Calculate the DC operating point and AC voltage gain of a common-emitter amplifier from the supply voltage, bias resistors, and collector and emitter resistors.

NPN approximation with a stiff bias divider: base current is neglected and IC โ‰ˆ IE. Assumed VBE starts at 0.7 V; change it for your device.

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Common Emitter Amplifier Formula

For a forward-active NPN transistor at midband, the calculator estimates base-to-collector small-signal voltage gain using the effective collector load and the unbypassed emitter resistance:

Aแตฅ โ‰ˆ - (RC โˆฅ RL) / (rโ€ฒโ‚‘ + RE,unbypassed) rโ€ฒโ‚‘ โ‰ˆ 0.026 V / IC
  • A_v is the approximate base-to-collector voltage gain (Vout/Vin). The negative sign indicates inversion.
  • R_C is the collector resistor (ฮฉ). R_C โˆฅ R_L is its parallel combination with the optional external load; with no external load, use R_C alone.
  • R_E,unbypassed is the unbypassed AC emitter resistance (ฮฉ). rโ€ฒ_e is the approximate intrinsic emitter resistance, using I_C in amperes, I_C โ‰ˆ I_E and 26 mV thermal voltage near room temperature.

Select DC operating point or AC voltage gain and enter the fields shown. DC uses the unloaded-divider approximation V_B = VCC Rโ‚‚/(Rโ‚ + Rโ‚‚), V_E = V_B โˆ’ VBE, I_C โ‰ˆ I_E = V_E/R_E, V_C = VCC โˆ’ I_C R_C and V_CE = V_C โˆ’ V_E. Base-current loading is ignored, so the divider must be stiff. VBE defaults to an assumed 0.7 V and is adjustable. Inputs outside the conducting forward-active model (V_E โ‰ค 0 or V_C โ‰ค V_B) are rejected.

What is a Common Emitter Amplifier?

Definition:

A common emitter amplifier is a basic transistor configuration where the emitter is common to both the input and output circuits. It is widely used in analog electronics to provide significant voltage gain with an inverted output signal.

How to Calculate a Common Emitter Amplifier?

Example Problem:

The following example uses the simpler unloaded, strong-emitter-degeneration approximation A_v โ‰ˆ โˆ’R_C/R_E. It applies when the unbypassed R_E is much larger than rโ€ฒ_e and the external load is negligible.

First, determine the collector resistor value. In this example, the collector resistor is 1000 ฮฉ.

Next, determine the emitter resistor value. In this case, the emitter resistor is 250 ฮฉ.

Finally, calculate the voltage gain using the formula above:

A_v โ‰ˆ โˆ’R_C/R_E

A_v โ‰ˆ โˆ’1000/250

A_v โ‰ˆ โˆ’4 V/V. For example, with I_C = 2 mA, rโ€ฒ_e โ‰ˆ 13 ฮฉ and no external load, the calculator gives โˆ’1000/(13 + 250) โ‰ˆ โˆ’3.802281 V/V.

FAQ

Why is there a negative sign in the voltage gain equation?

The negative sign indicates that the output signal is 180ยฐ out of phase with the input signal in a common emitter amplifier.

Can I use this calculator for designing high-frequency amplifiers?

This calculator estimates midband behavior with coupling and bypass capacitors effective, using large-ฮฒ approximations. It does not model frequency response, transistor output resistance, source attenuation, clipping or component ratings. Optional base input resistance excludes the bias-divider and source resistances.

Which fields can be left blank?

In AC mode, leave external load resistance blank for no external load, and leave ฮฒ blank to omit the base input-resistance estimate. Zero or blank unbypassed emitter resistance means fully bypassed for AC. Required fields are identified in the selected mode. This calculator does not solve a missing parameter by leaving a required field blank.