Contact Resistance
How Constriction and Film Resistance Add Up at a Junction
The physics of a metallic contact was largely settled by Ragnar Holm in the mid-twentieth century, and his model still governs how RF connector and joint specifications are written today. When two nominally flat surfaces are pressed together, they meet only at a sparse population of asperities. The combined true contact area, often less than one percent of the apparent area, carries the entire current. As the current lines spread into and out of these tiny conductive spots they are constricted, and that geometric crowding produces the dominant intrinsic term known as constriction resistance. For a single circular spot of radius a in a metal of resistivity ρ, the constriction resistance is simply ρ divided by 2a, which is why increasing contact force, by enlarging a, lowers resistance.
Real surfaces are rarely metallically clean. Aluminum grows a tenacious native oxide within seconds of exposure, silver tarnishes to silver sulfide, and even gold accumulates adsorbed organic films and particulate. Any such layer in the current path adds film resistance in series with the constriction term. Noble-metal plating, principally hard gold over a nickel barrier, is the standard RF defense because gold does not form an insulating oxide; a brief wiping action during mating also helps shear through thin films. The combination of force-dependent constriction resistance and film resistance is why connector data sheets pair a maximum milliohm spec with both a mating-cycle rating and a torque value.
At microwave frequencies a second concern overtakes simple loss. A junction whose resistance varies with instantaneous current, because asperity spots heat and films behave nonlinearly, acts as a weak diode. Two strong carriers passing through such a joint generate intermodulation products that fall back into sensitive receive bands. This is the mechanism behind passive intermodulation in base-station and satellite hardware, and it is why a connector can pass a DC milliohm test yet still fail a PIM test. Surface finish matters here as well, since surface roughness changes both the asperity distribution and the effective skin-depth current path.
Governing Equations
Rc = ρ / (2a) (one a-spot of radius a)
n parallel a-spots over a contact patch:
Rc ≈ ρ / (2na) + ρ / (2α) (Greenwood, α = cluster radius)
Force dependence (elastic-plastic):
Rc ≈ ρ / 2 × √(πH / F) ⇒ Rc ∝ 1 / √F
Total contact resistance:
Rcontact = Rconstriction + Rfilm
Where ρ = metal resistivity, a = a-spot radius, n = number of spots, H = material hardness, F = normal contact force. Example: gold, ρ ≈ 24 nΩ·m, single spot a = 5 μm → Rc ≈ 2.4 mΩ. Doubling F lowers Rc by ≈ 30%.
Plating and Joint Comparison
| Contact finish | Resistivity (nΩ·m) | Typical Rcontact | Oxide behavior | RF notes |
|---|---|---|---|---|
| Hard gold / Ni barrier | ~24 | 1 to 5 mΩ | No insulating oxide | Standard for precision RF connectors |
| Silver | ~16 | 2 to 8 mΩ (rises with tarnish) | Sulfide tarnish, semiconducting | Lowest ρ but PIM risk if tarnished |
| Tri-metal / passivated SS | ~700 (steel body) | 3 to 10 mΩ | Stable passive film | Rugged, used on N and 7/16 bodies |
| Tin (signal, not RF) | ~115 | 10 to 50 mΩ | Thick oxide, fretting prone | Avoid in RF; high PIM, frets |
| Aluminum (bare) | ~28 | 50 to 500 mΩ | Tenacious 2 to 4 nm oxide | Needs gas-tight or plated joint |
Frequently Asked Questions
Why does a four-wire Kelvin measurement matter for contact resistance?
A good RF junction is only a few milliohms, comparable to lead and probe resistance, so a two-wire ohmmeter reading is swamped by its own leads. A four-wire Kelvin method forces current through one pair of leads (typically 100 mA at a capped 20 mV open-circuit voltage so as not to punch through oxide films) and senses voltage across the junction with a separate pair. The sense leads carry negligible current, so their resistance drops out, giving resolution down to tens of microohms and an as-found film reading.
How does contact force affect contact resistance in an RF connector?
Constriction resistance scales as 1/√F, so doubling normal force lowers it by about 30 percent as asperities deform and the true contact area grows. Below roughly 50 to 100 grams per gold contact, resistance climbs steeply and turns unstable. This is why SMA connectors specify roughly a 5 in-lb mating torque and 2.92 mm connectors 8 in-lb: under-torqued or worn joints show elevated insertion loss and poor repeatability, while over-torquing wears plating and can deform the center pin.
What is the difference between constriction resistance and film resistance?
Constriction resistance comes from current squeezing through microscopic asperity spots far smaller than the apparent contact area; it depends on metal resistivity and spot radius, and falls with force. Film resistance is a separate series term from any oxide, tarnish, or organic layer in the path, such as silver sulfide or aluminum oxide. Constriction resistance is intrinsic; film resistance is largely removed by gold plating, a wiping mate, or fritting voltage. Total contact resistance is their sum.