TABLE 53.1 Lumped Circuit Element Parameters Per Unit Length for Typical Transverse Electromagnetic Parallel Plate Waveguides* Transmission Line Geometry 入 Two identical, thin (A >>b) 0,λ bThlb E Two identical, thick(A b) 可入 bThI 匮 lIliM μ,h,p入,6 d One thick(λ<b and one thick(A<< b) ohmic plate "The subscript n refers to parameters associated with a normal(ohmic)plate. Using these expressions, line input impedance, attenuation, and wave velocity can be calculated. a useful quantity for making engineering estimates. For example, the energy scale associated with Josephson oupling is L; I 2=(1。)2兀 A common weak link, known as the Josephson tunnel junction, is made by separating two superconducting films with a very thin(typically 20 A) insulating layer. Such a structure is conveniently analyzed using the sistively and capacitively shunted junction(RCSD)model shown in Fig. 53. 3. Under the RCS] model an ideal lumped junction [described by Eqs. (53.14)and (53. 15)] and a resistor R represent how the weak link structure influences the respective phases of the super and normal electrons. A capacitor C represents the physical capacitance of the sandwich structure. Parasitic capacitance created by the fields around a device interacting with a dielectric substrate is also included in this lumped element. If the ideal lumped junction portion of the circuit is treated as an inductor-like element, many Josephson tunnel junction properties can be calculated with the familiar circuit time constants associated with the model. For example, the quality factor Q of the RCS] circuit can be expressed as e 2000 by CRC Press LLC© 2000 by CRC Press LLC a useful quantity for making engineering estimates. For example, the energy scale associated with Josephson coupling is LjIc 2 = (IcFo )/2p. A common weak link, known as the Josephson tunnel junction, is made by separating two superconducting films with a very thin (typically 20 Å) insulating layer. Such a structure is conveniently analyzed using the resistively and capacitively shunted junction (RCSJ) model shown in Fig. 53.3. Under the RCSJ model an ideal lumped junction [described by Eqs. (53.14) and (53.15)] and a resistor Rj represent how the weak link structure influences the respective phases of the super and normal electrons. A capacitor Cj represents the physical capacitance of the sandwich structure. Parasitic capacitance created by the fields around a device interacting with a dielectric substrate is also included in this lumped element. If the ideal lumped junction portion of the circuit is treated as an inductor-like element, many Josephson tunnel junction properties can be calculated with the familiar circuit time constants associated with the model. For example, the quality factor Q of the RCSJ circuit can be expressed as TABLE 53.1 Lumped Circuit Element Parameters Per Unit Length for Typical Transverse Electromagnetic Parallel Plate Waveguides* Transmission Line Geometry Lo Co Ro *The subscript n refers to parameters associated with a normal (ohmic) plate. Using these expressions, line input impedance, attenuation, and wave velocity can be calculated. m + m t o h d db 2 2 l et d h 8 4 db o s˜ l d Ê Ë Á ˆ ¯ ˜ m + m t o h d d 2 l et d h 4 3 d o ds l ˜ d Ê Ë Á ˆ ¯ ˜ m + m + m t o n n h d d d l d 2 et d h 1 d n o n d s