Stripline

Last updated
Cross-section diagram of stripline geometry. Central conductor (A) is sandwiched between ground planes (B and D). Structure is supported by dielectric (C). Stripline geometry.svg
Cross-section diagram of stripline geometry. Central conductor (A) is sandwiched between ground planes (B and D). Structure is supported by dielectric (C).

In electronics, stripline is a transverse electromagnetic (TEM) transmission line medium invented by Robert M. Barrett of the Air Force Cambridge Research Centre in the 1950s. Stripline is the earliest form of planar transmission line.

Contents

Description

A stripline circuit uses a flat strip of metal which is sandwiched between two parallel ground planes. The insulating material of the substrate forms a dielectric. The width of the strip, the thickness of the substrate and the relative permittivity of the substrate determine the characteristic impedance of the strip which is a transmission line. As shown in the diagram, the central conductor need not be equally spaced between the ground planes. In the general case, the dielectric material may be different above and below the central conductor. A stripline that uses air as the dielectric material is known as an air stripline.

To prevent the propagation of unwanted modes, the two ground planes must be shorted together. This is commonly achieved by a row of vias running parallel to the strip on each side.

Like coaxial cable, stripline is non-dispersive, and has no cutoff frequency. Good isolation between adjacent traces can be achieved more easily than with microstrip. Stripline provides for enhanced noise immunity against the propagation of radiated RF emissions, at the expense of slower propagation speeds when compared to microstrip lines. The effective permittivity of striplines equals the relative permittivity of the dielectric substrate because of wave propagation only in the substrate. Hence striplines have higher effective permittivity in comparison to microstrip lines, which in turn reduces wave propagation speed (see also velocity factor) according to

History

Stripline, now used as a generic term, was originally a proprietary brand of Airborne Instruments Laboratory Inc. (AIL). The version as produced by AIL was essentially air insulated (air stripline) with just a thin layer of dielectric material - just enough to support the conducting strip. The conductor was printed on both sides of the dielectric. The more familiar version with the space between the two plates completely filled with dielectric was originally produced by Sanders Associates who marketed it under the brand name of triplate. [1]

Stripline was initially preferred to its rival, microstrip, made by ITT. Transmission in stripline is purely TEM mode and consequently there is no dispersion (provided that the dielectric of substrate is not itself dispersive). Also, discontinuity elements on the line (gaps, stubs, posts etc) present a purely reactive impedance. This is not the case with microstrip; the differing dielectrics above and below the strip result in longitudinal non-TEM components to the wave. This results in dispersion and discontinuity elements have a resistive component causing them to radiate. In the 1950s Eugene Fubini, at the time working for AIL, jokingly suggested that a microstrip dipole would make a good antenna. This was intended to highlight the drawbacks of microstrip, but the microstrip patch antenna has become the most popular design of antenna in mobile devices. [2] Stripline remained in the ascendent for its performance advantages through the 1950s and 1960s but eventually microstrip won out, especially in mass produced items, because it was easier to assemble and the lack of an upper dielectric meant that components were easier to access and adjust. As the complexity of printed circuits increased, this convenience issue became more important until today microstrip is the dominant planar technology. Miniaturisation also leads to favouring microstrip because its disadvantages are not so severe in a miniaturised circuit. However, stripline is still chosen where operation over a wide band is required. [3]

Comparison to microstrip

Microstrip is similar to stripline transmission line except that the microstrip is not sandwiched, it is on a surface layer, above a ground plane. Stripline is more expensive to fabricate than microstrip, and because of the second groundplane, the strip widths are much narrower for a given impedance and board thickness than for microstrip.

Characteristic Impedance

An accurate closed form equation for the characteristic impedance of a stripline with a thin centered conductor has been reported as [4]

Where:

Note that when the conductor thickness is small, T<<1 or t<<h, the equations simplify significantly.

Where:

The accuracy of the formula is claimed to be at least 1% for W/(H-T) > .05 and T< 0.025.


For thick conductors, Wheeler provides the following more accurate equations [5]

Where:

Where T and W are as defined the same as the above expression.

The accuracy is claimed to be at least 0.5% for C>0.25.

Non-centered conductor

For stripline conductors that are not centered, that is, the distance to the upper ground plane is not the same as to the lower ground plane, strategies exist to estimate the characteristic impedance in at least one of two ways.

Zo estimation using upper and lower capacitance

If the asymmetry of the conductor placement is not large, the lower and upper capacitance per unit length may be estimated for the upper ground plane and the lower ground plane using centered stripline equations and standard transmission line equations for homogeneous lines, , and where is the sped of light.

The of each stripline may be evaluated independently, and the results used to estimate the of the asymmetric stripline. Small errors are introduced in the estimation due to the slightly differing capacitance paths to the ground planes between the asymmetric case being estimated and the symmetric cases used to make the estimation, so only small asymmetric placement of the strip will be expected to produce an acceptable estimation for of the asymmetrically placed strip.

To summarize:

.

Where:

is the speed of light in a vacuum.

and are measured from center of the conductor to the lower and upper ground plane, respectively.

Co and Lo are the capacitance and inductance per unit length of the associated transmission line.

Zo estimation using microstrip metallic cover

If there is no dielectric in the asymmetric stripline, then the stripline looks like a microstrip with a dielectric of air, , inside a metallic enclosure. This permits the air characteristic impedance, , to be calculated using microstrip metallic enclosure equations. When is known, may be calculated using . The accuracy of this estimation is quantified and listed in the microstrip metallic enclosure equations.

See also

Related Research Articles

In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied by Giulio Fagnano and Leonhard Euler. Their name originates from their originally arising in connection with the problem of finding the arc length of an ellipse.

<span class="mw-page-title-main">Circulator</span> Electronic circuit in which a signal entering any port exits at the next port

In electrical engineering, a circulator is a passive, non-reciprocal three- or four-port device that only allows a microwave or radio-frequency (RF) signal to exit through the port directly after the one it entered. Optical circulators have similar behavior. Ports are where an external waveguide or transmission line, such as a microstrip line or a coaxial cable, connects to the device. For a three-port circulator, a signal applied to port 1 only comes out of port 2; a signal applied to port 2 only comes out of port 3; a signal applied to port 3 only comes out of port 1. An ideal three-port circulator thus has the following scattering matrix:

The propagation constant of a sinusoidal electromagnetic wave is a measure of the change undergone by the amplitude and phase of the wave as it propagates in a given direction. The quantity being measured can be the voltage, the current in a circuit, or a field vector such as electric field strength or flux density. The propagation constant itself measures the dimensionless change in magnitude or phase per unit length. In the context of two-port networks and their cascades, propagation constant measures the change undergone by the source quantity as it propagates from one port to the next.

<span class="mw-page-title-main">Transmission line</span> Cable or other structure for carrying radio waves

In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmission must be taken into account. This applies especially to radio-frequency engineering because the short wavelengths mean that wave phenomena arise over very short distances. However, the theory of transmission lines was historically developed to explain phenomena on very long telegraph lines, especially submarine telegraph cables.

The wave impedance of an electromagnetic wave is the ratio of the transverse components of the electric and magnetic fields. For a transverse-electric-magnetic (TEM) plane wave traveling through a homogeneous medium, the wave impedance is everywhere equal to the intrinsic impedance of the medium. In particular, for a plane wave travelling through empty space, the wave impedance is equal to the impedance of free space. The symbol Z is used to represent it and it is expressed in units of ohms. The symbol η (eta) may be used instead of Z for wave impedance to avoid confusion with electrical impedance.

<span class="mw-page-title-main">Coaxial cable</span> Electrical cable type with concentric inner conductor, insulator, and conducting shield

Coaxial cable, or coax, is a type of electrical cable consisting of an inner conductor surrounded by a concentric conducting shield, with the two separated by a dielectric ; many coaxial cables also have a protective outer sheath or jacket. The term coaxial refers to the inner conductor and the outer shield sharing a geometric axis.

<span class="mw-page-title-main">Poynting vector</span> Measure of directional electromagnetic energy flux

In physics, the Poynting vector represents the directional energy flux or power flow of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre (W/m2); kg/s3 in base SI units. It is named after its discoverer John Henry Poynting who first derived it in 1884. Nikolay Umov is also credited with formulating the concept. Oliver Heaviside also discovered it independently in the more general form that recognises the freedom of adding the curl of an arbitrary vector field to the definition. The Poynting vector is used throughout electromagnetics in conjunction with Poynting's theorem, the continuity equation expressing conservation of electromagnetic energy, to calculate the power flow in electromagnetic fields.

<span class="mw-page-title-main">Capacitance</span> Ability of a body to store an electrical charge

Capacitance is the capacity of a material object or device to store electric charge. It is measured by the charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related notions of capacitance: self capacitance and mutual capacitance. An object that can be electrically charged exhibits self capacitance, for which the electric potential is measured between the object and ground. Mutual capacitance is measured between two components, and is particularly important in the operation of the capacitor, an elementary linear electronic component designed to add capacitance to an electric circuit.

In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller than any relevant dimension of the body; so that its geometry and the constitutive properties of the material at each point of space can be assumed to be unchanged by the deformation.

<span class="mw-page-title-main">Twin-lead</span> Two-conductor flat cable used to carry radio frequency signals

Twin lead cable is a two-conductor flat cable used as a balanced transmission line to carry radio frequency (RF) signals. It is constructed of two, stranded copper wires, or solid copper-clad steel wires. The wires are held a fixed distance apart by a plastic ribbon that is a good insulator at radio frequencies. It is also called ribbon cable. The uniform spacing of the wires is the key to the cable's function as a transmission line: Any abrupt change in spacing would cause some of the signal to reflect back toward the source, rather than passing through. The plastic also covers and insulates the wires. The name twin lead is most often used to refer specifically to 300 Ω (Ohm) ribbon cable, the most common type, but on occasion, twin lead is used to refer to any type of parallel wire line. Parallel wire line is available with several different values of characteristic impedance such as twin lead ribbon cable (300 Ω), window line, and open wire line or ladder line (500~650 Ω).

Chebyshev filters are analog or digital filters that have a steeper roll-off than Butterworth filters, and have either passband ripple or stopband ripple. Chebyshev filters have the property that they minimize the error between the idealized and the actual filter characteristic over the operating frequency range of the filter, but they achieve this with ripples in the passband. This type of filter is named after Pafnuty Chebyshev because its mathematical characteristics are derived from Chebyshev polynomials. Type I Chebyshev filters are usually referred to as "Chebyshev filters", while type II filters are usually called "inverse Chebyshev filters". Because of the passband ripple inherent in Chebyshev filters, filters with a smoother response in the passband but a more irregular response in the stopband are preferred for certain applications.

<span class="mw-page-title-main">Microstrip</span> Conductor–ground plane electrical transmission line

Microstrip is a type of electrical transmission line which can be fabricated with any technology where a conductor is separated from a ground plane by a dielectric layer known as "substrate". Microstrip lines are used to convey microwave-frequency signals.

The method of image charges is a basic problem-solving tool in electrostatics. The name originates from the replacement of certain elements in the original layout with fictitious charges, which replicates the boundary conditions of the problem.

In electrical engineering, dielectric loss quantifies a dielectric material's inherent dissipation of electromagnetic energy. It can be parameterized in terms of either the loss angleδ or the corresponding loss tangenttan(δ). Both refer to the phasor in the complex plane whose real and imaginary parts are the resistive (lossy) component of an electromagnetic field and its reactive (lossless) counterpart.

<span class="mw-page-title-main">Substrate-integrated waveguide</span> Waveguide formed by posts inserted in a dielectric substrate

A substrate-integrated waveguide (SIW) is a synthetic rectangular electromagnetic waveguide formed in a dielectric substrate by densely arraying metallized posts or via holes that connect the upper and lower metal plates of the substrate. The waveguide can be easily fabricated with low-cost mass-production using through-hole techniques, where the post walls consists of via fences. SIW is known to have similar guided wave and mode characteristics to conventional rectangular waveguide with equivalent guide wavelength.

<span class="mw-page-title-main">Non-radiative dielectric waveguide</span>

The non-radiative dielectric (NRD) waveguide was introduced by Yoneyama in 1981. In Fig. 1 the crosses shown: it consists of a dielectric rectangular slab of height (a) and width (b), which is placed between two metallic parallel plates of a suitable width. The structure is practically the same as the H waveguide, proposed by Tischer in 1953. Due to the dielectric slab, the electromagnetic field is confined in the vicinity of the dielectric region, whereas in the outside region for suitable frequencies, the electromagnetic field decays exponentially. Therefore, if the metallic plates are sufficiently extended, the field is practically negligible at the end of the plates and therefore the situation does not greatly differ from the ideal case in which the plates are infinitely extended. The polarization of the electric field in the required mode is mainly parallel to the conductive walls. As it is known, if the electric field is parallel to the walls, the conduction losses decrease in the metallic walls at the increasing frequency, whereas, if the field is perpendicular to the walls, losses increase at the increasing frequency. Since the NRD waveguide has been devised for its implementation at millimeter waves, the selected polarization minimizes the ohmic losses in the metallic walls.

Circuit quantum electrodynamics provides a means of studying the fundamental interaction between light and matter. As in the field of cavity quantum electrodynamics, a single photon within a single mode cavity coherently couples to a quantum object (atom). In contrast to cavity QED, the photon is stored in a one-dimensional on-chip resonator and the quantum object is no natural atom but an artificial one. These artificial atoms usually are mesoscopic devices which exhibit an atom-like energy spectrum. The field of circuit QED is a prominent example for quantum information processing and a promising candidate for future quantum computation.

<span class="mw-page-title-main">Planar transmission line</span> Transmission lines with flat ribbon-like conducting or dielectric lines

Planar transmission lines are transmission lines with conductors, or in some cases dielectric (insulating) strips, that are flat, ribbon-shaped lines. They are used to interconnect components on printed circuits and integrated circuits working at microwave frequencies because the planar type fits in well with the manufacturing methods for these components. Transmission lines are more than simply interconnections. With simple interconnections, the propagation of the electromagnetic wave along the wire is fast enough to be considered instantaneous, and the voltages at each end of the wire can be considered identical. If the wire is longer than a large fraction of a wavelength, these assumptions are no longer true and transmission line theory must be used instead. With transmission lines, the geometry of the line is precisely controlled so that its electrical behaviour is highly predictable. At lower frequencies, these considerations are only necessary for the cables connecting different pieces of equipment, but at microwave frequencies the distance at which transmission line theory becomes necessary is measured in millimetres. Hence, transmission lines are needed within circuits.

<span class="mw-page-title-main">Wheeler incremental inductance rule</span> Rule of thumb for estimating skin effect resistance of parallel transmission lines

The incremental inductance rule, attributed to Harold Alden Wheeler by Gupta and others is a formula used to compute skin effect resistance and internal inductance in parallel transmission lines when the frequency is high enough that the skin effect is fully developed. Wheeler's concept is that the internal inductance of a conductor is the difference between the computed external inductance and the external inductance computed with all the conductive surfaces receded by one half of the skin depth.

<span class="mw-page-title-main">Loop-gap resonator</span> Type of electromagnetic resonator

A loop-gap resonator (LGR) is an electromagnetic resonator that operates in the radio and microwave frequency ranges. The simplest LGRs are made from a conducting tube with a narrow slit cut along its length. The LGR dimensions are typically much smaller than the free-space wavelength of the electromagnetic fields at the resonant frequency. Therefore, relatively compact LGRs can be designed to operate at frequencies that are too low to be accessed using, for example, cavity resonators. These structures can have very sharp resonances making them useful for electron spin resonance (ESR) experiments, and precision measurements of electromagnetic material properties.

References

  1. Oliner, pp.556-559
  2. Yarman, p. 67
  3. Oliner, pp. 558-562
  4. Steer, Michael (October 21, 2020). "3.7: Stripline - Engineering LibreTexts". Engineering LibreTexts.
  5. Rhea, Randall W. (1995). HF Filter Design and Computer Simulation. New York, NY, US: McGraw-Hill. pp. 106, 107. ISBN   0-07-052055-0.

Bibliography