Microstrip

Last updated
Cross-section of microstrip geometry. Conductor (A) is separated from ground plane (D) by dielectric substrate (C). Upper dielectric (B) is typically air. Microstrip geometry.svg
Cross-section of microstrip geometry. Conductor (A) is separated from ground plane (D) by dielectric substrate (C). Upper dielectric (B) is typically air.

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.

Contents

Typical realisation technologies are printed circuit board (PCB), alumina coated with a dielectric layer or sometimes silicon or some other similar technologies. Microwave components such as antennas, couplers, filters, power dividers etc. can be formed from microstrip, with the entire device existing as the pattern of metallization on the substrate. Microstrip is thus much less expensive than traditional waveguide technology, as well as being far lighter and more compact. Microstrip was developed by ITT laboratories as a competitor to stripline (first published by Grieg and Engelmann in the December 1952 IRE proceedings [1] ).

The disadvantages of microstrip compared with waveguide are the generally lower power handling capacity, and higher losses. Also, unlike waveguide, microstrip is typically not enclosed, and is therefore susceptible to cross-talk and unintentional radiation.

For lowest cost, microstrip devices may be built on an ordinary FR-4 (standard PCB) substrate. However it is often found that the dielectric losses in FR4 are too high at microwave frequencies, and that the dielectric constant is not sufficiently tightly controlled. For these reasons, an alumina substrate is commonly used. From monolithic integration perspective microstrips with integrated circuit/monolithic microwave integrated circuit technologies might be feasible however their performance might be limited by the dielectric layer(s) and conductor thickness available.

Microstrip lines are also used in high-speed digital PCB designs, where signals need to be routed from one part of the assembly to another with minimal distortion, and avoiding high cross-talk and radiation.

Microstrip is one of many forms of planar transmission line, others include stripline and coplanar waveguide, and it is possible to integrate all of these on the same substrate.

A differential microstrip—a balanced signal pair of microstrip lines—is often used for high-speed signals such as DDR2 SDRAM clocks, USB Hi-Speed data lines, PCI Express data lines, LVDS data lines, etc., often all on the same PCB. [2] [3] [4] Most PCB design tools support such differential pairs. [5] [6]

Inhomogeneity

The electromagnetic wave carried by a microstrip line exists partly in the dielectric substrate, and partly in the air above it. In general, the dielectric constant of the substrate will be different (and greater) than that of the air, so that the wave is travelling in an inhomogeneous medium. In consequence, the propagation velocity is somewhere between the speed of radio waves in the substrate, and the speed of radio waves in air. This behaviour is commonly described by stating the effective dielectric constant of the microstrip; this being the dielectric constant of an equivalent homogeneous medium (i.e., one resulting in the same propagation velocity).

Further consequences of an inhomogeneous medium include:

Characteristic impedance

A closed-form approximate expression for the quasi-static characteristic impedance of a microstrip line was developed by Wheeler: [12] [13] [14]

where weff is the effective width, which is the actual width of the strip, plus a correction to account for the non-zero thickness of the metallization:

Here Z0 is the impedance of free space, εr is the relative permittivity of substrate, w is the width of the strip, h is the thickness ("height") of substrate, and t is the thickness of the strip metallization.

This formula is asymptotic to an exact solution in three different cases:

  1. wh, any εr (parallel plate transmission line),
  2. wh, εr = 1 (wire above a ground-plane), and
  3. wh, εr ≫ 1.

It is claimed that for most other cases, the error in impedance is less than 1%, and is always less than 2%. [14] By covering all aspect-ratios in one formula, Wheeler 1977 improves on Wheeler 1965 [13] which gives one formula for w/h > 3.3 and another for w/h ≤ 3.3 (thus introducing a discontinuity in the result at w/h = 3.3).

Curiously, Harold Wheeler disliked both the terms 'microstrip' and 'characteristic impedance', and avoided using them in his papers.

A number of other approximate formulae for the characteristic impedance have been advanced by other authors. However, most of these are applicable to only a limited range of aspect-ratios, or else cover the entire range piecewise.

In particular, the set of equations proposed by Hammerstad, [15] who modifies on Wheeler, [12] [13] are perhaps the most often cited:

where εeff is the effective dielectric constant, approximated as:

Bends

In order to build a complete circuit in microstrip, it is often necessary for the path of a strip to turn through a large angle. An abrupt 90° bend in a microstrip will cause a significant portion of the signal on the strip to be reflected back towards its source, with only part of the signal transmitted on around the bend. One means of effecting a low-reflection bend, is to curve the path of the strip in an arc of radius at least 3 times the strip-width. [16] However, a far more common technique, and one which consumes a smaller area of substrate, is to use a mitred bend.

Microstrip 90deg mitred bend. The percentage mitre is 100x/d. Microstrip-bend.svg
Microstrip 90° mitred bend. The percentage mitre is 100x/d.

To a first approximation, an abrupt un-mitred bend behaves as a shunt capacitance placed between the ground plane and the bend in the strip. Mitring the bend reduces the area of metallization, and so removes the excess capacitance. The percentage mitre is the cut-away fraction of the diagonal between the inner and outer corners of the un-mitred bend.

The optimum mitre for a wide range of microstrip geometries has been determined experimentally by Douville and James. [17] They find that a good fit for the optimum percentage mitre is given by

subject to w/h ≥ 0.25 and with the substrate dielectric constant εr ≤ 25. This formula is entirely independent of εr. The actual range of parameters for which Douville and James present evidence is 0.25 ≤ w/h ≤ 2.75 and 2.5 ≤ εr ≤ 25. They report a VSWR of better than 1.1 (i.e., a return loss better than 26 dB) for any percentage mitre within 4% (of the original d) of that given by the formula. At the minimum w/h of 0.25, the percentage mitre is 98.4%, so that the strip is very nearly cut through.

For both the curved and mitred bends, the electrical length is somewhat shorter than the physical path-length of the strip.

See also

Related Research Articles

<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.

<span class="mw-page-title-main">Waveguide</span> Structure that guides waves efficiently

A waveguide is a structure that guides waves by restricting the transmission of energy to one direction. Common types of waveguides include acoustic waveguides which direct sound, optical waveguides which direct light, and radio-frequency waveguides which direct electromagnetic waves other than light like radio waves.

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">Relative permittivity</span> Measure of the electric polarizability of a dielectric, compared with that of a vacuum

The relative permittivity is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulator measures the ability of the insulator to store electric energy in an electrical field.

<span class="mw-page-title-main">Permittivity</span> Measure of the electric polarizability of a dielectric

In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ε (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in response to an applied electric field than a material with low permittivity, thereby storing more energy in the material. In electrostatics, the permittivity plays an important role in determining the capacitance of a capacitor.

Vacuum permittivity, commonly denoted ε0, is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric constant, or the distributed capacitance of the vacuum. It is an ideal (baseline) physical constant. Its CODATA value is:

A dielectric resonator is a piece of dielectric material, usually ceramic, that is designed to function as a resonator for radio waves, generally in the microwave and millimeter wave bands. The microwaves are confined inside the resonator material by the abrupt change in permittivity at the surface, and bounce back and forth between the sides. At certain frequencies, the resonant frequencies, the microwaves form standing waves in the resonator, oscillating with large amplitudes. Dielectric resonators generally consist of a "puck" of ceramic that has a large dielectric constant and a low dissipation factor. The resonant frequency is determined by the overall physical dimensions of the resonator and the dielectric constant of the material.

<span class="mw-page-title-main">Stripline</span> Early electronic transmission line medium

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.

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">Metamaterial antenna</span>

Metamaterial antennas are a class of antennas which use metamaterials to increase performance of miniaturized antenna systems. Their purpose, as with any electromagnetic antenna, is to launch energy into free space. However, this class of antenna incorporates metamaterials, which are materials engineered with novel, often microscopic, structures to produce unusual physical properties. Antenna designs incorporating metamaterials can step-up the antenna's radiated power.

<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.

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">Coplanar waveguide</span> Type of planar transmission line

Coplanar waveguide is a type of electrical planar transmission line which can be fabricated using printed circuit board technology, and is used to convey microwave-frequency signals. On a smaller scale, coplanar waveguide transmission lines are also built into monolithic microwave integrated circuits.

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

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.

Spoof surface plasmons, also known as spoof surface plasmon polaritons and designer surface plasmons, are surface electromagnetic waves in microwave and terahertz regimes that propagate along planar interfaces with sign-changing permittivities. Spoof surface plasmons are a type of surface plasmon polariton, which ordinarily propagate along metal and dielectric interfaces in infrared and visible frequencies. Since surface plasmon polaritons cannot exist naturally in microwave and terahertz frequencies due to dispersion properties of metals, spoof surface plasmons necessitate the use of artificially-engineered metamaterials.

<span class="mw-page-title-main">Nicolson–Ross–Weir method</span>

Nicolson–Ross–Weir method is a measurement technique for determination of complex permittivities and permeabilities of material samples for microwave frequencies. The method is based on insertion of a material sample with a known thickness inside a waveguide, such as a coaxial cable or a rectangular waveguide, after which the dispersion data is extracted from the resulting scattering parameters. The method is named after A. M. Nicolson and G. F. Ross, and W. B. Weir, who developed the approach in 1970 and 1974, respectively.

References

  1. Grieg, D. D.; Engelmann, H. F. (Dec 1952). "Microstrip-A New Transmission Technique for the Klilomegacycle Range". Proceedings of the IRE. 40 (12): 1644–1650. doi:10.1109/JRPROC.1952.274144. ISSN   0096-8390.
  2. Olney, Barry. "Differential Pair Routing" (PDF). p. 51.
  3. Texas Instruments (2015). "High-Speed Interface Layout Guidelines" (PDF). p. 10. SPRAAR7E. When possible, route high-speed differential pair signals on the top or bottom layer of the PCB with an adjacent GND layer. TI does not recommend stripline routing of the high-speed differential signals.
  4. Intel (2000). "High Speed USB Platform Design Guidelines" (PDF). p. 7. Archived from the original (PDF) on 2018-08-26. Retrieved 2015-11-27.
  5. Silicon Labs. "USB Hardware Design Guide" (PDF). p. 9. AN0046.
  6. Kröger, Jens (2014). "Data Transmission at High Rates via Kapton Flexprints for the Mu3e Experiment" (PDF). pp. 19–21.
  7. 1 2 Denlinger, E. J. (January 1971). "A frequency dependent solution for microstrip transmission lines". IEEE Transactions on Microwave Theory and Techniques. MTT-19 (1): 30–39. Bibcode:1971ITMTT..19...30D. doi:10.1109/TMTT.1971.1127442.
  8. Pozar, David M. (2017). Microwave Engineering Addison–Wesley Publishing Company. ISBN   978-81-265-4190-4.
  9. Cory, H. (January 1981). "Dispersion characteristics of microstrip lines". IEEE Transactions on Microwave Theory and Techniques. MTT-29: 59–61.
  10. Bianco, B.; Panini, L.; Parodi, M.; Ridetlaj, S. (March 1978). "Some considerations about the frequency dependence of the characteristic impedance of uniform microstrips". IEEE Transactions on Microwave Theory and Techniques. MTT-26 (3): 182–185. Bibcode:1978ITMTT..26..182B. doi:10.1109/TMTT.1978.1129341.
  11. Oliner, Arthur A. (2006). "The evolution of electromagnetic waveguides". In Sarkar, Tapan K.; Mailloux, Robert J.; Oliner, Arthur A.; Salazar-Palma, Magdalena; Sengupta, Dipak L. (eds.). History of wireless. Wiley Series in Microwave and Optical Engineering. Vol. 177. John Wiley and Sons. p. 559. ISBN   978-0-471-71814-7.
  12. 1 2 Wheeler, H. A. (May 1964). "Transmission-line properties of parallel wide strips by a conformal-mapping approximation". IEEE Transactions on Microwave Theory and Techniques. MTT-12 (3): 280–289. Bibcode:1964ITMTT..12..280W. doi:10.1109/TMTT.1964.1125810.
  13. 1 2 3 Wheeler, H. A. (March 1965). "Transmission-line properties of parallel strips separated by a dielectric sheet". IEEE Transactions on Microwave Theory and Techniques. MTT-13 (2): 172–185. Bibcode:1965ITMTT..13..172W. doi:10.1109/TMTT.1965.1125962.
  14. 1 2 Wheeler, H. A. (August 1977). "Transmission-line properties of a strip on a dielectric sheet on a plane". IEEE Transactions on Microwave Theory and Techniques. MTT-25 (8): 631–647. Bibcode:1977ITMTT..25..631W. doi:10.1109/TMTT.1977.1129179.
  15. E. O. Hammerstad (1975). Equations for Microstrip Circuit Design. 1975 5th European Microwave Conference. pp. 268–272. doi:10.1109/EUMA.1975.332206.
  16. Lee, T. H. (2004). Planar Microwave Engineering. Cambridge University Press. pp. 173–174.
  17. Douville, R. J. P.; James, D. S. (March 1978). "Experimental study of symmetric microstrip bends and their compensation". IEEE Transactions on Microwave Theory and Techniques. MTT-26 (3): 175–182. Bibcode:1978ITMTT..26..175D. doi:10.1109/TMTT.1978.1129340.