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Figure 134 Proper way to work with bends in microstrip lines: (a)
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miter; (b) curve
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Microstrip transmission line design Use the following equation to plug in different microstrip widths to obtain the desired impedance:
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377 W 1 Er Er h characteristic impedance of the microstrip, ohms width of the microstrip conductor (use same units as h) thickness of the substrate between the ground plane and the microstrip conductor (use same units as W) dielectric constant of the board material Z0
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where Z0 W h Er
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133 Microstrip as equivalent components
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Distributed components such as inductors, transformers, and capacitors can be formed from microstrip transmission line sections on PCBs at microwave frequencies A series or shunt inductor can be formed from a thin trace (Fig 135), a shunt capacitor can be formed by a wide trace (Fig 136), and a transformer can be formed by varying the width of the microstrip (Fig 137)
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Distributed equivalent component design It is important to never make a dis-
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tributed component longer than 30 degrees out of the 360 degrees of an entire wavelength or the equivalent component effect will depart more and more from that of an ideal lumped component To calculate how long 30 degrees is out of 360 degrees, simply divide 30 by 360, then multiply this value by the actual wavelength of the signal on the PCB, keeping in mind that the signal s wavelength in the substrate will not be the same as if it were traveling through a vacuum To find the actual wavelength of the signal, which is being slowed down by the substrate material, calculate the microstrip s velocity of propagation (VP) First, find the effective dielectric constant (EEFF) of the microstrip, since, as
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Wireless Essentials
Wireless Essentials
Figure 135 A distributed inductor
Figure 136 A distributed capacitor
Figure 137 Using a distributed transformer for resistive matching
stated above, the signal will be partly in the dielectric and partly in the air above the microstrip, which will affect the propagation velocity through this combination of the two dielectric mediums: EEFF Er 2 1 Er 2 1 1 1 12h W
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where EEFF Er h W Then:
effective dielectric constant that the microstrip sees actual dielectric constant of the PCB s substrate material thickness of the substrate material between the top conductor and the bottom ground plane of the microstrip width of the top conductor of the microstrip
1 EEFF
where VP fraction of the speed of light compared to light in a vacuum Then calculate the wavelength of the signal of interest in a perfect vacuum: 11,800 f
where
11,800 f
wavelength of the frequency of interest (f) , mils, in a true vacuum speed of light value to obtain a VAC in mils while using an f in GHz frequency of the signal of interest, GHz
Then multiply the velocity of propagation (VP) times the wavelength ( VAC) of the signal as calculated above in order to arrive at the wavelength of the signal of interest ( ), in mils, when the signal is placed into the microstrip: VP
Distributed parallel (shunt) capacitor First, knowing the capacitance of the
desired component for your circuit, calculate the reactance of the shunt capacitor required, at the frequency of interest, by the common formula Xc 1 2 fC
Second, utilize 30-ohm microstrip (ZL 30 ohms) for the substrate s dielectric Find the microstrip width required for this 30-ohm value by using one of the many microstrip calculation programs available free on the Web (such as HP s AppCad, or AWR s TXLine, or Daniel Swanson s MWTLC), or use the formula above As shown in Fig 138, the microstrip of the equivalent shunt capacitor is open, and not grounded, at its end The capacitor section is also attached to the 50-ohm microstrip transmission line by a small tapered section to improve the transition A further improvement is possible by splitting the capacitor in two and placing it on both sides of the transmission line
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