For a foil-and-braid shielded twisted pair, the characteristic impedance is calculated as Z₀ = 276 × log(1.2 × D / (f × d)) / √ε, where D is insulation diameter, d is conductor diameter, ε is the insulation dielectric constant, and f is a stranding factor between 0.939 and 1.000 depending on strand count [S3].
This is the canonical shielded-pair form, distinct from the unshielded version (Z₀ = 1016 / √(ε × C)) and the overall shielded-and-cabled form (Z₀ = 347 × log(1.5 × D / (f × d)) / √ε) tabulated in standard design references [S3]. All three forms converge on the same D/d ratio philosophy, but the constants differ because of the proximity effect of the surrounding shield.
Why 100 Ω, 120 Ω, and 85 Ω: the canonical targets
100 Ω is the value the bulk of Ethernet twisted-pair shipments are designed around, and it is also the differential impedance target for RS-485, CAN, and most industrial fieldbuses derived from balanced signalling. 120 Ω shows up where the bus is heavier and the capacitance budget tighter, as in PROFIBUS DP and the IEC 61158 2-wire variants, which call for a controlled 120 Ω differential along the run. 85 Ω is the lower-impedance legacy data-bus spec offered by some manufacturers, with 85-100 Ω impedance options listed as standard catalog constructions for high-speed balanced-pair cable [S2].
On a TDR or VNA, a 100 Ω cable read through a 50 Ω test port is not measured directly, it is reconstructed through S-parameters and a balun fixture, a method described in early work on balanced-cable characterisation [S8]. Off-the-shelf 120 Ω STP can be sanity-checked with a NanoVNA-style reflectometer if the test port is set up correctly, and a 100 Ω reference resistor is used to calibrate the differential reading [S7].
The four variables that actually move impedance
D/d ratio. The log term in all three Digi-Key equations is sensitive to the ratio of insulation diameter to conductor diameter. Holding d fixed and increasing D pushes the pair further apart, raises characteristic impedance, and lowers mutual capacitance. The shielded-pair constant is 1.2× in the log argument, versus 1.3× for the unshielded version [S3].
Dielectric constant. Insulation ε ranges roughly from 2.1 (TFE Teflon) to 7.7 (PVC semi-rigid) in the published reference table, with Vp (velocity of propagation as a percent of c) spanning 45-69 % across the same materials [S3]. Higher ε raises capacitance and lowers impedance, all else equal. A common engineering shortcut: doubling ε drops Z₀ by a factor of √2, so swapping from polyethylene (ε ≈ 2.3) to PVC (ε ≈ 5.0) costs roughly 32 % of the impedance budget.
Stranding factor. A solid conductor (1 strand) has f = 1.000. As strand count rises to 7, 19, 37, 61, 91, the factor settles at 0.939, 0.970, 0.980, 0.985, 0.988 respectively, the stranded bundle behaves like a slightly larger-diameter solid for AC purposes [S3].
Shield presence. The shielded-pair capacitance formula is C = 3.7 × ε / log(1.2 × D / (f × d)) pF/ft, compared with C = 2.2 × ε / log(1.3 × D / (f × d)) pF/ft for the unshielded case, a 68 % increase that explains why a 100 Ω UTP becomes something closer to 85-90 Ω once it is wrapped in a foil-and-braid shield with the same insulation geometry [S3]. The classic online twisted-pair impedance calculator (Newark) is built around the same D/d and ε inputs and also returns propagation delay, useful when a long run is being spec'd for a high-speed link [S1].
Shielding effectiveness: impedance is not the only number
Transfer impedance Zt is the intrinsic, installation-independent figure of merit for the shield itself, normalised to 1 m of cable as V_inner (V) / I_shield (A) [S4]. A practical shortcut is that the shield's DC resistance is the low-frequency value of Zt, so a braid with lower DCR performs better at the bottom of the spectrum, while at higher frequencies the leakage inductance through the braid's apertures dominates and skin effect rapidly attenuates coupling through a solid tube [S4].
For differential signalling, the more relevant figure is the Differential Transfer Impedance Ztd, which folds in the unbalance of the twisted pair itself, an unbalance that would otherwise convert common-mode noise into differential noise on the data lines [S4]. This is why an S/UTP construction with a poorly balanced pair can be more EMC-noisy in practice than its raw Zt would suggest.
The pair itself also has a published velocity-of-propagation ceiling. A typical signal propagation delay figure cited in interface application notes is 13 ns/m max for general-purpose twisted-pair constructions [S5]. When the application note is read against a 100 m industrial run, the one-way delay budget is on the order of 1.3 µs, and a faster Vp (closer to 70 % of c in foamed PE or cellular PP) trims that to roughly 4.8 ns/m.
Selection: matching the cable to the protocol
For Ethernet (10BASE-T, 100BASE-TX, 1000BASE-T, 2.5G/5G/10GBASE-T), specify 100 Ω differential with a return-loss and insertion-loss mask out to the relevant symbol rate, and use Cat 5e / Cat 6 / Cat 6A constructions accordingly. For PROFIBUS DP and similar 12 Mbit/s fieldbuses, 150 Ω is the older characteristic, with many current installations actually wired at 120 Ω to match connector and terminator availability. [S5]
For RS-485 and CAN, the impedance is a controlled-impedance requirement, not just a DC-resistance one, and 100 Ω ± 10 % is the typical vendor envelope with a 120 Ω termination resistor at each end. The 1.2×D/d log-argument constant in the shielded-pair equation [S3] is the right formula to use for any of these designs. For audio and microphone-level balanced runs, 100-110 Ω is the historical norm, and the same equations apply, but capacitance per foot tends to dominate selection more than the exact Z₀ number.
The construction usually paired with these targets is an overall foil + braid shield with a drain wire that makes electrical contact with the foil for low-impedance termination at the connector [S6]. Drain wire sizing is a separate decision, but it is what allows the shield to be tied to chassis ground at one end (or both ends, in the case of harsh-environment installations) without relying on the connector shell alone.
Measurement caveats and common pitfalls
Radiated shielding-effectiveness tests can swing 6 dB or more between configurations, which is why the EMC community has shifted to conducted transfer-impedance measurement as the more repeatable intrinsic figure of merit [S4]. A 100 Ω cable will read approximately 14 dB worse when SE is measured with an H-field (loop) antenna than with an E-field antenna below 50 MHz, because the loop setup stresses the cable in near-field conditions where the field is not plane-wave [S4].
On the bench, the VNA / NanoVNA approach requires a 100 Ω calibration reference and ideally a balun, or a S-parameter de-embedding routine, because a 50 Ω single-ended port cannot drive a 100 Ω differential pair directly [S7][S8]. A 1 m sample is the practical minimum; shorter samples have too little delay to extract Z₀ from the time-domain reflectometry trace with any usable resolution.
Finally, the impedance the datasheet quotes is the nominal value at a single frequency, often 100 MHz or 1 MHz depending on the manufacturer. The actual Z₀ of the same cable at 10 MHz and at 1 GHz can differ by 5-15 % because of dielectric dispersion and skin-effect-induced proximity shifts, so if the design runs at 10 Gbps, the S-parameter plot, not the nominal figure, is the spec that matters.
Track the IEC 61158 and TIA-568 revision cycles for the 120 Ω and 100 Ω masks, watch for any new transfer-impedance test method harmonisation work in IEC 62153, and re-validate impedance on the next reel-to-reel variation when the dielectric supplier changes.
Spec-level background on the components involved: shielded cable, cable gland, and cable tray.
This topic is covered further in Belt vs Screw Conveyor for Enclosed Dusty Material.