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BJT Collector Current (Early Effect)

Models BJT collector current including the Early effect, where output resistance is finite.

Written by the Vorzep Team

Semiconductor DevicesBJT

BJT Collector Current Calculator Early Effect Model

IC = IS · eVBE / VT · (1 + VCE / VA)
IC = collector current  ·  IS = saturation current  ·  VBE = base‑emitter voltage  ·  VT = thermal voltage  ·  VCE = collector‑emitter voltage  ·  VA = Early voltage
⟹ Solve ⟷ IC, IS, VBE, VCE, VA
A
A
V
V
V
V (typical 25.85 mV at 300 K)
Please fix the errors above.
Solve for:
Presets:
Collector Current —
—
IC: — IS: — VBE: — VCE: — VA: —
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Collector Current Gauge —
Low (< 1 mA) Medium (1–10 mA) High (> 10 mA)
IC = IS · eVBE/VT · (1 + VCE/VA)  ·  VT ≈ 25.85 mV at 300 K. All currents in amperes.

Interpretation

BJT collector current including Early effect: I_C = I_S·e^(V_BE/V_T)·(1 + V_CE/V_A).
The Early effect causes I_C to increase with V_CE due to base‑width modulation.
Example: If V_A=50V and V_CE=10V, the factor (1+10/50)=1.2, so current is 20% higher than the ideal value.

I_C = I_S·e^(V_BE/V_T)·(1 + V_CE/V_A)
BJT Collector Current (Early Effect)

Variables

SymbolQuantityUnit
I_CCollector currentA
I_SSaturation current (scale current)A
V_BEBase-emitter voltageV
V_TThermal voltage (kT/q, ≈26mV at 300K)V
V_CECollector-emitter voltageV
V_AEarly voltage (finite output impedance parameter)V

What it means

The Early effect is the increase in collector current with increasing V_CE due to the base‑width modulation. The collector current is I_C = I_S · e^(V_BE/V_T) · (1 + V_CE/V_A), where V_A is the Early voltage (a parameter of the transistor). The factor (1 + V_CE/V_A) accounts for the increase. The Early effect is a non‑ideality that affects the output resistance of the transistor. It reduces the amplifier gain and must be considered in high‑precision analog designs. Example: If V_A = 50V, at V_CE = 10V, the factor is (1 + 10/50) = 1.2. So the current is 20% higher than the ideal value. This must be accounted for in a current mirror or amplifier design.

Worked example

BJT Collector Current with Early Effect – Practical Example

Real‑World
Scenario: A BJT has IS = 1×10⁻¹⁵ A, VBE = 0.65 V, VT = 26 mV, VCE = 5 V, and VA = 50 V. Calculate IC considering Early effect.
ParameterValue
IS1×10⁻¹⁵ A
VBE0.65 V
VT0.026 V
VCE5 V
VA50 V
FormulaIC = IS·eVBE/VT·(1 + VCE/VA)
1e0.65/0.026 = e25 ≈ 7.2×10¹⁰
2IC = 1e-15 × 7.2e10 × (1 + 5/50) = 7.2e-5 × 1.1 = 7.92e-5 A
Final Design IC ≈ 79.2 µA ✓ Includes Early effect
Why: Early effect causes IC to increase with VCE – this finite output resistance is important in amplifier design.

Common mistakes

  • I_S: Saturation current – depends on the transistor.
  • Thermal voltage V_T: About 25 mV at room temperature.
  • Early voltage V_A: Accounts for base‑width modulation – higher V_A means better.
  • V_CE: Collector‑emitter voltage – must be sufficient for forward‑active region.
  • Exponential: The current depends exponentially on V_BE.

Applications

BJT collector current including Early effect: I_C = I_S·e^(V_BE/V_T)·(1 + V_CE/V_A). This accounts for base‑width modulation, which causes the collector current to increase with V_CE. Engineers use this model to predict output resistance, to design amplifiers with high gain, and to minimise distortion. The Early voltage V_A is a parameter that characterises the transistor's output impedance. By understanding the Early effect, professionals can design more linear and stable circuits. This formula is important for high‑precision analog design and for SPICE simulation modelling.

  • High‑gain amplifier design with improved linearity
  • Output resistance and load driving capability analysis
  • SPICE model parameter extraction and simulation
  • Current source and cascode circuit design
  • Educational understanding of transistor output characteristics

Frequently Asked Questions

Q01What is the BJT collector current equation including the Early effect?
A01

The collector current is I_C = I_S·e^(V_BE/V_T)·(1 + V_CE/V_A), where V_A is the Early voltage. This accounts for the finite output resistance of the BJT in the forward‑active region.

Q02What is the Early effect and why is it important?
A02

The Early effect (base‑width modulation) causes the collector current to increase with V_CE even when V_BE is constant. This leads to a finite output resistance, affecting amplifier gain.

Q03How does the Early voltage V_A affect the output resistance?
A03

The output resistance r_o = V_A / I_C. A larger V_A means a higher output resistance, which is desirable for high‑gain amplifiers.

Q04What are common mistakes when using the Early effect formula?
A04

Common errors: 1) Forgetting the (1 + V_CE/V_A) factor, 2) Using V_A as a fixed value (it varies with doping and geometry), 3) Applying the formula in saturation, 4) Using the formula for PNP without adjusting the sign, 5) Ignoring the effect of temperature on V_A.

Q05What are practical applications of the Early effect?
A05

Used in: 1) Analysing BJT amplifier gain (r_o loads the collector), 2) Designing current mirrors (Early effect causes mismatch), 3) Understanding the output impedance of cascode circuits, 4) RF amplifier design.

Q06How does the Early effect affect the voltage gain of a common-emitter amplifier?
A06

The voltage gain is A_v = −g_m (R_C || r_o). The Early effect reduces the gain because r_o is finite. Including r_o gives a more accurate gain calculation.

Q07What is the typical range of Early voltages?
A07

For small‑signal BJTs, V_A is typically 50‑200 V. For power transistors, it may be lower.

Q08How do you measure the Early voltage?
A08

By measuring I_C as a function of V_CE at constant V_BE, extrapolating the linear region to find the intercept on the V_CE axis (negative of V_A).