Insertion Loss from S21
IL = −20 × log10(|S21|)
Quick answer
This calculator solves IL = −20 × log₁₀(|S₂₁|) for Insertion Loss. With |S21| Magnitude 0.5, the result is 6.021 dB. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Insertion loss quantifies how much signal power is lost when a component (filter, cable, connector, PCB trace) is inserted between a source and load. It is derived from the S-parameter S₂₁, which represents the forward transmission coefficient. |S₂₁| = 1 means no loss (IL = 0 dB), |S₂₁| = 0.5 means 6 dB loss (half the voltage, quarter the power). Insertion loss is positive by convention (a "loss"). It is the primary specification for evaluating cables, connectors, PCB vias, and filter passband performance.
Variables
- IL — Insertion loss (dB, positive value)
- |S₂₁| — Forward transmission coefficient magnitude (0 to 1)
Practical Notes
Typical insertion losses: SMA connector < 0.03 dB, 1 m RG-58 coax at 1 GHz ≈ 0.7 dB, FR-4 via (through board) at 5 GHz ≈ 0.5-1 dB, PCB SMA launch ≈ 0.1-0.3 dB. For passive components, |S₂₁| can never exceed 1 (0 dB). For amplifiers, |S₂₁| > 1 represents gain, and IL becomes negative (i.e., there is actually gain, not loss).
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| IL | Insertion Loss | dB | dB |
| S21 | |S21| Magnitude | — | — |
Step by step
- 1. What you know: |S21| Magnitude 0.5
- 2. The relation: IL = −20 × log₁₀(|S₂₁|)
- 3. Substitute: S21 = 0.5
- 4. Result: Insertion Loss = 6.021 dB
Worked examples
Minimum range
Given: |S21| Magnitude 0.025
Result: Insertion Loss = 32.04 dB
Low range
Given: |S21| Magnitude 0.25
Result: Insertion Loss = 12.04 dB
Typical
Given: |S21| Magnitude 0.5
Result: Insertion Loss = 6.021 dB
High range
Given: |S21| Magnitude 0.8
Result: Insertion Loss = 1.938 dB
Maximum range
Given: |S21| Magnitude 8
Result: Insertion Loss = -18.06 dB
Solving for each variable
Solve for Insertion Loss
|S21| Magnitude 0.025 → 32.04 dB
Solve for |S21| Magnitude
Insertion Loss 0.3 dB → 0.9661
How Insertion Loss changes with |S21| Magnitude
| |S21| Magnitude (input) | Insertion Loss (result) |
|---|---|
| 0.05 | 26.02 dB |
| 0.125 | 18.06 dB |
| 0.25 | 12.04 dB |
| 0.375 | 8.519 dB |
| 0.5 | 6.021 dB |
| 0.75 | 2.499 dB |
| 2 | -6.021 dB |
| 3.5 | -10.88 dB |
| 5 | -13.98 dB |
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<p><a href="https://vbatpower.com/formulas/insertion-loss/">Insertion Loss from S21</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Insertion Loss from S21?
Use IL = −20 × log₁₀(|S₂₁|). With |S21| Magnitude 0.5, Insertion Loss works out to 6.021 dB.
How do you calculate insertion loss s21?
Rearrange for Insertion Loss: with |S21| Magnitude 0.25, Insertion Loss is 12.04 dB.
What is the formula for Insertion Loss from S21?
The formula is IL = −20 × log₁₀(|S₂₁|). Insertion loss quantifies how much signal power is lost when a component (filter, cable, connector, PCB trace) is inserted between a source and load.
How do you find |S21| Magnitude when you know the other values?
Rearrange for |S21| Magnitude: with Insertion Loss 0.3 dB, |S21| Magnitude is 0.9661.
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