About this calculator
This voltage divider bias NPN BJT common collector calculator analyzes a common-collector amplifier built with an NPN bipolar junction transistor and a voltage-divider bias network. Enter your component values and it immediately finds the DC operating point (IC, VCE and the operating region), the small-signal parameters, voltage, current and power gain, input and output impedance, the output waveform with its clipping limits, the frequency response and the power dissipated in every component. Each result can be expanded to show the equation used and the numbers substituted into it, so you can follow or check the working by hand.
How to use it
- Enter the supply rails (VCC and VEE; use 0 V for a grounded lower rail).
- Type the resistor values and pick Ω, kΩ or MΩ, or type suffixes directly, such as
4.7kor1M. Enterinffor an open-circuit load. - Set the transistor parameters β, VBE(on), VCE(sat), temperature and Early voltage.
- Enter the signal amplitude, frequency and source resistance Rsig.
- Switch on Frequency Response to add the coupling and internal capacitances and see the Bode plot, fL and fH.
- Use the link button to copy a URL that reopens the calculator with your values.
How the common collector amplifier works
In the common-collector (CC) amplifier, better known as the emitter follower, the signal enters at the base and the output is taken from the emitter. The collector is at AC ground, connected to the supply directly or through a small resistor. The emitter voltage follows the base voltage one base–emitter drop away, so the voltage gain is slightly less than one and the output is in phase with the input.
Its value is impedance transformation. The resistance in the emitter is multiplied by (β + 1) when seen from the base, which gives a high input impedance. The output impedance is the source resistance divided by (β + 1) plus re, often only a few ohms to a few tens of ohms. That makes the emitter follower the standard buffer between a high-impedance stage and a low-impedance load such as a speaker, a cable or the next stage.
The gain approaches unity when gm·RL′ is much larger than one, where RL′ = RE ∥ RL ∥ ro. With heavy loads the output swing can become limited on the side where the transistor would cut off, because the emitter current cannot fall below zero. Check the “maximum undistorted swing” result when RL is small.
Voltage-divider bias
Voltage-divider bias, also called four-resistor bias, is the most widely used discrete BJT bias network. R1 and R2 form a divider that holds the base near a fixed voltage, and RE converts that voltage into an emitter current. Replacing the divider by its Thevenin equivalent gives VTH = VEE + (VCC − VEE)·R2/(R1 + R2) and RTH = R1 ∥ R2, and then IB = (VTH − VBE − VEE)/(RTH + (β + 1)·RE).
When (β + 1)·RE is much larger than RTH (a common rule of thumb is a factor of ten), the emitter current hardly depends on β at all. The calculator always uses the exact Thevenin equation instead of the stiff-divider approximation, so it stays accurate even for a “soft” divider with large resistors. Remember that the divider also appears in parallel with the transistor’s input, so very small R1 and R2 stabilize the bias at the cost of input impedance.
NPN polarity and conventions
An NPN transistor conducts when its base is about 0.6–0.7 V above its emitter. Conventional current flows into the collector and the base and out of the emitter, so in a single-supply circuit the emitter is connected toward ground and the collector load toward the positive rail. All voltages in this calculator follow that convention: VBE, VCE and VCB are positive in the forward-active region. Saturation is detected when VCE falls to VCE(sat), and the calculator then re-solves both loop equations instead of simply flagging the problem.
For the complementary circuit, see the Voltage Divider Bias PNP BJT Common Collector calculator. Comparing the two is a quick way to check your PNP/NPN sign conventions.
Equations used
The calculator follows the standard two-step method taught in electronics courses. It first solves the DC bias circuit with all capacitors open, then replaces the transistor with its small-signal model and the capacitors with short circuits to find the mid-band AC behavior. These are the equations for this common-collector circuit with the default component values.
DC analysis
- Thevenin Base Voltage (VTH)
VTH = VEE + (VCC − VEE) × R2 / (R1 + R2) - Thevenin Base Resistance (RTH)
RTH = R1 ∥ R2 - Base Current (IB)
IB = (VTH − VBE − VEE) / (RTH + (β + 1)·RE) - Collector Current (IC)
IC = β × IB - Emitter Current (IE)
IE = (β + 1) × IB - VCE (assuming active)
VCE = (VCC − VEE) − IC·RC − IE·RE
Small-signal analysis
- Thermal Voltage (VT)
VT = k·T / q = T / 11604.5 - Transconductance (gm)
gm = IC / VT - Base–Emitter Resistance (rπ)
rπ = β / gm - Output Resistance (ro)
ro = VA / IC - Emitter AC Load (RL′)
RL′ = RE ∥ RL ∥ ro - Resistance Looking into Base (Rib)
Rib = rπ + (β + 1)·RL′ - Voltage Gain (Av = vo / vb)
Av = (β + 1)·RL′ / Rib - Overall Gain (Gv = vo / vs)
Gv = Av × Zin / (Zin + Rsig) - Current Gain (Ai = io / ii)
Ai = Av × Zin / RL - Power Gain (Ap)
Ap = |Av × Ai| - Input Impedance (Zin)
Zin = RTH ∥ Rib - Output Impedance (Zout)
Zout = RE ∥ ro ∥ (rπ + Rsig ∥ RTH)/(β + 1)
The frequency-response section adds one low-frequency pole for each coupling or bypass capacitor, using the resistance that capacitor sees (short-circuit time constants), and estimates the upper cut-off frequency from the transistor’s internal capacitances using open-circuit time constants. The exact −3 dB points are then found numerically from the combined response.
Worked example
The calculator opens with a ready-to-use example circuit: VCC = 12 V, VEE = 0 V, R1 = 10 kΩ, R2 = 10 kΩ, RC = 0 Ω, RE = 1 kΩ, RL = 1 kΩ, β = 100, VBE(on) = 0.7 V, VCE(sat) = 0.2 V, T = 300 K, VA = 100 V, signal amplitude = 10 mV peak, signal frequency = 1000 Hz, Rsig = 50 Ω. The analysis of that circuit, with frequency response switched on and the default capacitor values, gives:
| Operating region | Forward-active |
|---|---|
| Collector Current (IC) | 5 mA |
| VCE | 6.95 V |
| gm | 193.4 mS |
| rπ | 517 Ω |
| ro | 20 kΩ |
| Voltage gain Av | 0.9896 V/V |
| Overall gain Gv (from Rsig) | 0.9788 V/V (−0.186 dB) |
| Input impedance Zin | 4.544 kΩ |
| Output impedance Zout | 5.577 Ω |
| Output amplitude at 1 kHz | 9.787 mV peak |
| Lower cut-off fL | 16.54 Hz |
| Upper cut-off fH | 1.029 GHz |
| Transistor power PT | 34.78 mW |
| Total supply power | 67.5 mW |
The transistor is in the forward-active region with IC = 5 mA and VCE = 6.95 V, which leaves 2.525 V of undistorted output swing. The stage has a voltage gain of 0.9896 V/V, so a 10 mV peak input signal produces an output of about 9.787 mV peak, in phase with the input. The mid-band region extends from 16.54 Hz to 1.029 GHz. Change any value above to see how the results move.
Key characteristics of the common-collector stage
| Property | Typical behavior | Default example |
|---|---|---|
| Voltage gain | ≈ 1, non-inverting | 0.9896 V/V |
| Current gain | High (≈ β + 1) | 4.496 A/A |
| Power gain | ≈ current gain | 4.45 |
| Input impedance | High (≈ (β + 1)·RL′ ∥ bias) | 4.544 kΩ |
| Output impedance | Very low | 5.577 Ω |
| Phase shift | 0° | 0° |
| Typical uses | Buffers, output stages, impedance matching | |
Design tips
- Bias the emitter near the middle of the available voltage range so the output can swing symmetrically.
- For a low output impedance the source driving the base should itself have a low resistance, since Zout ≈ (Rs′ + rπ)/(β + 1).
- With a small load, raise the bias current so that IE·(RE ∥ RL) exceeds the required peak output. Otherwise the peaks on the cut-off side clip.
Frequently asked questions
Why is the voltage gain of an emitter follower less than one?
The output is the emitter voltage, which is the base voltage minus the base–emitter voltage. For signals, a small part of the input appears across re instead of the load, so the gain is gm·RL′/(1 + gm·RL′), always slightly below one.
Why use a common-collector stage if it has no voltage gain?
It provides large current gain and turns a high-impedance source into a low-impedance one. A weak signal source that could not drive a low-resistance load directly can drive it through an emitter follower with almost no loss of amplitude.
Does the emitter follower invert the signal?
No. The emitter moves in the same direction as the base, so the phase shift is 0° in mid-band.
Why is voltage-divider bias more stable than fixed bias?
The divider fixes the base voltage instead of the base current, and the emitter resistor converts that voltage into a current. A change in β mainly changes the small base current, which barely moves a stiff divider, so the collector current stays almost constant.
What values of β and VBE should I use?
Use the datasheet’s typical hFE at your collector current, often 100 to 300 for small-signal parts such as the 2N3904 or BC547. VBE(on) of 0.7 V is the standard hand-analysis value for silicon. Try the minimum and maximum β from the datasheet to see how sensitive your design is.
What voltage gain does this CC amplifier give with the default values?
With the default components the calculator gives Av = 0.9896 V/V (−0.0907 dB) from the base to the load, and an overall gain of 0.9788 V/V from the 50 Ω signal source, with Zin = 4.544 kΩ and Zout = 5.577 Ω.