Abstract: A method for performing a signal integrity analysis on an integrated circuit (IC) that includes a plurality of scatterers by dividing the scatterers into subgroups using a nested Huygens' equivalence principle algorithm and solving a set of equations realized thereby with a reduced coupling matrix. The method includes decomposing the IC design into a plurality of small non-overlapping circuit sub-domains, wherein each of the sub-domains is formed as a small, enclosed region. Each sub-domain is analyzed independently of the other sub-domains using only electric fields to represent the interactions of each sub-domains with the other sub-domains as equivalent currents on equivalent surfaces of the plurality of sub-domains. Neighboring equivalent sub-domains are grouped together to form larger sub-domains using equivalent currents on equivalent surfaces to represent the interactions of the sub-domains.

Abstract: A method for performing a signal integrity analysis on an integrated circuit (IC) that includes a plurality of scatterers by dividing the scatterers into subgroups using a nested Huygens' equivalence principle algorithm and solving a set of equations realized thereby with a reduced coupling matrix. The method includes decomposing the IC design into a plurality of small non-overlapping circuit sub-domains, wherein each of the sub-domains is formed as a small, enclosed region. Each sub-domain is analyzed independently of the other sub-domains using only electric fields to represent the interactions of each sub-domains with the other sub-domains as equivalent currents on equivalent surfaces of the plurality of sub-domains. Neighboring equivalent sub-domains are grouped together to form larger sub-domains using equivalent currents on equivalent surfaces to represent the interactions of the sub-domains.

Abstract: A method for performing a signal integrity analysis on an integrated circuit (IC) that includes a plurality of scatterers by dividing the scatterers into subgroups using a nested Huygens' equivalence principle algorithm and solving a set of equations realized thereby with a reduced coupling matrix. The method includes decomposing the IC design into a plurality of small non-overlapping circuit sub-domains, wherein each of the sub-domains is formed as a small, enclosed region. Each sub-domain is analyzed independently of the other sub-domains using only electric fields to represent the interactions of each sub-domains with the other sub-domains as equivalent currents on equivalent surfaces of the plurality of sub-domains. Neighboring equivalent sub-domains are grouped together to form larger sub-domains using equivalent currents on equivalent surfaces to represent the interactions of the sub-domains.

Abstract: A method for performing a signal integrity analysis on an integrated circuit (IC) that includes a plurality of scatterers by dividing the scatterers into subgroups using a nested Huygens' equivalence principle algorithm and solving a set of equations realized thereby with a reduced coupling matrix. The method includes decomposing the IC design into a plurality of small non-overlapping circuit sub-domains, wherein each of the sub-domains is formed as a small, enclosed region. Each sub-domain is analyzed independently of the other sub-domains using only electric fields to represent the interactions of each sub-domains with the other sub-domains as equivalent currents on equivalent surfaces of the plurality of sub-domains. Neighboring equivalent sub-domains are grouped together to form larger sub-domains using equivalent currents on equivalent surfaces to represent the interactions of the sub-domains.

Abstract: Borehole NMR logging apparatus and methods, and methods for the interpretation thereof. A logging tool is provided which produces a strong, static and homogeneous magnetic field B.sub.0 in a Volume of an adjacent formation on one side of the tool to measure nuclear magnetic resonance characteristics thereof. In the preferred embodiment, the tool has an RF antenna mounted on the outside of the metal body of the tool, directing focussed oscillating magnetic fields B.sub.1 at said Volume to polarize or tip the magnetic moments of hydrogen nuclei of fluids within rock pores. The same antenna can be used to receive signals of proton precession in the Volume of interest immediately after transmission of the RF polarizing field B.sub.1. Extremely rapid damping of the antenna between the transmitting and receiving modes of operation is accomplished by a Q-switch disclosed herein. The invention provides for the direct measurement of NMR decay having transverse relaxation time T.sub.

Abstract: Borehole NMR logging apparatus and methods, and methods for the interpretation thereof. A logging tool is provided which produces a strong, static and homogeneous magnetic field B.sub.0 in a Volume of an adjacent formation on one side of the tool to measure nuclear magnetic resonance characteristics thereof. In the preferred embodiment, the tool has an RF antenna mounted on the outside of the metal body of the tool, directing focussed oscillating magnetic fields B.sub.1 at said Volume to polarize or tip the magnetic moments of hydrogen nuclei of fluids within rock pores. The same antenna can be used to receive signals of proton precession in the Volume of interest immediately after transmission of the RF polarizing field B.sub.1. Extremely rapid damping of the antenna between the transmitting and receiving modes of operation is accomplished by a Q-switch disclosed herein. The invention provides for the direct measurement of NMR decay having transverse relaxation time T.sub.

Abstract: A well logging apparatus is disclosed which employs slot antennas having a plurality of conductive probes traversing the slot. Also disclosed are a logging apparatus having electrically isolated antenna probes and a logging apparatus with an improved means for generating and applying a reference signal used in phase detection.

Abstract: A method and apparatus investigating a circumferential segment of a borehole with an array of elements, which in effect spatially samples the segment, is described whereby, with a single circumferentially oriented array of spaced-apart elements sufficient overlap can be synthesized so as to reduce artifacts attributable to the spatial sampling. Measurements derived from circumferentially successive elements are combined, such as by summing to establish a desired overlap. In the described embodiment to a single lateral array of small electrodes is used to inject survey currents into the borehole wall and each current is measured. Measurements derived from pairs of successive survey currents are then summed to provide the desired overlap.

Abstract: A wall-engaging apparatus for microinductively investigating a characteristic of earth formations traversed by a borehole includes an antenna set mounted in a longitudinally elongated body adapted for a sliding engagement with the wall of the borehole. The antenna set includes a conductive backplane member mounted in the body parallel to the wall-engaging face of the body and first, second, and third half-loop antenna elements. The half-loop antenna elements are coaxial located symmetrically about the half-loop of the first antenna element, with their respective ends located at the backplane member to couple image currents in the backplane. The locations of the second and third antenna elements are further selected to place the second and third antenna elements in electromagnetic symmetry relative to the first antenna element. A differential coupler is included for coupling the second and third antenna elements.

Abstract: A wall-engaging apparatus for microinductively investigating a characteristic of an earth formation traversed by a borehole includes an antenna set mounted in a sensing body adapted for sliding engagement with the wall of the borehole. The antenna set includes first, second and third antenna elements. The second and third elements, being structurally identical but differentially coupled, are positioned in electromagnetic symmetry about the first antenna element. Either the first antenna element or the differentially coupled second and third antenna elements may be energized by suitable circuits, while the other is coupled to circuits for receiving signals indicative of a set characteristic.

Abstract: A well logging apparatus is disclosed which employs slot antennas having a plurality of conductive probes traversing the slot. Also disclosed are a logging apparatus having electrically isolated antenna probes and a logging apparatus with an improved circuit for generating and applying a reference signal used in phase detection.

Abstract: A wall-engaging apparatus for microinductively investigating a characteristic of an earth formation traversed by a borehole comprises an antenna set mounted in an longitudinally elongated body adapted for a sliding engagement with the wall of the borehole. The antenna set includes a transmitter antenna mounted in the body for coupling electromagnetic energy into a formation; a receiver antenna for sensing a signal indicative of the characteristic; and at least one electroquasistatic shield element mounted coaxially with the magnetic dipole axis of the transmitter antenna.

Abstract: A wall-engaging apparatus for microinductively investigating a characteristic of earth formation traversed by a borehole includes an antenna set mounted in a longitudinally elongated body adapted for a sliding engagement with the wall of the borehole. The antenna set includes a first antenna element, a second antenna element, and a third antenna element, the respective locations and orientations of the second and third antenna elements being selected to place the second and third antenna elements in electromagnetic symmetry relative to the first antenna element. Differentially coupling the second and third antenna elements. Either the first antenna element or the differentially-coupled second and third antenna elements may be energized by suitable means, while the other is coupled for receiving signals indicative of the characteristic.