Transistor as Amplifier

Part of The Transistor

A transistor in its active region amplifies signals by using a small base current to control a much larger collector current — the fundamental mechanism behind every audio amplifier, radio receiver, and instrumentation circuit.

Why This Matters

The ability to amplify signals is one of the most transformative capabilities in electronics. Without amplification, a microphone cannot drive a speaker, a radio antenna cannot produce listenable audio, a sensor cannot control a machine, and weak signals disappear into noise. The vacuum tube amplifier made radio broadcasting possible in the 1920s. The transistor amplifier made portable radios, hearing aids, and eventually computers possible from the 1950s onward.

A transistor amplifier can boost a signal by a factor of 100–1,000 in voltage, turning the millivolt output of a microphone into the volts needed to drive a speaker. Cascaded stages can amplify by a million or more. Understanding how to design and analyze amplifier circuits is the core competency that separates someone who can use salvaged electronics from someone who can build new electronics.

The Active Region: Where Amplification Happens

Transistor amplification operates in the active region:

• Base-emitter junction: forward biased (V_BE ≈ 0.6–0.7 V for silicon)
• Collector-base junction: reverse biased (V_CE > V_CE_sat ≈ 0.3 V)

In this region: I_C = β × I_B

β (current gain, also written h_FE) is typically 100–300 for small-signal silicon transistors. A 1 µA change in base current produces a 100–300 µA change in collector current. This is current amplification.

Voltage amplification is achieved when the collector current variation produces a voltage across the collector resistor R_C:

ΔV_out = ΔI_C × R_C = β × ΔI_B × R_C

And since the input voltage change ΔV_in ≈ ΔI_B × r_be (where r_be is the dynamic base-emitter resistance):

Voltage gain A_v = −β × R_C / r_be

The r_be value: r_be = 26 mV / I_C (at room temperature, from transistor physics)

For I_C = 1 mA: r_be = 26 Ω For R_C = 4.7 kΩ and β = 150: A_v = −150 × 4700 / 26 = −27,000

Wait — this means voltage gain should be thousands? In practice, biasing resistors, emitter resistors, and source impedances reduce this. A practical single-stage gain of 20–200 is typical.

Biasing: Setting the Operating Point

An amplifier must be biased — a DC operating point established — before it can amplify AC signals. The operating point must be in the middle of the active region:

• V_CE ≈ VCC/2 (maximum output swing before clipping)
• I_C at the desired quiescent value

Voltage divider bias is the standard approach:

Circuit:

• R1, R2: form a voltage divider from VCC to ground
• R_C: collector resistor from VCC to collector
• R_E: emitter resistor from emitter to ground (stabilizes bias against β variation and temperature)
• C_E: bypass capacitor across R_E (shorts R_E for AC signals, restoring gain)
• C_in, C_out: coupling capacitors to block DC from input/output

Design procedure for VCC = 12V, I_C_Q = 2 mA:

1. Set V_E = 10–20% of VCC: V_E = 1.2 V → R_E = 1.2/0.002 = 600 Ω (use 560 Ω)
2. Set V_C ≈ 50–60% of VCC: V_C = 7 V → voltage across R_C = 12−7 = 5 V → R_C = 5/0.002 = 2.5 kΩ (use 2.7 kΩ)
3. V_B = V_E + 0.6 = 1.8 V
4. Set divider current ≈ 10× I_B: I_B = 2mA/100 = 20 µA; divider current = 200 µA
5. R2 = V_B / I_div = 1.8/0.0002 = 9 kΩ (use 10 kΩ)
6. R1 = (VCC − V_B) / I_div = 10.2/0.0002 = 51 kΩ (use 47 kΩ)

Result: Stable bias, V_CE ≈ 5.8 V (good midpoint), I_C = 2 mA.

Small-Signal Model and Gain Calculation

For AC analysis, replace the transistor with its small-signal equivalent:

The transconductance model:

• r_be = V_T / I_B = β × V_T / I_C = β × 26mV / I_C
• g_m = I_C / V_T = I_C / 0.026 (transconductance in amperes per volt)
• Output: current source g_m × V_be

Voltage gain of common-emitter with bypassed emitter resistor:

A_v = −g_m × R_C_parallel = −(I_C / 0.026) × R_C

For I_C = 2 mA, R_C = 2.7 kΩ: A_v = −(0.002 / 0.026) × 2700 = −0.0769 × 2700 = −208

The negative sign indicates phase inversion — common emitter inverts the signal (180° phase shift).

Without C_E (emitter resistor not bypassed):

A_v = −R_C / (R_E + 1/g_m) = −2700 / (560 + 13) = −4.7

Emitter degeneration dramatically reduces gain but greatly improves linearity and stability. For a high-fidelity amplifier where low distortion matters more than high gain, remove the bypass capacitor.

Three Amplifier Configurations

Common-Emitter (Standard Amplifier)

• Input: base, Output: collector
• Voltage gain: high (50–500 typical), inverts signal
• Input impedance: medium (1–10 kΩ)
• Output impedance: high (≈ R_C, typically kΩ)
• Use: voltage amplification, most common configuration

Common-Collector (Emitter Follower)

• Input: base, Output: emitter
• Voltage gain: ≈1 (no voltage amplification), no inversion
• Input impedance: very high (β × R_E, typically 100 kΩ+)
• Output impedance: very low (R_E ∥ 1/g_m, typically 10–100 Ω)
• Use: impedance matching, driving low-impedance loads from high-impedance sources

Common-Base

• Input: emitter, Output: collector
• Voltage gain: high, no inversion
• Input impedance: very low (1/g_m, typically 10–50 Ω)
• Output impedance: very high
• Use: RF amplifiers, high-frequency circuits (no Miller effect from C_CB)

Multi-Stage Amplifier

A single stage provides gain of ~20–200. For voice communication, you need gain of 1,000–100,000. Cascade stages:

Two-stage amplifier:

• Stage 1: common-emitter (voltage gain = −50)
• Stage 2: emitter follower (voltage gain ≈ −1, impedance buffer)
• Overall voltage gain: 50 (magnitude), output can drive speaker load
• Coupling between stages: capacitor (10 µF) blocks DC operating points from affecting each other

Audio amplifier chain for a crystal microphone → 8Ω speaker:

1. Crystal microphone output: ~100 mV, impedance ~100 kΩ
2. Stage 1 (common emitter, gain 40): 100 mV → 4 V
3. Stage 2 (emitter follower, gain 1): 4 V → 4 V, output impedance drops to ~47 Ω
4. Speaker (8 Ω) receives 4 V peak — substantial audio output

Distortion and Linearity

All transistor amplifiers introduce some distortion because the I_C vs V_BE characteristic is exponential, not linear. Techniques to minimize distortion:

Emitter degeneration: Adding R_E (not bypassed) linearizes the characteristic. Distortion drops proportionally to gain reduction.

Reduce signal amplitude: Keep input signal small (10–100 mV peak) relative to the bias voltage swing (several volts). The exponential curve looks linear over small excursions.

Negative feedback: Feed a fraction of the output back to the input in phase opposition. This reduces gain but linearizes the response dramatically. A feedback factor of 10 reduces distortion by 10× while reducing gain by 10×.

Summary

Transistor as Amplifier — At a Glance

• Active region: V_BE ≈ 0.7 V, V_CE > 0.3 V, I_C = β × I_B — small base current controls large collector current
• Voltage gain = g_m × R_C = (I_C / 0.026) × R_C — increases with collector current and load resistance
• Voltage divider bias sets operating point: V_CE ≈ VCC/2, I_C at design value
• Common-emitter: high voltage gain (50–500), signal inversion, medium impedances — standard amplifier
• Emitter follower: unity gain, high input impedance, low output impedance — impedance buffer
• Emitter degeneration (R_E without bypass): reduces gain but reduces distortion and stabilizes bias
• Two-stage cascade: stages multiply, not add — two stages of gain 50 give overall gain 2,500