Editing Josephson effect (section)

== The RCSJ model ==
The Resistively Capacitance Shunted Junction (RCSJ) model,<ref>{{Cite journal |last=McCumber |first=D. E. |date=1968-06-01 |title=Effect of ac Impedance on dc Voltage-Current Characteristics of Superconductor Weak-Link Junctions |journal=Journal of Applied Physics |volume=39 |issue=7 |pages=3113–3118 |doi=10.1063/1.1656743 |bibcode=1968JAP....39.3113M |issn=0021-8979}}</ref><ref>{{Cite journal |last1=Chakravarty |first1=Sudip |last2=Ingold |first2=Gert-Ludwig |last3=Kivelson |first3=Steven |last4=Zimanyi |first4=Gergely |date=1988-03-01 |title=Quantum statistical mechanics of an array of resistively shunted Josephson junctions |journal=Physical Review B |volume=37 |issue=7 |pages=3283–3294 |doi=10.1103/PhysRevB.37.3283 |pmid=9944915 |bibcode=1988PhRvB..37.3283C|url=https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/40643 }}</ref> or simply shunted junction model, includes the effect of AC impedance of an actual Josephson junction on top of the two basic Josephson relations stated above.

As per [[Thévenin's theorem]],<ref>{{Cite web |title=AC Thevenin's Theorem |url=http://hyperphysics.phy-astr.gsu.edu/hbase/electric/acthev.html |website=hyperphysics.phy-astr.gsu.edu |access-date=2020-01-03}}</ref> the AC impedance of the junction can be represented by a capacitor and a shunt resistor, both parallel<ref>{{Cite web |title=Dynamics of RF SQUID |url=http://phelafel.technion.ac.il/~orensuch/theory/Theory.html |website=phelafel.technion.ac.il |access-date=2020-01-11 |archive-date=2021-06-13 |archive-url=https://web.archive.org/web/20210613133720/http://phelafel.technion.ac.il/~orensuch/theory/Theory.html |url-status=dead}}</ref> to the ideal Josephson Junction. The complete expression for the current drive <math>I_\text{ext}</math> becomes:

:<math>I_\text{ext} = C_J \frac{\operatorname{d}\!V}{\operatorname{d}\!t} + I_c \sin \varphi + \frac{V}{R},</math>

where the first term is displacement current with <math>C_J</math> – effective capacitance, and the third is normal current with <math>R</math> – effective resistance of the junction.