Transmission Line Input Impedance Calculator
Transform an entered complex load through an ideal lossless line and report input impedance and mismatch.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Evaluate the lossless ABCD transformation using sine and cosine so quarter-wave cases do not require tangent singularities.
Zin=Z0(ZL cosθ+j Z0 sinθ)/(Z0 cosθ+j ZL sinθ); θ=2πf length/(c VF)
Worked example
A purely 100 Ω load on a 50 Ω line transforms to 25 Ω at a quarter wavelength; the reflection magnitude is 1/3 and VSWR is 2.
Assumptions and input details
Real positive Z0 and strictly positive load resistance. No conductor/dielectric loss, dispersion, connectors or frequency-dependent load. Positive reactance is inductive. Extreme near-resonant inputs may exceed the numeric range.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
SI prefixes are explicit: for example, milli means one thousandth, micro one millionth and kilo one thousand. Changing a unit changes the interpretation of the entered number.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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