What is “gain”? What role does it play in electronics?
“Gain” represents the ratio of output signal to input signal, a concept more rigorous than “amplification factor”. It can describe both amplification (gain ≥ 1) and attenuation (gain < 1), making it ideal for characterizing the operating state of electronic components like operational amplifiers.
I. Decibel Representation of Gain in Circuits
Operational amplifiers often have extremely high open-loop gains (typically 10^5 to 10^7). While expressing this in raw multiples would be cumbersome, using the logarithmic unit decibel (dB) simplifies representation.
Common gain definitions in decibels:
- Voltage gain: G_{\\text{dB}} = 20\\lg\\left(\\frac{V_{\\text{out}}}{V_{\\text{in}}}\\right)
- Power gain: G_{\\text{dB}} = 10\\lg\\left(\\frac{P_{\\text{out}}}{P_{\\text{in}}}\\right)
- Sound pressure gain: G_{\\text{dB}} = 20\\lg\\left(\\frac{\\text{Sound Pressure (Pa)}}{\\text{Reference Pressure 20μPa}}\\right)
Why the difference between 10× and 20× coefficients? It stems from the fundamental nature of physical quantities.
II. Origin of the Decibel Coefficients
1. The 10× Coefficient
Decibels were originally defined for power ratios:
G_{\\text{dB}} = 10\\lg\\left(\\frac{P_{\\text{out}}}{P_{\\text{in}}}\\right).
The general formula is:
X_{\\text{dB}} = 10\\lg\\left(\\frac{\\text{Measured Value}}{\\text{Reference Value}}\\right),
where the 10× coefficient is a standardized convention.
2. The 20× Coefficient
Voltage itself isn’t power, but from P = \\frac{V^2}{R}, we derive:
Thus, voltage gain uses 20×. Similarly, quantities like current and sound pressure (field quantities) have squared relationships with power, so their decibel conversions use 20×. Power/energy ratios retain the original 10× coefficient.
III. Common Gain (dB) to Amplitude Ratio Table
| dB Value | Amplitude Ratio | Description |
|---|---|---|
| 0dB | 1 | No gain/attenuation |
| 3dB | 1.4 | Gain increase |
| 6dB | 2 | Gain increase |
| 9dB | 2.8 | Gain increase |
| 12dB | 4 | Gain increase |
| 18dB | 8 | Gain increase |
| 20dB | 10 | Gain increase |
| -3dB | 0.707 | Attenuation |
| -6dB | 0.5 | Attenuation |
| -10dB | 0.1 | Attenuation |
| -20dB | 0.01 | Attenuation |
| -60dB | 0.001 | Attenuation |
IV. Three Critical Gain Points in Operational Amplifiers
1. Gain Crossover Frequency
The frequency where open-loop gain drops to 1 (0dB). This point is critical for stability analysis: if phase shift exceeds 180° at this frequency, the closed-loop circuit may oscillate.
2. Unity Gain Bandwidth
The frequency at which open-loop gain reaches 0dB. Related to the gain-bandwidth product (GBW), where:
GBW = Unity Gain Frequency × DC Open-Loop Gain.
This defines the operational amplifier’s usable frequency range.
3. Cutoff Frequency (-3dB Point) in Filters
Marks the boundary between a filter’s passband and stopband:
- Low-pass filter: -3dB is where high frequencies begin attenuating; signals below this frequency pass with <3dB loss.
- High-pass filter: -3dB is where low frequencies begin attenuating; signals above this frequency pass with <3dB loss.
- Band-pass/band-stop filters: -3dB defines passband/stopband edges (signals within passband have <3dB loss; stopband signals have >3dB loss).
V. Conclusion
While gain appears simple, practical PCB design often leads to errors like mixing up 10lg/20lg or overlooking op-amp -3dB points. May this guide help you avoid such pitfalls!
Wishing all engineers:
- Boards soldered by hand succeed on first try
- Waveforms stay clean and never “magical”
- Loops remain stable without oscillation
- And嘉立创EDA (LCEDA) stays smooth to use!
Feel free to supplement in the comments if anything remains unclear~