Eddie guidesA field team faces an unresolved physical question: How much read boundary does a poor match cost? They must answer it before changing vswr on the real device. Predict the direction first.
See the relationship before changing it
The figure reads from left to right. The blue card is vswr. The middle card applies this page's relationship. The green card is wavelength. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This added model holds every other chapter fixture fixed, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline for vswr is 10.
- 2
Name the relationship. |Γ| = 9/11 = 0.818 τ = 1 - 0.818² = 0.331 Lm = -10 log10(0.331) = 4.81 dB dnew = 4.0 x 10^(-4.81/20) = 2.30 m
- 3
Substitute the chapter fixture. Set vswr to 10. The page ledger gives wavelength as 0.333 m.
- 4
Read the result. Keep m beside the value. Use it only inside the technical boundary on this page.
Predict, then change vswr
Try Predict the direction of wavelength. Move one control, calculate, then check your prediction.
Observe The dB loss converts to distance with a 20-log relationship because free-space power scales with distance squared. Reset the control to 10 and compare wavelength.
Explain Only vswr moves here. The other chapter fixtures remain fixed.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
1. Start with the physical story
Metal can shift a tag antenna away from the chip's conjugate match, reflecting intercepted power before the chip can use it.
2. Name every algebra move
Convert VSWRUse |Γ| = (VSWR − 1)/(VSWR + 1).
Deliver powerUse τ = 1 − |Γ|².
Price lossUse Lm = −10 log10 τ.
Screen rangeUse dnew/dold = 10^(−Lm/20).
3. Reproduce the chapter case
τ = 1 − 0.818² = 0.331
Lm = −10 log10(0.331) = 4.81 dB
dnew = 4.0 × 10^(−4.81/20) = 2.30 m
The contraction is only the mismatch contribution; conductive surfaces can add separate near-field and reflection effects.
4. Try one real input
TryMove VSWR from a modest match toward a severely detuned tag and watch the whole loss chain recompute.
ObserveAt VSWR 10:1, two-thirds of available power reflects and the 4 m matched screen contracts to about 2.30 m.
ExplainThe dB loss converts to distance with a 20-log relationship because free-space power scales with distance squared.
This isolates terminal mismatch as one loss term.
- Reference
- Real tag chips use complex, power-dependent impedances; a 50 Ω VNA fixture needs a justified de-embedding method.
- Surface
- Metal and liquid also alter fields, radiation efficiency, polarisation, and multipath.
- Reads
- The calculation does not turn loss into a predicted success count such as 6/40.
Correct, not complete: this ledger does not prove the cause of a field failure.
5. Use the result in the lab
Measure the tag in its real mounting state, then compare spacer, on-metal construction, orientation, and reader power without changing multiple factors at once.
6. Record the evidence state
Keep tag and chip, fixture and calibration plane, surface stack, VSWR trace, reader settings, boundary reads, and uncertainty.
7. Check yourself
Does VSWR 1:1 reflect power?
Does 4.81 dB loss halve distance exactly?
Can this ledger predict 6 successful reads out of 40?
The ledger turns an explicit VSWR hypothesis into one reproducible mismatch-loss screen.
- Computed
- Reflection, delivered power, loss, and ideal range contraction are reproducible.
- Specified
- The exact chip impedance, fixture, frequency, and matched boundary replace the example.
- Observed
- Mounted impedance traces and controlled read trials decide whether mismatch caused the failure.
Correct, not complete: retain the wider troubleshooting tree.