Patch Antenna Input Impedance Formula
To go to our main antenna page to go to our main microstrip page The microstrip antenna was first proposed by G.A. Deschamps in 1953, but didn't become practical until the 1970s when it was developed further by researchers such as Robert E. Munson (now in our ) and others using low-loss soft substrate materials that were just becoming available. Also referred to as microstrip antenna, or abbreviated MSA. For now we will only be discussing rectangular, single-polarization microstrip antennas, there are many other variations, enough to fill a book.
A good volume on this subject is Broadband Microstrip Antennas, by Kumar and Ray. Go to our and we'll help you order it from Amazon!
Transmission Line
The Basics of Patch Antennas. • Patch (impedance) width. A patch antenna radiates power in certain directions and we say that the antenna has. I have gone through many threads in the forum about finding the input impedance of patch antenna, however all the replies can't catch my mind. Some thread say used Z.
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Advantages of microstrip antennas include:. Low cost to fabricate. Conformal structures are possible (it's easy to form curved surfaces, as long as the curve is in one direction only). Easy to form a large array, spaced at half-wavelength or less. Light weight Disadvantages include:. Limited bandwidth (usually 1 to 5%, but much more is possible with increased complexity.
Patch Antenna Input Impedance
Low power handling The size of a microstrip antenna is inversely proportional to its frequency. At frequencies lower than microwave, microstrip patches don't make sense because of the sizes required.
At X-band a microstrip antenna is on the order of 1 centimeter long (easy to realize on soft-board technology). If you wanted to make a microstrip antenna to receive FM radio at 100 MHz it would be on the order of 1 meter long (which is a very large circuit for any type of substrate!) For AM radio at 1000 KHz, the microstrip patch would be the size of a football field, utterly impractical. One everyday application where microstrip patches are used is in satellite radio receivers (XM and Sirius). Here the antenna is often mounted in a vehicle, where the angle in the X-Y plane relative to the satellite is not fixed (like it is for the satellite television dish mounted to your house.) Thus circular polarization is employed for satellite radio, and the angle that the patch is with respect to the satellite doesn't matter. Rectangular, single polarization microstrip antennas This is by far the most popular type of MSA. The figure below shows the geometry of the rectangular microstrip antenna, not including the ground plane and dielectric which would be underneath. The dimension L is universally taken to mean the long dimension, which causes resonance at its half-wavelength frequency.
The radiating edges are at the ends of the L-dimension of the rectangle, which sets up the single polarization. Radiation that occurs at the ends of the W-dimension is far less and is referred to as the cross-polarization. The image below is a side view which attempts to show a snapshot of the E-field under the patch.
Note that the fields under the L-edges are of opposite polarity (due to the half-wave nature of the patch) and when the field lines curve out and finally propagate out into the direction normal to the substrate they are now in the same direction (both facing left). In the far field perpendicular to the substrate, the radiation from the two sides adds up because the fields are in phase and voila you have a an antenna! As you look out in directions off of boresight, the intensity drops off as the fields of the two edges become farther and farther out of phase. At two angles the fields exactly cancel.
(We'll explain that more later). Thus the microstrip patch radiation intensity depends on what direction you are facing it from (it has gain and directivity).
For a microstrip antenna to work, you want to think the opposite thoughts that you might want to think if you were designing a microstrip MMIC. You want the thing to radiate! The path toward this is threefold. First, the structure needs to be a half-wavelength resonator. Second, use a low dielectric constant under the patch. Third, use a thicker dielectric than you normally would, but keep in mind the height must still be just a fraction of a wavelength. To use an audio analogy, a glockenspiel uses half-wavelength resonators suspended at nodes placed a apart.
Like the microstrip antenna, the width of the keys are significantly less than their length. The primary mode is a resonance along L, but by forcing W to be 1/4 L, if any mode is excited in the W direction it is harmonically related and it doesn't hurt your ears!
The image below is a depiction of the relative intensity (and direction) of the E and H-fields along the L-dimension, ignoring the radiation that occurs at the edges. The magnetic field is perpendicular to the E-field according to (it is in and out of your monitor).
At the edge of the strip (X/L=0 and X/L=1) the H-field drops to zero, because there is no conductor to carry the RF current, it is maximum in the center. The E-field intensity is at maximum magnitude (and opposite polarity) at the edges (X/L=0 and X/L=1) and zero at the center.
The ratio of E to H field is proportional to the impedance that you see when you feed the patch. If you adjust the location of the feed point between the center and the edge, you can get any impedance you'd like, including fifty ohms! Perhaps another intuitive way to look at the input impedance to a microstrip patch is to think about how far you are from an open circuit.
If you feed it at the center, you are looking at a short circuit in both directions, because you are a quarter-wave from an open circuit. If you feed it at the edge you see an open circuit, because you are a half-wave from another open. The image below shows two ways to feed the microstrip patch, on the left is a microstrip feed and on the right is a coax feed. What dielectric constant defines the half wavelength? The dielectric constant that controls the resonance of the antenna is the effective dielectric constant of the microstrip line. You can use our to come up with the value! What is the best choice for the dimension W?
The dimension helps maximize efficiency. You need to pick W so that: W=c/(2F0xSQRT(ER+1)/2))) In other words, use the average of the value for ER of the substrate and ER of air(=1) to obtain a half-wavelength. What controls the bandwidth? Bandwidth is proportional to h/SQRT(ER) More to come!
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Low-profile, low-cost antennas support the operation of many modern communication systems. Microstrip patch antennas represent one family of compact antennas that offers the benefits of a conformal nature and the capability of ready integration with a communication system's printed circuitry. By using a straightforward transmission-line model, it is possible to accurately model and analyze microstrip-line inset-fed patch antenna designs. In addition, by applying a curve-fit formula, it is possible to locate the exact inset length needed for a 50-Ω input impedance. The feed mechanism plays an important role in the design of microstrip patch antennas. A microstrip patch antenna can be fed either by coaxial probe or by an inset microstrip line.
Coaxial probe feeding is sometimes advantageous for applications like active antennas, while microstrip line feeding is suitable for developing high-gain microstrip array antennas. In both cases, the probe position or the inset length determines the input impedance.
The input impedance behavior for a coaxial probe-fed patch antenna has been studied analytically by means of various models, including the transmission-line model and the cavity model, and by means of full-wave analysis. 1-3 Experimentally and theoretically, it has been found that a coaxial-probe fed-patch antenna's input impedance exhibits behavior that follows the trigonometric function: cos 20/L) where: L = the length of the patch and y 0 = the position of the feed from the edge along the direction of the patch length L. On the other hand, it has been found experimentally 4 that on low-dielectric-constant materials, the input impedance of an inset-fed probe antenna exhibits fourth-order behavior following the function: cos 40/L) Fortunately, a simple analytical approach has been developed using the transmission-line model to find the input impedance of an inset-fed microstrip patch antenna.
Using this approach, a curve-fit formula can be derived to find the inset length to achieve a 50-Ω input impedance when using modern thin dielectric circuit-board materials. Is a graphical depiction of an inset-fed microstrip patch antenna. The parameters ε r, h, L, W, w f, and y 0, respectively, are used to denote substrate dielectric constant, thickness, patch length, patch width, feed-line width, and feed-line inset distance. The input impedance of an inset-fed microstrip patch antenna depends mainly on the inset distance, y 0, and to some extent on the inset width (the spacing between the feed line and the patch conductor).
Variations in the inset length do not produce any change in resonant frequency, but a variation in the inset width will result in a change in resonant frequency. Hence, in the following discussion, the spacing between the patch conductor and feed line is kept constant, equal to the feed line's width; variations in the input impedance at resonant frequency with respect to inset length will studied as a function of various parameters. Assuming the patch antenna is divided into four regions, it can be modeled as a series of transmission lines loaded by radiating slots of different length. Lists the parameters (width and length) of the three transmission lines as well as the width and lengths of the three radiating slots.
Radiating slots A, B, and C can be modeled according to the guidelines presented in ref. Following the strategy outlined earlier, a patch antenna with the parameters ε r = 2.42, h = 0.127 cm, W = 5.94 cm, L = 4.04 cm, and y 0 = 0.99 cm was analyzed. Shows a comparison between the results obtained using the transmission-line-model method presented here and data obtained using a commercial computer-aided-engineering (CAE) electromagnetic (EM) simulator. Even though there is a shift in the resonant frequency, the transmission-line model tracks the return loss profile predicted by the EM simulator very closely. The small shift in the resonant frequency can be attributed to a failure to consider the discontinuity between the inset feed line and the patch.
The transmission-line model was used to perform parametric studies of the patch for various values of ε r (2 ≤ ε r ≤ 10). Shows that a rectangular microstrip patch antenna fed by a microstrip line at the edge (y 0 = 0) will have a higher input resistance varying from approximately 150 to 450 Ω for varying ε r.
Also, it was observed that the input impedance falls rapidly as the inset position is moved from the edge of the patch toward the center compared to the coaxially probe fed patch antennas. These parametric studies have been used to derive the curve-fit formula (Eq. 1) to find the exact inset length to achieve 50-Ω input impedance for commonly used thin dielectric substrates: The accuracy of this formula has been checked for a patch with ε r = 5.0, h = 0.127 cm, W = 4.1325 cm, L = 2.8106 cm, and y 0 = 0.9009 cm. To confirm the validity of the formula, the patch was analyzed using an EM simulator; offers a comparison between results generated by the transmission-line model and predictions from the EM simulation. Even though there is a one-percent shift in the resonant frequency between the two sets of data, close agreement is apparent between the return-loss profiles predicted by the two approaches. ACKNOWLEDGMENTS The authors greatly appreciate the comments of Motorola iDEN group members.
REFERENCES. K.A. Carver and J.A. Mink, 'Microstrip antenna technology,' IEEE Transactions on Antennas & Propagation, Vol. 29, January 1981, pp. What is an.ngc file.
Van De Capelle, 'Accurate transmission line model for the rectangular microstrip antenna,' IEEE Proceedings on Microwaves, Optics & Antennas, Vol. 134, 1984, pp. Pozar, 'Input impedance and mutual coupling of rectangular microstrip antennas,' IEEE Transactions on Antennas & Propagation, Vol. AP-30, November 1982, pp. Basilio, Michael A.Khayat, Jeffery Williams, and Stuart A. Long, 'The Dependence of the Input Impedance on Feed Position of Probe and Microstrip Line − Fed patch Antennas,' IEEE Transactions on Antennas & Propagation, Vol. 49, January 2001, pp.
Schaubert, Frederick G. Farrar, Arthur Sindoris, and Scott T.
Hayes, 'Microstrip antennas with frequency agility and polarization diversity,' IEEE Transactions on Antennas & Propagation, Vol. 29, January 1981, pp.