Abstract: A phase locked loop for recovering a clock signal from a data signal including a delay locked loop with a nonlinear digital phase detector. The delay locked loop that is embedded in the phase locked loop acts like a linear phase detector. The phase locked loop of the present invention can be produced at low cost and is particularly suitable for use in data communication.

Abstract: A PLL-controlled oscillator that can be suitably used for such purposes as a jitter filter in an optical transmission system includes an input voltage-switching control oscillator as a voltage-controlled oscillator (VCO). The input voltage-switching control oscillator includes: an oscillation closed loop that is provided with a variable-voltage capacitance element; and a switch for interchangeably selecting one of a plurality of voltages in accordance with a selection signal and applying the selected voltage as a control voltage to the variable-voltage capacitance element.

Abstract: A transmitter (10) based on a frequency synthesizer includes an LC tank (12) of a digitally controlled oscillator (DCO) with various arrays of capacitors. The LC tank 12 is divided into two major groups that reflect two general operational modes: acquisition and tracking. The first group (process/voltage/temperature and acquisition) approximately sets the desired center frequency of oscillation initially, while the second group (integer and fractional tracking) precisely controls the oscillating frequency during the actual operation. For highly accurate outputs, dynamic element matching (DEM) is used in the integer tracking controller to reduce non-linearities caused by non-uniform capacitor values. Also, a preferred range of the integer tracking capacitor array may be used for modulation after the selected channel has been acquired. A digital sigma-delta modulator circuit (50) drives a capacitor array (14d) in response to the fractional bits of the error word.

Abstract: A quadrature coupled controlled oscillator comprising a first and a second circuit module, each of the circuit modules (100 and 100′) comprising an astable multivibrator circuit (103). The first circuit module is coupled with the second circuit module and the second circuit module is cross coupled with the first circuit module. Each of the circuit modules (100 and 100′) comprises a first and a second Voltage Controlled Current Source (101) (VCCS). In each of the circuit modules, each VCCS is coupled to a phase shifter (102) for shifting the phase of a current (110) supplied by the VCCS to a resonator (104) included in that circuit module. A communication arrangement (300) for communicating via a bi-directional communication channel (304), comprises an oscillator (303) as described above for generating a periodic signal. A receiving module (301) generates an output signal from the periodic signal and a receiving signal received from the channel (304).

Abstract: Piezo oscillators having a quick start-up circuit, which applies a start-up quickening voltage to the piezo resonator only for a predetermined length of time after the application of power supply voltage, added to a piezo oscillating circuit. The start-up time taken for the piezo oscillators to reach the steady-estate oscillation from the non-oscillating state can be significantly shortened. The phase noise characteristics and frequency stability characteristics are not affected, since the start-up quickening voltage is removed after the predetermined length of time.

Abstract: An LC oscillator includes inductors, a variable capacitor section, an adjusting section for varying the capacitance of the variable capacitor section in response to a control voltage supplied in accordance with a digital control signal, and an additional variable capacitor section for varying its capacitance in response to an additional control voltage. The variable capacitor section includes first to Kth capacitors, where K is an integer greater than one. The adjusting section includes buffer section, each of which selectively generates one of a first voltage and a second voltage lower than the first voltage in response to a kth bit of the digital control signal, where k is an integer varying from one to K, thereby generating first to Kth control voltages to be supplied to the first to Kth capacitors.

Abstract: A balanced oscillator includes a differential oscillator circuit having two output terminals, and a differential amplifier circuit having two input terminals each being connected with a respective one of the two output terminals of the differential oscillator circuit. The direct-current path of the differential oscillator circuit is connected in series with the direct-current path of the differential amplifier circuit.

Abstract: A circuit is shown which outputs a pulse width having a duty cycle of less than 50% and the circuit having an oscillator providing a desired repetition rate controlled by a changing RC time constant.

Abstract: A circuit for producing a reliable duty cycle for a low power oscillator. The circuit produces a square wave signal based on the differences between the oscillating output signal driven by a piezoelectric crystal and a phase shifted output signal. This circuit provides a quick start for a clock signal, generates a reliable fifty percent duty cycle and is better protected from common mode noise. This circuit can also be configured to be programmable to provide for an adjustable duty cycle.

Abstract: A discontinuity, such as a via, in a signal transmission line can introduce a parasitic element that affects the signal transmission. The method in accordance with embodiments of the present invention are directed to counteracting the transmission line parasitic element discontinuity. The method includes determining the amount of parasitic capacitance or inductance that is introduced at a portion of the transmission line, such as by the via. A suitable amount of delay is introduced to the transmission line by way of correction impedance in order to counteract the affects of the parasitic element. The delay is calculated taking into account at least in part the correction impedance and the parasitic element effect. The correction impedance is suitably added to a portion of the transmission line at which the parasitic element is present.

Abstract: A device and method for tuning a planar filter through a wide range of center frequencies are disclosed. The tuning assembly includes a superconductive tuning tip and an actuator configured and adapted to move the tuning tip through a sufficient range of distances from a resonator or a portion thereof to vary the resonant frequency of the resonator by at least about 10% of the untuned frequency in at least one increment of 0.01% or smaller. An actuator and a position-sensor can be employed in a closed loop feedback system to control the position of the tuning tips. The present invention also provides a method of tuning a filter that includes moving a tuning tip through a sufficient range of distances from a resonator to vary the resonant frequency of the resonator by at least about 10% in at least one increment of 0.01% or smaller.

Abstract: A balancing/unbalancing (balun) structure for operating at frequency f1 includes a microstrip printed circuit board (PCB). A balun on the PCB includes two input ports are coupled to a differential signal. An isolated port is connected to ground through a matched resistance. An output port is coupled to a single-ended signal corresponding to the differential signal. A plurality of traces on the PCB connect the two input ports, the load connection port and a tap point to the output port. A f2 rejection filter on the PCB is wrapped around the balun and includes a first folded element with a transmission length of &lgr;2/4 and connected to the output port. A second folded element has a transmission length of &lgr;2/4 and connected to the tap point. A third folded element connects the tap point to the output port and has a transmission length of &lgr;2/4.

Abstract: Composite media having simultaneous negative effective permittivity and permeability over a common band of frequencies. A composite media of the invention combines media, which are either themselves separately composite or continuous media, having a negative permittivity and a negative permeability over a common frequency band. Various forms of separate composite and continuous media may be relied upon in the invention. A preferred composite media includes a periodic array of conducting elements that can behave as an effective medium for electromagnetic scattering when the wavelength is much longer than both the element dimension and lattice spacing. The composite media has an effective permittivity &egr;eff(&ohgr;) and permeability &mgr;eff(&ohgr;) which are simultaneously negative over a common set of frequencies. Either one or both of the negative permeability and negative permittivity media used in the invention may be modulable via external or internal stimulus.

Abstract: Scheme for processing an input signal A(t) by N resonators (17), each having parameters characterizing it, to generate N individual output signals. Then each of the N individual output signals is weighted using a corresponding weight to generate N individual weighted output signals which are superposed to obtain M output signals C(t). One of the parameters or the weight depend on a time signal P(t).

Abstract: A flat group-delay low-pass filter includes a series element connected between an input terminal and an output terminal, and a shunt element with one end thereof grounded. Inductors define the series element, a parallel circuit including a capacitor and a series circuit including a resistor and a capacitor defines the shunt element. The flat group-delay low-pass filter thus eliminates the need for inserting a fixed attenuator to control the effect of reflections due to impedance mismatching between the filter and other components. The resulting flat group-delay low-pass filter and an optical signal receiver including the filter have very low manufacturing costs and component costs.

Abstract: A multilayer LC filter includes two LC resonance circuits (21 and 22) in a two-stage circuit configuration. First and second resonator inductors (L21 and L22) formed by two strip-like electrical paths (14 and 15) extend laterally in parallel and are patterned on the same inductor layer (c). A strip-shaped shielding or ground path (35) is formed between, and in parallel with, the two strip-shaped electrical paths (14 and 15) such that the electrical paths are in the shape of a fork on the inductor layer c. The magnetic coupling between the resonator inductors (L21 and L22) is thus weakened and, even when pattern dislocations occur during the patterning of the paths, there is substantially no variation in the magnetic coupling characteristics of multilayer LC filters of this construction.

Abstract: A modular electronic signal filter assembly is provided, including a plurality of modular filter housing members joined to one another in a longitudinal direction via a plurality of coupling members. The outer peripheral surfaces of the filter housing members are provided with mechanical engagement members that engage and mate with a corresponding mechanical engagement member provided on the inner peripheral surface of the coupling members to secure the filter housing members to one another without solder. The coupling members also include an electrical connection member for electrically connecting the filter housing members in a solderless manner. The modularity of the filter housing assembly of the present invention provides heretofore unrealizable flexibility and applicability of a single filter housing unit for any filter application. Moreover, the present invention enables the assembly of modular filter housing and coupling member units without the need for solder.

Abstract: A DMS filter is proposed with first and second interdigital transducers as a signal input or output that are located between reflector structures, wherein at least one acoustic track has a middle transducer that is split into partial transducers symmetric with respect to the perpendicular to the direction of propagation. The DMS filter is connected in a symmetrical manner to a housing using connection pads or connection pins in order to produce an axis-symmetrical connection layout.

Abstract: A rectangular penetration hole is formed opening in the opposite two main surfaces of a first dielectric substrate. Conductors for grounding are respectively formed on the main surfaces, to cover the openings of the penetration hole. A conductor layer is formed on opposite inner walls in the penetration hole of the dielectric substrate. A waveguide is structured by a space surrounded by the conductors and the conductor layers. The waveguide is magnetically coupled with an input/output line on a second dielectric substrate through a coupling slot. Because a waveguide has walls made continuous in the dielectric substrate, a low-loss waveguide can be realized. Hence, a high-performance radio frequency module can be realized.

Abstract: A connection structure is provided, which can perform an electrical connection between high-frequency circuit substrates in a manner of high workability and productivity. A connection structure comprises: a high-frequency transmission line lead frame connecting a first high-frequency transmission line formed on a first high-frequency circuit substrate to a second high-frequency transmission line formed on a second high-frequency circuit substrate; a plurality of GND electrode lead frames disposed in parallel to the high-frequency transmission line lead frame on both sides thereof, and providing a connection between a first GND electrode of the first high-frequency circuit substrate and a second GND electrode of the second high-frequency circuit substrate; and a reinforcing substrate integrally securing the high-frequency transmission line lead frame and a plurality of GND electrode lead frames.

Abstract: An electrically isolating iso bearing for a circuit breaker is provided that comprises an inner surface, an outer surface, and a body extending therebetween, said inner surface comprising a pair of bosses and a pair of openings, said outer surface comprising at least one boss, said body comprising a pair of rotor protective flaps.

Abstract: A micro-electro-mechanical (MEMS) switch (10, 110) has an electrode (22, 122) covered by a dielectric layer (23, 123), and has a flexible conductive membrane (31, 131) which moves between positions spaced from and engaging the dielectric layer. At least one of the membrane and dielectric layer has a textured surface (138) that engages the other thereof in the actuated position. The textured surface reduces the area of physical contact through which electric charge from the membrane can tunnel into and become trapped within the dielectric layer. This reduces the amount of trapped charge that could act to latch the membrane in its actuated position, which in turn effects a significant increase in the operational lifetime of the switch.

Abstract: A magnetic latching solenoid including a solenoid operating mechanism, and further comprising a magnetic latching subassembly cooperating with, but positioned independently of the solenoid operating mechanism. In a preferred embodiment, the solenoid operating system may be of a bi-directionally operated structure arranged for alternative magnetically latching function. Independently operated, magnetic latching subassemblies are spaced apart from one another and from opposite ends of the bi-directionally operated solenoid operating mechanism.

Abstract: An actuator comprises a magnet yoke and a carrier member movable relative to the magnet yoke. The magnet yoke has at least one permanent magnet and the carrier member is positioned in the magnetic field produced by this magnet. The carrier member has an auxiliary magnetic member that produces a relative bias force between the carrier member and the magnet yoke. The bias force will be used to compensate for a weight applied to the device and acts as a bearing with a very large compliance. The carrier member also comprises a coil. Passing current through the coil produces a Lorentz force for further control of the actuator; alternatively, the device provides a velocity transducer by sensing the EMF generated in the coil by relative motion of the carrier member and magnet yoke.

Abstract: A chip inductor is made up of a coiled conducting wire and a magnetic member which is formed by sintering and in which the coiled conducting wire is embedded. Both end portions of the coiled conducting wire are exposed to both end surfaces of the magnetic member. External electrodes are formed with conducting thin films and are connected to respective end portions of the coiled conducting wire. An inorganic material is interposed in a clearance between winds of both end portions of the conducting wire and external surfaces of the magnetic member and a clearance between adjoining winds of the conducting wire.

Abstract: A coil-embedded dust core and a method for manufacturing the coil-embedded dust core are provided. The coil-embedded dust core comprises a coil formed from a flat conductor wound in a coil configuration, and a green body consisting of insulating material-coated ferromagnetic metal particles. This results in a coil-embedded dust core more compact in size but with larger inductance. A rectangular wire can be used as the flat conductor. In addition, parts of the coil may function as terminal sections. In this case, the terminal sections of the coil may be formed wider than other part of the coil. The coil-embedded dust core is less prone to joint failures between a coil and terminal sections and to insulation failures of the coil and the terminal section with respect to the magnetic powder. The coil-embedded dust core is more compact while achieving larger inductance.

Abstract: An inductance component includes a magnetic core (11, 12) forming a magnetic circuit having a magnetic gap, an exciting coil (14) wound around the magnetic core, and a permanent magnet (13) disposed in the magnetic gap. The permanent magnet is greater in sectional area than the magnetic core.

Abstract: A configuration for producing electrical power from a magnetic field includes a three-dimensional winding configuration formed from a central core of a magnetic material on which at least three windings are fitted. The windings have winding axes each disposed at right angles to one another and intersecting at a common point. Each of the windings is connected to a rectifier. Each of the windings is, preferably, connected to a resonant capacitor to form a resonant circuit.

Abstract: A fuse has a fuse element (6) with a fusible conductor (7) of a conductor material (8) such as Ag, Cu or Al and is provided with doping points (9) following one another at regular intervals. There, the conductor material (8) has a directly adjoining layer of a first compound (10) of the same with a doping material such as In or Ge. It forms mixed crystals which contain the conductor material (8) and the doping material in a fixed stoichiometric ratio, such as for example Ag2In, and is separated from said conductor material by a stable phase boundary. The doping points (9) weaken the fusible conductor by lowering the melting point to below 250° C., so that arc formation rapidly occurs there when there are short-circuit currents, although its electrical resistance per unit of length is under some circumstances only a few percent greater than in the remaining region. The fusible conductor (7) bears a continuous layer of a burn-up material (12).

Abstract: A key fob for use in accessing first and second motor vehicles includes a portable housing defining a hole for receiving a key chain and first and second motor vehicle selector buttons connected to integrated circuit logic within the housing and accessible through the housing. The fob further includes at least one function selector button connected to the integrated circuit logic and accessible through the housing. The integrated circuit logic is configured to select the first or second motor vehicle upon activation of the first or second motor vehicle selector buttons respectively. The integrated circuit logic controls a lock of the selected motor vehicle upon activation of the function selector button.

Abstract: A system of locker compartments at various locations is controlled by a central system processor. A communication system from the central processor to all locations, and all lockers within a location, enables central control of rewritable locker access codes, reservation of appropriate lockers for delivery of orders, and monitoring of status of all lockers in the system. The assignment of lockers and codes can be web-based, and can be done by a vendor, a delivery company or an online customer.

Abstract: A novel technique and system for improved monitoring of the storage security of firearms (and other objects) and, through a microprocessor radio-controlled transceiver embedded within the firearm, enabling detection of theft or removal, and then radio-tracking of the stolen firearm by police or others with continual identification of that firearm, and also with the further feature of providing automatic warning to schools or other public buildings or locations of the intrusion in their vicinity of a bearer carrying the stolen firearm.

Abstract: The response of an object to a single time-varying magnetic field is sensed to determine object position and/or manipulation on a horizontal or vertical surface. A time-varying interrogation signal, which interacts with tags disposed on the surface, is read by an array of sensing coils. Control circuitry receives signals from the sensing coils representing this interaction and, based thereon, determines the identity, position, and manipulation of each of the objects based on the sensed signals and the known positions of the sensing coils. Feedback to the user can be provided in the form of a localized output (e.g. light, sound, heat, etc.) physically coincident with the object.

Abstract: Presented is a communications protocol for use by interconnected hazardous condition detectors, such as smoke and carbon monoxide detectors for use in dwellings and other structures. This communications protocol provides conventional signaling to indicate the presence of a smoke condition necessitating the generation of a smoke temporal pattern by all interconnected detectors. The protocol further defines a signaling method by which conventional smoke detectors that are incapable of providing temporal patterns other than that required for a smoke alarm condition will not be sent into an alarm mode of operation upon receipt of a signal other than the conventional smoke alarm signal. This communications protocol defines a pulsed signal to indicate a non-smoke alarm condition that is of a duration that will not trigger the conventional smoke alarms.

Abstract: The present invention relates to a cable (K1, K2) which has integrated identification transmitters (KG1-KG5) for cable-specific data. This data can be checked by using wires or without wires. In this way, for example, extensive details relating to the cable (K1, K2) and the wiring of the cable (K1, K2) can be provided by electrical means to a fitter at any time.

Abstract: The invention is for a vandal resistant latch/starter-interlock assembly for a bus door. In the assembly of the invention, the alarm and the starter-interlock are part of the same assembly. The assembly includes box through which a modified latch bolt extends laterally. The latch bolt is locked by a vandal lock. When unlocked, the latch bolt slides or moves to allow the door to be opened. The alarm and starter-interlock are activated after unlocking the vandal lock. Typically, the alarm is activated when the latch bolt is moved, usually by moving a door latch. While the starter-interlock can also be activated by moving the latch bolt, it is preferably activated by unlocking the vandal lock.

Abstract: To make it possible to take appropriate action promptly in response to a report from a vehicle of an abnormality such as a theft, an accident, or a failure. A terminal apparatus is included in vehicles to transmit an abnormality report and thereby providing a notification of the occurrence of an abnormality to a control apparatus. The terminal apparatus includes abnormality information C from an abnormality detecting sensor, identifying information A of the vehicle, attribute information D for indicating attributes of the vehicle itself, and position information D of the vehicle. The control apparatus can thereby detect the occurrence of the abnormality of the vehicle, identify the vehicle having the abnormality, identify the attributes of the vehicle having the abnormality, and identify the location where the abnormality has occurred. It is thus possible to take appropriate action promptly such as sending an appropriate report and sending an appropriate request to a maintenance service.

Abstract: A data transmission-reception unit which operates by means of energy of a received electromagnetic wave and serves as a main circuit, is provided with a sensor circuit as an additional circuit, and a transponder having a sensor power circuit for supplying electric power only to the sensor circuit is constituted. From a sensor charging circuit of an interrogator, an electromagnetic wave of a lower frequency different from a frequency of electromagnetic wave for data communication is radiated, or loop coil-shaped charging antennas are electromagnetic-coupled to thereby charge a capacitor for the sensor power circuit. Thereby, a secondary battery and the capacitor such as a large scale capacitor can be easily charged from an outside, and further, a power consumption for the capacitor can be restrained.

Abstract: A dual technology motion or occupancy sensor, and a method for using the same, to control a lighting circuit to activate and deactivate lights in a monitored area. The sensor employs an infrared energy sensor, a microwave energy sensor, and a controller. The infrared energy sensor outputs an infrared energy detection signal indicative of detection or non-detection of infrared energy, and the microwave energy sensor outputs a microwave energy detection signal indicative of detection or non-detection of microwave energy. The controller outputs a control signal to control activation and deactivation of the lighting circuit in response to a condition of the infrared energy detection signal and a condition of the microwave energy detection signal.

Abstract: An apparatus for supporting a patient comprises a frame, a mattress supported by the frame, and a patient position detection system including an alarm and at least one sensor configured to detect a position of the patient relative to the mattress. The patient position detection system has at least three different modes of operation.

Abstract: Cameras 31, 32 take images of an image space around a door. A distance calculation unit 33 calculates the distance to an object in the taken images. A coordinate transformation unit 34 detects the three-dimensional position of the object in the image space. The image space covered by the cameras 31, 32 is divided into a plurality of voxels. Some of these voxels are optionally set as constituents of the detection area. A judgement unit 36 judges whether the detected three-dimensional position of the object locates within or outside the detection area. If the object is present within the detection area, an output unit 37 produces an object detection signal, so that the door is allowed to open.

Abstract: This invention provides a sleepy alarm apparatus for a vehicle driver, which is activated by a heart pulse meter, of which the measured heart pulse rate is lower than the preset threshold sleepy pulse rate. When a driver is sleepy while driving, the pulse rate is gradually decreasing. This invention continuously monitors the time interval for the predetermined number of the driver's pulses and converts the time interval into a pulse rate. If the measured pulse rate is lower than the preset threshold pulse rate, the system will trigger an alarm unit, which is a part of the present invention. The preset threshold pulse rate can be adjusted by the increase or decrease switch. The apparatus may be made to be wearable on a wrist or made to be attachable on the steering wheel of the vehicle being driven. In which case, the device includes a cuff for placing a finger in it in order to monitor the heart pulses.

Abstract: In an on-board control system, a body ECU executes various control operations in response to the supply of power voltage from a battery. There is connected on the power line of the battery a voltage holding circuit which is formed of a capacitor so that the variation of battery voltage slows. A switch input circuit samples the on/off states of external switches periodically under control of a microcomputer. The microcomputer determines a fall of battery voltage, causing the switch input circuit to stop sampling of switch states. Stopping the circuit operation and thus reducing the battery load current slows the voltage fall at the occurrence of collision of vehicle, allowing adequate time to store collision data in a collision memory circuit.

Abstract: An apparatus of monitoring motor vehicle's electric power and method thereof are provided. The apparatus is disposed in the motor vehicle and includes a monitor and alarm device parallel connected to both a battery to be measured and a starting motor of the motor vehicle. The starting motor is taken as a load for forming an outer loop sampling circuit, 1/t second is set as a sampling time interval during discharging, voltage and current curves are formed by connecting a plurality of continuous voltage values each sampled in 1/t second, a minimum voltage of the voltage curve is compared with a predetermined alarm value for determining a status of the battery to be measured, and an alarm is issued in time if the status of the battery to be measured is abnormal.

Abstract: A tamper-indicating fastener has a cylindrical body with threads extending from one end along a portion of the body, and a tamper indicating having a transducer for converting physical properties of the body into electronic data; electronics for recording the electronic data; and means for communicating the recorded information to a remote location from said fastener. The electronics includes a capacitor that varies as a function of force applied by the fastener, and non-volatile memory for recording instances when the capacitance varies, providing an indication of unauthorized access.

Abstract: An apparatus for providing wireless transmission of information in electronic display systems and methods of using the same. In particular, the present invention is directed to an air interface and protocol to facilitate wireless transmission of information from a communication base station or other controlling device to individual electronic display modules.

Abstract: A method and system for the remote controlling of appliances includes an adaptive remote controller that adapts itself automatically to its environment so as to remotely control a plurality of appliances. The adaptive remote controller is RF based and has the capability of two way communication with appliances. The adaptive remote controller provides information, alerts and help to a user.

Abstract: A remote control, particularly for wireless remote control of a closing device in a motor vehicle, has a first transmitter for outputting an optical signal, and a second transmitter for outputting a radio signal. The two transmitters are able to be activated for signal output by at least one actuation element. An input of the first transmitter and/or of the second transmitter is connected to a clock transmitter in order to output the optical signal and/or the radio signal in pulsed fashion at particular intervals of time in order to save energy. Also an associated remotely controllable device and a full remote control configuration are disclosed.

Abstract: A method for improving ROP and reducing hazards in drilling subterranean wells by using an acoustical system 15 to look ahead of the drill bit 14, detects and analyzes geologic features ahead of the bit 14 which may be qualified as drilling hazards 17. Detection of such hazards 17 may facilitate use of more aggressively penetrating bits 14 such as PDC bits as opposed to roller cone bits. In addition, other drilling parameters may be adjusted to improve ROP due to the ability to timely respond to identified hazards 17 before they may be detrimentally encountered by the bit 14. The acoustic system 15 may look ahead of the bit 14 by at least 100 meters, using propagated acoustic waves 19 to locate changes in acoustic impedance which may represent drilling hazards 17. In addition, bulk resistivity ahead of the bit 14 may also be measured and used to locate drilling hazards 17.

Abstract: A system and method for transferring wave energy into or out of a periodic structure having a characteristic wave impedance profile at a prime frequency, the characteristic wave impedance profile comprising a real portion and an imaginary portion, comprising: locating one or more energy transfer elements each having a wave impedance at the prime frequency approximately equal to the real portion of the characteristic wave impedance at one or more points on the periodic structure with the imaginary portion approximately equaling zero; and employing the one or more energy transfer elements to transfer wave energy into or out of the periodic structure. The energy transfer may be repeaters. Quarter-wave transformers can be provided at one or more points on the periodic structure with the imaginary portion approximately equaling zero to transmit waves across one or more discontinuities. A terminator can be employed for cancellation of waves.