Transistor Bias Calculator: Voltage-Divider Bias, Q Point, Load Line and Gain

Find the operating point of a bipolar transistor with voltage-divider bias, and check it is in the active region.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the supply voltage, the two base resistors, the collector and emitter resistors, the current gain and the base-emitter voltage.

The calculator finds the Thevenin equivalent of the base divider, then the base, collector and emitter currents and the collector-emitter voltage.

It checks that the transistor is active, draws the DC load line with the Q point, and gives the small-signal gain with and without an emitter bypass capacitor.

Formulas used

  • V_{TH} = V_{CC}\frac{R_2}{R_1 + R_2}
  • I_B = \frac{V_{TH} - V_{BE}}{R_{TH} + (\beta + 1)R_E}
  • V_{CE} = V_{CC} - I_CR_C - I_ER_E
  • A_v = -\frac{R_C}{r_e}

Worked example

With the default numbers in the calculator above:

  1. Thevenin voltage and resistance seen from the base: 2.11 V and 8.25 kohm
  2. Base current: 12.86 uA
  3. Collector current: 1.29 mA
  4. Emitter current: 1.30 mA
  5. Collector-emitter voltage: 7.87 V
  6. Load line end points: saturation current and cut-off voltage: 3.75 mA and 12.00 V
  7. Small-signal emitter resistance: 19.90 ohm
  8. Voltage gain with the emitter resistor bypassed by a capacitor: -110.57
  9. Voltage gain with the emitter resistor not bypassed: -2.16

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is the Q point?

The quiescent point: the DC current and voltage of the transistor with no signal. The signal swings around it.

Where should the Q point be?

Near the middle of the load line, so the signal can swing up and down without clipping.

Why use an emitter resistor?

It gives negative feedback that holds the current steady when the transistor current gain or the temperature changes.

Why does a bypass capacitor raise the gain?

It removes the emitter resistor from the signal path, so the gain is the collector resistor over the small emitter resistance r_e.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Sedra and Smith, Microelectronic Circuits (BJT biasing); Boylestad and Nashelsky, Electronic Devices and Circuit Theory.

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