Monthly Archives: April 2014


Key to the insertion of superconducting microwave circuits into electronic systems is the integration of the HTS compo­nents with a cryogenic refrigerator and its associated control electronics. Clearly, for HTS technology to be ultimately suc­cessful, the user must be rendered able to ignore the fact that cryogenics are used at all, by providing long-lifetime cryocool – ers and optimally small cryogenic packages with standard en­velop characteristics and interfaces (e. g., 19 in rack mounts and back-plane blind-mate connectors).

Many important considerations enter into the design of a cryogenic package suitable for a microwave HTS subsystem. Figure 15 is a schematic representation of this package, show­ing its main elements and the various heat inputs that must be considered for an appropriate thermal design. Ref. 41 pro­vides specific details on the cryogenic package for a communi­cations filter subsystem.

The choice of a cryocooler will depend on the system and the cooling requirements. An airborne military application may require the use of a small Stirling-cycle cooler because of volume restrictions. On the other hand, a communications ground station in a remote location that needs to operate un­attended for a long time may require a larger, more reliable refrigerator of the Gifford-McMahon type. Cooling require­ments are imposed by the component or subsystem to be cooled and will determine the amount of cooling power re­quired at the operating temperature. Typical sample system and cooling requirements and some comments as to their sig­nificance are given in Tables 4 and 5, respectively.

Figure 16. Photograph of a HTS filter assembly for commercial wire­less applications (courtesy of Superconductor Technology, Inc.).

Cryocoolers likely to be used in microwave HTS technology will typically have from 1 W to 5 W of cooling capacity. A primary concern systems designers have is the reliability of cryogenic refrigerators, which varies greatly depending on their type and size. Leveraging developments in other fields, such as infrared detectors, the reliability of small, military tactical cryocoolers has steadily increased in recent years, with some manufacturers claiming up to 20,000 h of mean­time to failure (MTTF). On the other hand, larger laboratory or industrial units and specialized coolers for aerospace appli­cations operate for 5 years to 10 years and require minimal servicing. Table 6 lists some of the cryocooler types of inter­est. The intent here is not to be all-inclusive but to provide a basic reference to the type of coolers most likely to be em­ployed in HTS microwave technology. Reference 56 as a good source of the latest developments in cryocooler technology. Figure 16 is a photograph of a commercial HTS filter subsys­tem, showing the cryocooler and associated electronics in their open package.


High-temperature superconductor microwave technology of­fers unique advantages derived from the low microwave loss of HTS materials and the inherent low thermal noise in cryo – genically cooled components. The main applications to date are related to increased microwave receiver sensitivity, and this is most likely to have an impact on wireless military and commercial communications systems. The reason is that re­ceiver sensitivity and dynamic range must be preserved in the presence of a large number of spurious signals which, if unfiltered, degrade receiver performance. Generation of clean transmitted signals requires filtering in the transmitter and this, coupled with the need to reject unwanted high-power signals at the receiver, has spurred work on high-power han­dling in HTS filters. Great interest in the United States and abroad exists in the wireless commercial communications market and several companies are testing base-station re­ceiver front-ends consisting of cryogenically-cooled filter-LNA subassemblies.

HTS microwave filters are therefore a promising technol­ogy, especially at frequencies below 3 GHz where the loss in conventional microwave materials force high-performance filters to be very large in order to achieve the required low insertion losses and selectivity. Leveraging developments in infrared imaging detector technology and perhaps new devel­opments of cooled semiconductor components for fast com­puter workstations, cryocooler technology is progressing to the point where long lifetimes and small-size, low-weight cool­ers are now widely available.

FitzHugh-Nagumo Oscillator

By simplifying the classical Hodgkin-Huxley equations [5] for modeling nerve membranes and action potential gener­ation, FitzHugh [7] and Nagumo et al. [8] gave the follow­ing two-variable equation, widely known as the FitzHugh – Nagumo model,


x — c[y — f (x) + I ]


y — —(x + by — a)/c

where f(x) is as defined in Eq. (2), I is the injected current, and a, b, and c are system parameters satisfying the condi­tions: 1 > b > 0, c2 > b, and 1 > a > 1 — 2b/3. In neurophys – iological terms, x corresponds to the neuronal membrane potential, and y plays the aggregate role of three variables in the Hodgkin-Huxley equations. Given that the x null­cline is a cubic and the y nullcline is linear, the FitzHugh – Nagumo equation is mathematically similar to the van der Pol equation. Typical relaxation oscillation with two time scales occurs when c > 1. Because of the three parameters and the external input I, the FitzHugh-Nagumo oscillator has additional flexibility. Depending on parameter values, the oscillator can exhibit a stable steady state or a stable periodic orbit. With a perturbation by external stimulation, the steady state can become unstable and be replaced by an oscillation; the steady state is thus referred to as the excitable state.

Morris-Lecar Oscillator

In modeling voltage oscillations in barnacle muscle fibers, Morris and Lecar [9] proposed the following equation,


x — —gCam<x (x)(x — 1) — gKy(x — xk) — gL(x — xl ) + I (4)

y — – s[y^ (x) — y]/ty (x) (4)


m^ (x) — {1 + tanh[(x — x1)/x2]}/2

y^ (x) — {1 + tanh[(x — x3)/x4]}/2

Ty (x) — 1/cosh[(x — x3)/(2×4)]

and xi x2, x3, x4, gCa, gK, gL, xK, and xL are parameters. Ca stands for calcium, K for potassium, L for leak, and I is the injected current. The parameter є controls relative time scales of x and y. Like Eq. (3), the Morris-Lecar oscillator is closely related to the Hodgkin-Huxley equations, and it is used as a two-variable description of neuronal membrane properties or the envelope of an oscillating burst [10]. The x variable corresponds to the membrane potential, and y corresponds to the state of activation of ionic channels.

The x nullcline of Eq. (4) resembles a cubic and the y nullcline is a sigmoid. When є is chosen to be small, the Morris-Lecar equation produces typical relaxation oscilla­tions. From the mathematical point of view, the sigmoidal y nullcline marks the major difference between the Morris – Lecar oscillator and the FitzHugh-Nagumo oscillator.

Mathematical Model for Rayleigh Fading

In Fig. 8, the X-Y plane is assumed to be the horizontal ground plane. Consider a mobile receiver moving with veloc­ity v along the X-axis. The model (1) is that the signal re­ceived consists of a number of horizontally traveling plane waves each with random amplitude (but equal on average) and random angle of arrival. The phases of the waves are uniformly distributed in [0, 2w] and are assumed to be statis­tically independent of the amplitudes.

Let the angle of the nth incoming wave be an w. r.t. the X – axis. We assume a fixed transmitter with a vertically polar­ized antenna and a mobile receiver with a whip/monopole an­tenna. The vehicular motion introduces a Doppler shift given by


Work on superconducting delay lines started at Lincoln Labo­ratory well before the advent of high-temperature supercon­ductivity, and concentrated mostly on linearly dispersive de­lay lines for analog signal processing. Linearly dispersive delay lines have delay characteristics which vary linearly with frequency over a certain operating bandwidth and can be used to perform pulse compression, a technique to process and detect small signals which may be below the receiver noise floor (1). The pioneering work at Lincoln Laboratory in this area using LTS and, more recently, HTS thin-film tech­nologies has been extensively documented in the literature (1,51).

Table 4. Sample System Requirements That Will Affect the Choice of Cooler and Cryogenic Packaging Approach



Size and weight Cool-down time


Power consumption and power supply type Mode of operation Temperature stability and control Unattended lifetime Vacuum lifetime

Stringent in almost all applications

Some applications may require very fast turn-on time (e. g., a few minutes). They would be a driver to­ward higher cooler power and lower HTS device thermal mass For example, a minute amount of mechanical distortion on a circuit caused by vibration from the cooler may generate a phase modulation that degrades the circuit performance E. g., 120 V ac

E. g., continuous, intermittent, short missions and then mostly idle, etc.

While any fine temperature feedback control loop (<±0.01 K) tends to be done using heaters and a tem­perature sensor, some applications may require a certain degree of cooling engine control (<±0.5 K) Some applications (e. g., space) may require a lifetime on the order of 10 years or more All-welded construction; use of getters in a clean, well-conditioned (baked) system

SUPERCONDUCTING FILTERS AND PASSIVE COMPONENTS 727 Table 5. Cooling Requirements That Will Influence the Cooling Power (Heat Lift) Required for a Given Application

Power dissipated in the device

Number of microwave and dc control leads

Surface area

Thermal mass

A filter with a 0.5 dB insertion loss that must pass a 20 W signal will dissipate 2 W of heat that must be re­moved by the cryocooler. Also, semiconductor devices such as low-noise amplifiers, which improve in noise and gain performance when cooled, always dissipate a certain amount of heat which must be taken into consideration

These are the electrical interface between the cryocooled device and the outside world. For example, a filter might require two microwave leads (input and output) and two pairs of dc control lines for the heat sensor and a small heater to keep the temperature constant. These conductors represent a heat loss that the cooler must overcome because they connect the outside ambient temperature with the cold device. While the dc control lines are typically made of thin low-thermal-conductivity, high-resistivity wire (e. g., gauge 32 manganin), the microwave leads must achieve a compromise between insertion and thermal loss Radiation loss is another form of heat loss that the cooler must overcome and therefore must be minimized. The total surface area and their infrared radiation emmisivity are important design parameters. Low-em – misivity radiation shields are typically used between the warm vacuum vessel wall and the cold device For those applications that have a cool-down time requirement, the thermal mass of the device to be cooled is important and will be affected by the microwave packaging material and its shape

Table 6. Some Cryogenic Refrigerator Types Likely to Be Used in HTS Technology

Cooler Type

Heat-Lift Range Available at 80 K


Split Stirling

0.5-3 W

Available from many manufacturers; used primarily in the tactical military infrared detector in­dustry. Has a cold head separated from a compressor by a metallic transfer line up to 15 cm long

Integral Stirling

0.5-5 W

Also used in infrared detectors; at least one version is being used in an HTS development proto­type. The compressor and cold finger are integrated into one unit


2->200 W

Widely used in the support of vacuum systems for semiconductor industry; highly reliable and versatile. The compressor and cold head are separate units connected by fluid lines that can be several meters long


~4 W

Reliable and low cost. The compressor and cold head are separate units connected by fluid lines that can be several meters long


0.5-2 W

Generally used as an open-cycle cooling system for short tactical missile IR detector applica­tions

Pulse tube

0.5-2 W

Emerging technology, low cold-head vibration and long lifetime potential

Nondispersive delay lines have a constant delay-versus – frequency characteristic and are typically used as analog memory elements that can store a signal for, say, up to a few hundred nanoseconds while the system is engaged in other processing steps. Work on HTS nondispersive delay lines has also been significant (52-55). Including two recent instanta­neous frequency measurement subsystems based on banks of delay lines (52,55). Clearly, the advantages of superconductiv­ity are that a long length of line can be fabricated in a small volume by defining a long, planar transmission line on a wa­fer. Ref. 54 compares conventional nondispersive delay lines, which require amplifiers between sections of transmission line (e. g., coaxial), with HTS delay lines using projections based on measurements made on relatively short (22 ns) de­lay lines. Key delay-line parameters are delay, bandwidth, in­sertion loss, and third-order intercept point. Conventional de­lay lines that must resort to amplification to boost the signal are limited in dynamic range by the amplifiers.


We begin our technical discussion by describing the sub­systems that make up a missile system. In addition to a warhead, a missile contains several key supporting sub­systems. These subsystems may include 1) a target-sensing system, 2) a missile-navigation system, 3) a guidance sys­tem, 4) an autopilot or control system, and 5) the physical missile (including airframe and actuation subsystem); see Fig. 1.

Target-Sensing System

The target-sensing system provides target “information” to the missile guidance system, e. g. relative position, velocity, line-of-sight angle, and rate. Target-sensing systems may be based on several sensors, e. g., radar, laser, heat, acoustic, or optical sensors. Optical sensors, for example, may be as simple as a camera for a weapon systems officer (WSO) to visualize the target from a remote location. They may be a sophisticated imaging system (see below). For some applications, target coordinates are known a priori (e. g., via satellite or other intelligence) and a target sensor becomes irrelevant.

Navigation System

A navigation system provides information to the mis­sile guidance system about the missile position in space relative to some inertial frame of reference, e. g., flat – Earth constant-gravity model for short-range flights and rotating-Earth variable-gravity model for long-range flights. To do so, it may use information obtained from a variety of sensors, which may include simple sensors such as accelerometers or a radar altimeter. It may include more sophisticated sensors such as a global positioning system (GPS) receiver or an optical terrain sensor that relies on comparisons between an image of the terrain below with a stored image and a stored desired trajectory. Optical stellar sensors rely on comparisons between an image of the stars above with a stored image and a stored desired trajectory.

Guidance System

Target and missile information are used by the guidance system to compute updated guidance commands, which when issued to the missile autopilot should ideally guide (or steer) the missile toward the target (4, 5). When target coordinates are known a priori, missile coordinates pro­vided by the navigation system (e. g., GPS-based) are pe­riodically compared with the (pre-programmed) target co­ordinates to compute appropriate guidance corrections. In general, the quality of the computed guidance commands depends on the quality of the gathered sensor data and the fidelity of the mathematical models used for the missile and target. Targets may be stationary, mobile, or highly maneu­verable (e. g., silo, ship, fighter aircraft). Physically, guid­ance commands may represent quantities such as desired thrust, desired (pitch/yaw) acceleration, desired speed, de­sired flight path or roll angle, and desired altitude. Guid­ance commands issued by the guidance system to the mis­sile autopilot are analogous to the speed commands is­sued by automobile drivers to the cruise control systems in their cars. In this sense, the missile guidance system is like the automobile driver and the missile autopilot is like the automobile cruise control system. Missile guidance commands are computed in accordance with a guidance al­gorithm. Guidance algorithms and navigational aids will be discussed below.


The primary function of the autopilot—sometimes referred to as the flight control system (FCS) or attitude control sys­tem (ACS)—is to ensure 1) missile attitude stability and 2) that commands issued by the guidance system are fol­lowed as closely as possible (4). The autopilot accomplishes this command-following objective by computing and issu­ing appropriate control commands to the missile’s actu­ators. These actuators may include, for example, rocket thrusters, ramjets, scramjets (for hypersonic missiles), or servomotors that move aerodynamic control surfaces. More specifically, the autopilot compares commands issued by the guidance system with real-time measurements (e. g., acceleration, attitude and attitude rate, and altitude) ob­tained from onboard sensors (e. g., accelerometers, gyro­scopes, and radar altimeters) and/or external tracking sys­tems. This comparison, essentially a subtraction of signals, produces a feedback error signal, which is then used to compute control commands for the missile actuators. This computation, the purpose of the autopilot, maybe based on a and is based on the autopilot design and hence its com­plexity. Autopilot design, however, is based on a very com­plex mathematical model that captures the following dy­namical features: missile airframe, aerodynamics (depend­ing on speed, dynamic pressure, angle-of-attack, slide-slip angle, etc.), actuators, sensors, flexible modes, and uncer­tainty descriptions, e. g., dynamic uncertainty, parametric uncertainty (6, 7), and disturbance/noise bounds. It should be noted that commands that are issued by the guidance system to the autopilot cannot always be followed exactly because of the presence of multiple sources of uncertainty. Sources of uncertainty may include disturbances acting on the missile, sensor noise, unmodeled or uncertain missile airframe, actuator, and sensor dynamics.

Flight Phases

The flight of a missile can be broken into three phases: 1) a launch, separation, or boost phase; 2) a mid-course or cruise phase; and 3) an endgame or terminal phase. During each phase, a missile may use distinct guidance, navigation, and control systems, specifically designed to accommodate the requirements during that phase of the flight. During each phase, the missile may very well use different sets of sen­sors, actuators, and power sources.

Guidance System Performance Terminology

To describe the function and performance ofa guidance sys­tem, some terminology is essential. The imaginary line that connects a missile center-of-gravity (cg) to the target cg is referred to as the line-of-sight (8). The length of this line is called the range. The associated vector from missile to tar­get is referred to as the range vector. The time derivative of the range vector is called the closing velocity. The most im­portant measure of performance for any missile guidance system is the so-called miss distance. Miss distance is de­fined to be the missile-target range at that instant when the two are closest to one another (8). The objective ofmost guidance systems is to minimize the miss distance within an allotted time period. For some applications (hit-to-kill), zero miss distance is essential. For some applications (e. g., to minimize collateral damage), it is essential to impact the target at a specific angle. Because miss distance is sensi­tive to many variables and small variations from missile to missile, other quantities are used to measure performance. One of the most common measures used is circular error probability (cep). The cep for a missile attempts to provide an average miss distance for a class of missile-target en­gagements (i. e., Monte Carlo runs). If a missile has a cep of 10 m, then most of the time, say, 68% of the time, it will detonate within 10 m of the target.