Common Emitter Amplifier
The common emitter amplifier is the most widely used transistor circuit configuration in all of electronics. Open the schematic of almost any piece of radio equipment — a transceiver, a receiver, a power amplifier, a signal generator — and you will find common emitter stages in abundance. It provides both voltage gain and current gain, which makes it the natural first choice whenever you need to amplify a small signal and deliver it with more power to the next stage. It also inverts the phase of the signal, which is an important characteristic to understand when designing cascaded amplifier chains.
In this lesson you will learn exactly how the common emitter circuit works, how to calculate its voltage gain, why it inverts the phase, what determines its input and output impedance, and how the emitter bypass capacitor dramatically changes its behaviour. All of these characteristics are directly visible on a radio schematic once you know what to look for.
A complete common emitter amplifier with voltage-divider bias. The emitter is common to both input (base) and output (collector) signal paths — hence the name. The bypass capacitor CE across RE is what gives this circuit its high AC gain.
View LargerThe Common Emitter Circuit
The "common emitter" name comes from the topology of the circuit. In a BJT amplifier, one of the three terminals (base, collector, emitter) must be shared between the input port and the output port — otherwise you would not have a two-port amplifier. In the common emitter configuration, the emitter terminal is that shared terminal. The input signal is applied between the base and emitter, and the output is taken between the collector and emitter. Both input and output share the emitter as a common reference point.
A complete common emitter amplifier contains more components than just the transistor:
- RC (collector resistor): Converts collector current changes into voltage changes at the output. This is the load resistor for the amplifier stage.
- RE (emitter resistor): Sets the quiescent current and provides DC stability. It also reduces AC gain unless bypassed.
- R1 and R2 (bias resistors): Form a voltage divider that sets the base bias voltage, establishing the transistor's DC operating point. This is the voltage-divider bias network discussed in detail in lesson M09F.
- Cin (input coupling capacitor): Blocks DC from the signal source while allowing AC signals to pass. Without this, connecting a signal source to the base would upset the bias.
- Cout (output coupling capacitor): Blocks DC from reaching the next stage while passing the amplified AC signal.
- CE (emitter bypass capacitor): Short-circuits RE for AC signals, dramatically increasing the AC voltage gain. Without CE, RE reduces both DC stability and AC gain.
You will encounter this exact collection of components in nearly every discrete transistor amplifier stage in a radio circuit. The values of each component determine the gain, bandwidth, and stability of the stage — which is why learning to calculate them is so valuable.
How the CE Amplifier Amplifies
To understand how a common emitter stage amplifies, trace what happens when the input signal swings positive. A positive-going signal at the base of an NPN transistor increases the forward bias of the base-emitter junction. This causes the transistor to conduct more collector current (recall that Ic = β × Ib, where β is the current gain). More collector current flows through RC, which means a larger voltage drop appears across RC. Since the supply voltage VCC is constant, a larger drop across RC means a smaller voltage remains at the collector. The output voltage — taken at the collector — goes negative when the input goes positive.
This is the key insight: increasing the input produces a decreasing output. The amplifier inverts. When the input swings negative, the base bias decreases, the transistor conducts less, the voltage drop across RC decreases, and the collector voltage rises. Input negative → output positive. This is a 180° phase inversion, and it is a fundamental characteristic of every common emitter amplifier — it is not a malfunction, it is how the circuit is designed to work.
The amplification factor — the voltage gain — comes from the fact that a small change in base voltage produces a large change in collector voltage. A 10 mV change at the base might produce a 500 mV change at the collector, giving a voltage gain of 50. The mechanism is the transistor's ability to control a large collector current with a small base current, and the transformation of that collector current change into a voltage change by the collector resistor.
Phase Inversion Explained
The 180° phase inversion of the common emitter stage has practical consequences in radio design. When you cascade two common emitter stages, the phase inversions cancel: the first stage inverts, the second stage re-inverts, and the output is in phase with the original input. Three cascaded stages produce an overall 180° inversion. This matters because in some circuits — oscillators in particular — positive feedback (where output is fed back in phase with the input) is required to sustain oscillation. In a three-stage CE chain, you cannot create positive feedback by connecting the output directly back to the input, because the overall phase shift is 180°. You would need to add a further 180° of phase shift in the feedback network, which is precisely how certain oscillator configurations work.
In power amplifiers and signal chains, the phase inversion is usually irrelevant to the function of the circuit because the absolute phase of an audio or RF signal does not affect its information content. However, if you are designing a circuit where two signals must be combined — such as a balanced modulator or a push-pull driver — you need to track the phase through every stage carefully.
Phase inversion in the common emitter amplifier. When the input (blue) swings positive, the output (red) swings negative. The output amplitude is larger — this is the voltage gain in action.
View LargerCalculating Voltage Gain
The voltage gain of a common emitter amplifier can be derived from first principles. When the emitter bypass capacitor CE is present (shorted for AC), the AC gain is determined by the ratio of the collector resistance to the transistor's intrinsic emitter resistance re. This intrinsic resistance is not a physical resistor — it is the small-signal resistance of the base-emitter junction itself.
The value of re depends on the quiescent collector current Ic:
re = 26 mV / Ic
where Ic is the quiescent (no-signal) collector current in milliamperes.
AC voltage gain with bypass capacitor:
Av = −RC / re
The negative sign indicates phase inversion.
AC voltage gain without bypass capacitor:
Av = −RC / (re + RE) ≈ −RC / RE (when RE >> re)
The 26 mV figure in the re formula is derived from the thermal voltage at room temperature (approximately 300 K): kT/q = (1.38 × 10⁻²³ × 300) / 1.6 × 10⁻¹⁹ ≈ 26 mV. At different temperatures re changes, which is why transistor gain can vary significantly with temperature — an important consideration in transmitter design.
Step 1: Find re
re = 26 mV / 2 mA = 13 Ω
Step 2: Find AC voltage gain
Av = −RC / re = −2200 / 13 = −169
The gain is 169 (with phase inversion). This means a 10 mV peak input produces a 1.69 V peak output.
Av = −RC / (re + RE) = −2200 / (13 + 470) = −2200 / 483 = −4.6
The gain drops from 169 to just 4.6. RE provides negative feedback that dramatically stabilises the stage but at the cost of gain. The same 10 mV input now produces only 46 mV output. The advantage is that this lower gain is very stable across temperature and transistor variation — two stages at gain 5 each will produce total gain 25 regardless of which transistors you install.
Common Emitter Voltage Gain Calculator
Calculates AC voltage gain for a common emitter stage. Gain is negative (phase inverting) — magnitude is shown. With bypass capacitor: Av = RC / re. Without bypass: Av = RC / (re + RE).
The Emitter Bypass Capacitor
The emitter bypass capacitor CE is one of the most important components in a CE amplifier, and understanding what it does reveals a deeper principle about AC and DC behaviour in circuits.
The emitter resistor RE serves a vital DC purpose: it provides negative feedback that stabilises the operating point. If the temperature rises and the transistor tries to conduct more current, the voltage across RE increases, which reduces the base-emitter voltage (since VBE = Vbase − VRE), which reduces the base current, which counteracts the increase in collector current. This self-regulation keeps the quiescent point stable across temperature and transistor-to-transistor variation — it is what makes a voltage-divider bias circuit robust in practice.
However, for AC signals, RE causes a problem. It appears in series with the signal path (in the emitter lead), and it creates a feedback voltage that opposes the input signal. This is exactly the same negative feedback that stabilises the DC point, but it now acts on the AC signal and reduces the voltage gain. Without CE, the gain is approximately −RC/RE, which is low and determined entirely by resistor values (very stable but low). With CE fitted, the emitter is held at AC ground — the bypass capacitor shorts RE for AC signals — and the gain rises to −RC/re, which is high but depends on Ic and temperature.
In practice, designers often use a split emitter: part of RE is bypassed by CE and part is left unbypassed. This gives intermediate gain that is more stable than the fully bypassed case but higher than the fully unbypassed case. You will find this technique commonly in preamp stages in HF receivers where a specific gain is needed regardless of transistor batch variation.
The value of CE must be chosen so that its reactance at the lowest operating frequency is much smaller than RE. A good rule of thumb: choose CE such that Xc = 1/(2πfC) ≤ RE/10 at the lowest frequency of interest.
Xc target ≤ 470/10 = 47 Ω at 300 Hz
C = 1 / (2π × 300 × 47) = 1 / (88,593) = 11.3 µF
Choose CE = 22 µF (next standard value, gives Xc = 24 Ω at 300 Hz — well below 47 Ω target).
For an RF amplifier at 1 MHz with RE = 100 Ω:
C = 1 / (2π × 1,000,000 × 10) = 15.9 nF
Choose CE = 18 nF or 22 nF (easily achievable with a ceramic capacitor).
Input and Output Impedance
The input impedance of a common emitter stage is the impedance "seen" at the base terminal. It is determined by three parallel paths: the bias resistors R1 and R2, and the transistor's own input impedance (β × re with bypass cap fitted, or β × (re + RE) without).
Zin = R1 ‖ R2 ‖ (β × re)
CE input impedance (without emitter bypass):
Zin = R1 ‖ R2 ‖ β × (re + RE)
CE output impedance:
Zout ≈ RC (for practical purposes)
The input impedance of a CE stage is typically in the range of a few hundred ohms to a few kilohms, depending on the bias network and operating current. This is important when connecting stages together: if the source impedance driving the CE stage is much higher than the CE input impedance, there will be significant signal attenuation at the junction (loading). This is why a common collector stage (emitter follower) is often used as a buffer before a CE stage — the emitter follower's very high input impedance presents a light load to the previous stage.
re = 26/2 = 13 Ω
Transistor input impedance = β × re = 100 × 13 = 1300 Ω = 1.3 kΩ
Bias network parallel: R1 ‖ R2 = (47k × 10k) / (47k + 10k) = 8.25 kΩ
Zin = 8.25 kΩ ‖ 1.3 kΩ = (8250 × 1300) / (8250 + 1300) = 1120 Ω ≈ 1.1 kΩ
The input impedance is dominated by the transistor's own input resistance (1.3 kΩ) because it is the lowest of the three parallel paths. A 50 Ω source driving this stage would lose very little signal to loading, but a 10 kΩ source would lose significant signal unless buffered.
Bias Resistor and Operating Point Calculator
For a voltage-divider biased common emitter stage. Enter supply voltage, desired collector current, transistor β (hFE), and resistor values to find the operating point.
Coupling Capacitors
The input and output coupling capacitors (Cin and Cout) isolate the DC bias conditions of one stage from the next while allowing AC signals to pass. This is essential in a multi-stage amplifier: each stage needs its own bias setting, and connecting them directly in DC would disturb each other's operating points.
The coupling capacitors must have low enough reactance at the frequencies of interest to avoid attenuating the signal. Together with the impedances they couple into, each capacitor forms a high-pass filter. The lower cut-off frequency is determined by:
where Z is the impedance the capacitor couples into (input impedance of the next stage, or output impedance of the previous stage).
C = 1 / (2π × 300 × 10,000) = 53 nF
Choose Cout = 100 nF (0.1 µF ceramic or film capacitor).
For an RF amplifier operating at 14 MHz (20-metre band), the coupling capacitor must be low enough reactance at 14 MHz to not attenuate the signal. With a 50 Ω load:
C = 1 / (2π × 14,000,000 × 5) = 2.3 nF (targeting Xc = 5 Ω)
Choose 2.2 nF or 4.7 nF RF-grade ceramic capacitor.
Worked Design Example: 40-Metre Band Receive Preamp
Here is a complete design walkthrough for a common emitter receive preamplifier for the 40-metre band (7.0–7.3 MHz). The target is a voltage gain of approximately 20 dB (×10) with a 50 Ω source and a 50 Ω output termination.
Step 1: Choose operating current.
Low noise preamps use low collector current. Choose Ic = 1 mA. This gives low noise figure and reasonable re.
Step 2: Calculate re.
re = 26/1 = 26 Ω
Step 3: Choose RC for gain.
Gain ≈ RC/re, so RC = Gain × re = 10 × 26 = 260 Ω. Use 270 Ω (nearest standard E12 value). Verify: Av = 270/26 = 10.4 ✓
Step 4: Set collector voltage at mid-rail.
For maximum swing, VC ≈ VCC/2 = 6 V.
Voltage across RC = VCC − VC = 12 − 6 = 6 V
Check: IC × RC = 0.001 × 270 = 0.27 V — this is too small. We need higher IC × RC.
Revise: With RC = 4.7 kΩ and Ic = 1 mA: VRC = 4.7 V, VC = 7.3 V. Gain = 4700/26 = 181. Too high.
Better approach for 20 dB gain: unbypassed emitter resistor.
Use RC = 2.7 kΩ, RE = 270 Ω (unbypassed), Av = RC/RE = 2700/270 = 10 ✓
IC = 1 mA: VRC = 2.7 V, VRE = 0.27 V, VC = 12 − 2.7 = 9.3 V, VE = 0.27 V, VCE = 9.03 V. Good headroom.
Step 5: Set bias.
VB = VE + VBE = 0.27 + 0.7 = 0.97 V
For a stiff divider, pass ≥10× IB through divider: IB = IC/β = 1mA/150 = 6.7 µA, so divider current ≥ 67 µA.
R2 = VB / Idiv = 0.97 / 0.0001 = 9.7 kΩ → use 10 kΩ
R1 = (VCC − VB) / Idiv = (12 − 0.97) / 0.0001 = 110 kΩ → use 100 kΩ
Verify: VB actual = 12 × 10k/(100k+10k) = 1.09 V. VE = 0.39 V, IC = 0.39/270 = 1.44 mA. Close enough.
Step 6: Coupling capacitors at 7 MHz.
Cin: couples 50 Ω source to ~1 kΩ input impedance. Use 100 pF (Xc at 7 MHz = 227 Ω — some attenuation, use 470 pF for Xc = 48 Ω).
Cout: couples to 50 Ω load. Use 100 pF gives Xc = 227 Ω. This divides output gain. Use 1 nF for Xc = 22 Ω.
Result: A simple three-resistor, three-capacitor common emitter preamp with about 20 dB gain at 40 metres and Class A operation for good linearity.
⚖ Experiment: Build and Test a Common Emitter Amplifier
This experiment demonstrates voltage gain, phase inversion, and the effect of the emitter bypass capacitor in a real common emitter circuit.
- One 2N3904 NPN transistor (or BC547)
- Resistors: 47 kΩ, 10 kΩ, 2.2 kΩ, 470 Ω (all ¼ W)
- Capacitors: 10 µF electrolytic × 2 (coupling), 22 µF electrolytic × 1 (bypass CE)
- 9 V battery and clip
- Breadboard and jumper wires
- Multimeter (AC volts setting) and a signal source, OR a function generator
- Optional: oscilloscope (highly recommended to see phase inversion)
- Build the standard voltage-divider biased CE circuit: R1 = 47 kΩ (VCC to base), R2 = 10 kΩ (base to ground), RC = 2.2 kΩ (VCC to collector), RE = 470 Ω (emitter to ground). Install the 22 µF bypass cap across RE (observe polarity: + to emitter, − to ground). Connect 10 µF input coupling cap at the base, 10 µF output coupling cap at the collector.
- Power the circuit with the 9 V battery. Measure DC voltages: base should be about 1.5 V, emitter about 0.8 V, collector should be between 4 V and 7 V (mid-supply). If collector is near 9 V, check R1/R2. If near 0 V, the transistor may be saturated — check RE is connected.
- Apply a small AC signal at the input: if using a function generator, set it to 1 kHz sine wave, 50 mV peak-to-peak. If you do not have a generator, use a 9 V radio headphone output feeding through a 10 kΩ series resistor to limit the level.
- Measure the AC voltage at the input (across the input coupling cap, measured to ground) and at the output (collector side of output coupling cap). The ratio is the gain. Expected: approximately 40–60 (gain = RC/re with bypass cap).
- If using an oscilloscope: observe the output waveform while watching the input. You will clearly see the output is inverted (when input goes up, output goes down) and larger in amplitude.
- Now remove the bypass capacitor CE from across RE. Remeasure the AC voltage gain. It should drop to approximately RC/RE = 2200/470 = 4.7. The phase inversion remains.
- Replace CE. The gain will return to the high value.
With CE fitted: output voltage = input voltage × 40 to 60 (varies with transistor β and exact bias). With CE removed: output voltage ≈ input voltage × 4.7. In both cases the output is inverted. This directly confirms the gain formulas: Av = RC/re (bypassed) and Av = RC/RE (unbypassed). The dramatic gain change caused by CE alone illustrates why bypass capacitors are critical components — a missing or failed bypass cap will sharply reduce a stage's gain.
Frequently Asked Questions
Why does the formula use −RC/re instead of RC/RE?
When the emitter bypass capacitor CE is fitted, it short-circuits RE for AC signals. The emitter terminal is effectively at AC ground, so RE plays no role in the AC gain. What remains in the emitter lead is only the transistor's intrinsic emitter resistance re, which is the small-signal resistance of the forward-biased base-emitter junction. The gain becomes RC/re. Without the bypass cap, RE is in series with re and since RE >> re in most practical designs, the gain ≈ RC/RE. The negative sign in both formulas indicates phase inversion — the output is 180° out of phase with the input.
Why does gain change with temperature?
Because re = 26 mV / Ic depends on the thermal voltage (26 mV at room temperature), which changes with absolute temperature. Also, as temperature rises, the transistor's β increases and its VBE decreases, which shifts the quiescent current Ic. A change in Ic changes re, which changes the gain. This is why circuits where precise gain is needed use the unbypassed emitter resistor configuration (gain ≈ RC/RE, set by stable resistors, independent of transistor parameters) or use negative feedback from the output to the input.
What is the maximum output voltage swing?
The output can swing from approximately VCC (when the transistor cuts off) down to the saturation voltage (approximately 0.2 V when the transistor is fully on). The usable linear swing is from the cut-off side limited by the quiescent collector voltage. For maximum symmetric swing, the quiescent collector voltage should be set near VCC/2. If VCC = 12 V and VC(quiescent) = 6 V, the maximum symmetric swing is ±5.8 V peak, or about 11.6 V peak-to-peak. Attempting to swing beyond these limits causes clipping — one or both peaks of the output waveform are flattened.
Test Your Knowledge
Answer the questions below to check your understanding. Every answer can be found in the lesson above.