Definition
Amplification increases signal strength:
y(t) = G \cdot x(t) + n_{amp}
In SCU terms: Amplification scales χ-mode amplitude—increasing signal power while adding amplifier-generated χ-mode noise.
The Amplification Challenge
Amplifiers add their own noise:
\text{SNR}_{out} \leq \text{SNR}_{in}
Goal: maximize gain G while minimizing added noise $n_{amp}$.
Noise Figure
Quantifies amplifier noise addition:
F = \frac{\text{SNR}_{in}}{\text{SNR}_{out}} \geq 1
Ideal amplifier: F = 1 (adds no noise)
Real amplifier: F > 1 (degrades SNR)
Amplifier Types
| Type | Function |
|---|---|
| Voltage | Scale χ-mode voltage |
| Current | Scale χ-mode current |
| Power | Deliver χ-mode power to load |
| Transimpedance | Current → voltage conversion |
Cascaded Amplifiers
Friis formula for stages:
F_{total} = F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3 - 1}{G_1 G_2} + ...
First stage noise dominates. Use low-noise amplifier first.
Technologies
| Technology | Characteristics |
|---|---|
| Transistor | Standard semiconductor |
| LNA | Low noise, front-end |
| HEMT | Cryogenic, ultra-low noise |
| Parametric | Near quantum-limited |
| Quantum | At quantum noise limit |
Quantum Limits
Heisenberg limits amplification:
n_{added} \geq \frac{1}{2} \text{ photon (phase-preserving)}
Quantum χ-mode fluctuations are irreducible.
Design Trade-offs
| Trade-off | Consideration |
|---|---|
| Gain vs bandwidth | Higher gain → narrower band |
| Noise vs power | Lower noise → more power |
| Linearity vs efficiency | Linear → inefficient |
The Key Insight
Amplification is χ-mode scaling with noise cost.
Increasing signal strength:
- Weak χ-modes need amplification
- Amplifiers add their own χ-mode noise
- First stage determines noise floor
- Quantum limits are fundamental
When we amplify, we're scaling χ-mode amplitude to usable levels—the art is doing so while adding minimal noise χ-modes.