Bias Current | Ic ≈ (Vb − Vbe) / Re | Base Voltage 0.33 V, Base-Emitter Voltage 0.726 V, Emitter Resistor 100 Ω → Collector Current = -3.96 mA |
| Common-Source JFET Gain | Av = −gm · Rd | Transconductance 100 µS, Drain Resistor 100 Ω → Voltage Gain = -0.01 |
| Common-Collector Current Gain | Ai = β + 1 | Current Gain β 0.055 → Current Gain = 1.055 |
Variables used across Discrete Amplifiers formulas
- VT — Thermal voltage (V)
- T — Absolute temperature (K)
- k — Boltzmann constant 1.381×10⁻²³ J/K
- q — Elementary charge 1.602×10⁻¹⁹ C
- re — Small-signal emitter resistance (Ω)
- Ie — DC emitter current (A)
- gm — Transconductance (S = A/V)
- Ic — Collector bias current (A)
- rd — Small-signal dynamic resistance (Ω)
- Id — DC bias current (A)
- Av — Voltage gain (negative = inverting)
- Rc — Collector load resistance (Ω)
- α — Common-base current gain (Ic/Ie, < 1)
- β — Common-emitter current gain (Ic/Ib)
- βtotal — Combined current gain
- β1 — First (driver) transistor gain
- β2 — Second (output) transistor gain
- Zin — Input impedance looking into the base (Ω)
- RE — Emitter resistance / load (Ω)
- Av(total) — Overall voltage gain
- Av1, Av2, Av3 — Individual stage gains (set unused = 1)
- Idss — Drain current at Vgs = 0 (A)
- Vgs — Gate-source voltage (V)
- Vp — Pinch-off / cutoff voltage (V)
- K — Conduction parameter ½µCox(W/L) (A/V²)
- Vth — Threshold voltage (V)
- Rb — Base resistor (Ω)
- Vin — Logic/drive high voltage (V)
- Vbe — Base-emitter drop (~0.7 V)
- Ap — Power gain
- Ai — Current gain (magnitude)
- Vb — Voltage at the base node (V)
- Re — Emitter resistor (Ω)
- Rd — Drain load resistance (Ω)
Questions people ask about Discrete Amplifiers
- Re = vt / ie small signal emitter resistance calculation — Small-Signal Emitter Resistance
- Transistor thermal voltage vt — Transistor Transconductance
- Dynamic resistance of diode formula rd = dv/di — Diode Dynamic Resistance
- Common emitter voltage gain formula — Common-Emitter Voltage Gain
- Bjt alpha beta relationship — BJT Alpha–Beta Relationship
- Bjt alpha beta — BJT Alpha–Beta Relationship
- Calculate the drain current for idss = 8ma, vp = −4 v and vgs = −2 v — JFET Drain Current (Shockley)
- Jfet common source amplifier gain calculation — Common-Source JFET Gain
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