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Single-stage 2N3904 common-emitter amplifier with voltage-divider bias, emitter degeneration, and an AC-bypass capacitor on the emitter. Classroom-canonical discrete BJT amp.
| REF | TYPE | VALUE | ROLE |
|---|---|---|---|
| Q1 | NPN BJT | β ≈ 200 | Active gain element — converts small base-current variations into much larger collector-current variations, producing voltage gain across Rc. |
| R1 | Resistor | 47 kΩ | Upper base-bias resistor — forms a divider with R2 to set the DC base voltage. |
| R2 | Resistor | 10 kΩ | Lower base-bias resistor — completes the divider, fixing Vb ≈ 2.1 V. |
| Rc | Resistor | 4.7 kΩ | Collector load resistor — drops a quiescent voltage across itself; output swing happens across this resistor. |
| Re | Resistor | 1 kΩ | Emitter degeneration resistor — provides DC bias stability and reduces sensitivity to β variations, at the cost of voltage gain. |
| Cin | Capacitor | 1 µF | AC coupling — blocks DC from the source so the bias point is preserved while passing audio-band signal. |
| Ce | Capacitor | 100 µF | Emitter bypass — shorts Re at signal frequencies, restoring full AC gain while keeping DC degeneration. |
| Cout | Capacitor | 1 µF | Output coupling — blocks the ~6 V collector DC bias from reaching the load. |
8 COMPONENTS IDENTIFIED
STAGES · 6
Bias network
R1 and R2 form a voltage divider from Vcc to set Vb ≈ 2.1 V. With Vbe ≈ 0.7 V, that puts Ve ≈ 1.4 V and Ie ≈ 1.4 mA through Re.
→ R1, R2
Input coupling
Cin AC-couples the source to the base, blocking DC interactions with the bias network.
→ Cin
Active stage
Q1 amplifies the base voltage variation, producing a large inverted swing at the collector.
→ Q1
Load
Rc converts collector current variations into voltage swing.
→ Rc
Emitter bypass
Ce shorts Re at audio frequencies (Xc ≪ Re above ~10 Hz), restoring full small-signal gain of -gm × Rc.
→ Re, Ce
Output coupling
Cout removes the ~6 V DC bias on the collector so the load only sees the AC signal.
→ Cout
FEEDBACK PATHS
DC feedback via Re — any tendency of Ie to rise increases Ve, which reduces Vbe, which counter-acts the original increase. Stabilizes the bias point against temperature and β spread.
KEY NODES
DOMAIN
audio
INDUSTRY
Discrete BJT amplification — once the dominant architecture in consumer electronics, now mostly used in audio (guitar pedals, hi-fi front ends), RF, and as a teaching tool. The 2N3904 is the most-produced transistor in history.
FREQUENCY
~20 Hz to ~5 MHz (lower limit set by Cin/Cout, upper limit set by 2N3904's fT ≈ 300 MHz divided by stage gain)
IMPEDANCE
Input impedance ≈ R1 ∥ R2 ∥ β·re ≈ 2 kΩ. Output impedance ≈ Rc = 4.7 kΩ.
APPLICATION
General-purpose voltage gain stage — guitar pedal front ends, microphone preamps, RF/IF gain blocks at lower frequencies, and the building block taught in every analog electronics course.
OPERATING PRINCIPLE
Q1 is biased so that a small DC current (~1.4 mA) flows from collector to emitter at all times. Vbe ≈ 0.7 V, so any AC voltage applied at the base directly modulates the base-emitter junction's exponential I-V curve. The result is that collector current swings proportionally to the input voltage with a transconductance gm = Ic/Vt ≈ 54 mA/V at room temperature. That current swing drops across Rc, producing an output voltage swing of -gm·Rc ≈ -250 (about -48 dB of gain) — except Re degenerates the gain at DC. Adding Ce in parallel with Re shorts the emitter to ground at signal frequencies, restoring the full -gm·Rc gain in the audio band while keeping DC stability. The collector output is inverted because rising base voltage means more collector current means more drop across Rc means lower Vc.
KEY PARAMETERS
Quiescent collector current
1.4mA
Ie ≈ (Vb - Vbe) / Re
Quiescent Vce
4.4V
Vcc - Ic·(Rc+Re) — comfortably out of saturation
Voltage gain (AC, Ce bypassed)
-45V/V
Approximate; gm·Rc'/(1 + gm·re_internal)
Voltage gain (DC, Ce removed)
-4.7V/V
-Rc/Re — set by ratio only, β-independent
Input impedance
~2kΩ
Output impedance
~4.7kΩ
Low-frequency cutoff
~7Hz
Set by Ce — 1/(2π·Re·Ce)
DESIGN DECISIONS
Voltage-divider bias plus emitter degeneration was the genius of 1950s discrete design — it tolerated huge β spread (50 to 400) without changing the operating point. The 47k/10k divider sets the base at about Vcc × R2/(R1+R2) = 2.1 V, stiff enough that base current loading doesn't perturb it as long as I_R2 ≫ I_b (rule of thumb: divider current ≥ 10× base current). Ic = 1.4 mA gives gm = 54 mA/V — sweet spot for low noise without burning excessive supply current. The Ce = 100 µF emitter bypass sets the LF -3 dB corner at 1/(2π·1k·100µF) = ~1.6 Hz; in practice the input/output coupling caps set the actual LF rolloff. Re = 1 kΩ is enough degeneration to absorb a ±50% β spread without shifting the bias point more than ~10%.
FAILURE MODES · 4
Clipping on large inputs
Output can swing from saturation (Vce_sat ≈ 0.2 V, so Vout ≈ 1.6 V) up to nearly Vcc (12 V). At Iq = 1.4 mA the symmetric peak-to-peak headroom is roughly ±5 V at the collector, which after the cap is ±5 V. Inputs > ~110 mV peak start to clip asymmetrically.
Thermal runaway (no Re or weak bias)
If Re is removed or shorted, Ic increases with temperature → die heats further → β rises → Ic rises further. The 2N3904 in TO-92 will happily eat itself this way. Re prevents it by sensing the rising current and pulling Vbe down.
Ce missing or wrong polarity
Without Ce, gain drops from -45 to -4.7 — a 20 dB loss. Reverse-biasing an electrolytic Ce will eventually short it and remove Re's stabilization too.
Distortion on large signals
Vbe's exponential curve makes the stage's gain non-linear at large signal swings — typically 1–3% THD at 100 mV peak input. Audible as warmth at low levels, fuzz at high levels. (This is why guitar pedals love this circuit.)
IMPROVEMENT SUGGESTIONS
◇ Lower distortion
Remove Ce and accept the lower gain, or use a cascode (add a second BJT in series with Q1's collector).
Heavy emitter degeneration linearizes the stage — distortion drops by an order of magnitude. Cascode keeps the gain by eliminating the Miller effect from Cbc.
◇ Higher input impedance
Add an emitter-follower (BJT common collector) buffer in front of the base.
Raises input impedance from ~2 kΩ to tens of kΩ, so high-impedance sources (guitar pickups, piezo discs) don't get loaded down.
◇ Higher bandwidth
Reduce Rc and Re proportionally, or swap to a higher-fT transistor (2N5179, MMBR901).
Bandwidth is limited by Rc·Ccb (Miller capacitance). Halving Rc doubles the high-frequency corner at the cost of gain.
[ END OF ANALYSIS ]
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