Cascaded Amplifier Gain
Av = Av1 · Av2 · Av3
Quick answer
This calculator solves Av(total) = Av1 × Av2 × Av3 for Total Gain. With Stage 1 Gain 1.1, Stage 2 Gain 2.35, Stage 3 Gain 0.235, the result is 0.6075. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
When amplifier stages are cascaded, their voltage gains multiply (their decibel gains add). This lets a large overall gain be built from modest, well-behaved stages, each loaded by the next stage’s input impedance. For unused stages set the gain to 1. The same rule extends to any number of stages.
Variables
- Av(total) — Overall voltage gain
- Av1 — Stage 1 gain (set unused = 1)
- Av2 — Stage 2 gain (set unused = 1)
- Av3 — Stage 3 gain (set unused = 1)
Practical Notes
In decibels the gains add: 20 dB + 20 dB + 20 dB = 60 dB = ×1000. Remember each stage’s gain already includes the loading of the following stage’s input impedance.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Avt | Total Gain | — | — |
| Av1 | Stage 1 Gain | — | — |
| Av2 | Stage 2 Gain | — | — |
| Av3 | Stage 3 Gain | — | — |
Step by step
- 1. What you know: Stage 1 Gain 1.1, Stage 2 Gain 2.35, Stage 3 Gain 0.235
- 2. The relation: Av(total) = Av1 × Av2 × Av3
- 3. Substitute: Av1 = 1.1, Av2 = 2.35, Av3 = 0.235
- 4. Result: Total Gain = 0.6075
Worked examples
Minimum range
Given: Stage 1 Gain 0.055, Stage 2 Gain 0.118, Stage 3 Gain 0.0118
Result: Total Gain = 7.66 × 10⁻⁵
Low range
Given: Stage 1 Gain 0.55, Stage 2 Gain 1.18, Stage 3 Gain 0.118
Result: Total Gain = 0.07658
Typical
Given: Stage 1 Gain 1.1, Stage 2 Gain 2.35, Stage 3 Gain 0.235
Result: Total Gain = 0.6075
High range
Given: Stage 1 Gain 1.76, Stage 2 Gain 3.76, Stage 3 Gain 0.376
Result: Total Gain = 2.488
Maximum range
Given: Stage 1 Gain 17.6, Stage 2 Gain 37.6, Stage 3 Gain 3.76
Result: Total Gain = 2488
Solving for each variable
Solve for Total Gain
Stage 1 Gain 0.055, Stage 2 Gain 0.118, Stage 3 Gain 0.0118 → 7.66 × 10⁻⁵
Solve for Stage 1 Gain
Total Gain 0.025, Stage 2 Gain 0.118, Stage 3 Gain 0.0118 → 17.95
Solve for Stage 2 Gain
Total Gain 0.025, Stage 1 Gain 0.055, Stage 3 Gain 0.0118 → 38.52
Solve for Stage 3 Gain
Total Gain 0.025, Stage 1 Gain 0.055, Stage 2 Gain 0.118 → 3.852
How Total Gain changes with Stage 1 Gain
| Stage 1 Gain (input) | Total Gain (result) |
|---|---|
| 0.11 | 0.06075 |
| 0.275 | 0.1519 |
| 0.55 | 0.3037 |
| 0.825 | 0.4556 |
| 1.1 | 0.6075 |
| 1.65 | 0.9112 |
| 2.2 | 1.215 |
| 4.4 | 2.43 |
| 7.7 | 4.252 |
| 11 | 6.075 |
Embed this calculator
Paste this into any page. It keeps working when this page updates, and credits the source.
<iframe src="https://vbatpower.com/embed/cascaded-gain/" width="100%" height="460" style="border:1px solid #1f2a37;border-radius:12px" loading="lazy" title="Cascaded Amplifier Gain"></iframe>
<p><a href="https://vbatpower.com/formulas/cascaded-gain/">Cascaded Amplifier Gain</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Cascaded Amplifier Gain?
Use Av(total) = Av1 × Av2 × Av3. With Stage 1 Gain 1.1, Stage 2 Gain 2.35, Stage 3 Gain 0.235, Total Gain works out to 0.6075.
What is the formula for Cascaded Amplifier Gain?
The formula is Av(total) = Av1 × Av2 × Av3. When amplifier stages are cascaded, their voltage gains multiply (their decibel gains add).
How do you find Stage 1 Gain when you know the other values?
Rearrange for Stage 1 Gain: with Total Gain 0.025, Stage 2 Gain 0.118, Stage 3 Gain 0.0118, Stage 1 Gain is 17.95.
How do you find Stage 2 Gain when you know the other values?
Rearrange for Stage 2 Gain: with Total Gain 0.025, Stage 1 Gain 0.055, Stage 3 Gain 0.0118, Stage 2 Gain is 38.52.
Related Concepts
All Discrete Amplifiers formulas →Need more features?
Save calculations, import telemetry data, simulate battery discharge, and collaborate with your team.
Try the App