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scubasteve
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Joined: 19 Feb 2017
Posts: 6
Location: USA

 Posted: Wed Mar 01, 2017 6:04 pm    Post subject: Slotted Waveguide Antenna Circuit Model Hi. I was reading the page on slotted waveguide antennas here and I had questions on the circuit model. I understand that when the slots are placed perfectly at wavelength/2 they are resonant and so the imaginary component of their impedance/admittance is 0 and consist of purely real resistance/conductance and that the distance to the shorted end of the antenna being wavelength/4 (or 3*wavelength/4 for mechanical reasons) causes it to be seen as a open circuit. Q1. You specify an equation for waveguide wavelength for the dominant TE01 mode. However on the previous page you say the dominant mode is TE10. Why is there a discrepancy between the two pages? Is this a mistake? What is the dominant mode and if there are conditions in which it is different what are they? Q2. You discuss how to get the input impedance once you know the slot admittance: but how can you determine the slot admittance? Is there an analytical way to calculate this based on antenna dimensions or other parameters? Or is it expected that you simply find the value from some simulation software? Q3. Assuming you have the slot admittance and thus the input impedance, how can you use that to actually calculate losses in the antenna? As it's purely resistive the only losses associated with this resistance should be conductive heating losses in the material itself right (ignoring possible reflection from the transmission line feeding the waveguide)? How can you determine this resistive loss? Even if you somehow determined a voltage and current as the input to the circuit(doing so may be another question entirely) what would this circuit model tell you about the losses? It would simply show all the power being consumed by the N number of slots, each slot consuming 1/N of the total power, right? Thanks.
e.fannio
Antenna Theory Regular

Joined: 12 Jul 2018
Posts: 10
Location: Naples, Italy

Posted: Fri Jul 13, 2018 1:47 pm    Post subject: Re: Slotted Waveguide Antenna Circuit Model

 scubasteve wrote: Hi. I was reading the page on slotted waveguide antennas here and I had questions on the circuit model. I understand that when the slots are placed perfectly at wavelength/2 they are resonant and so the imaginary component of their impedance/admittance is 0 and consist of purely real resistance/conductance and that the distance to the shorted end of the antenna being wavelength/4 (or 3*wavelength/4 for mechanical reasons) causes it to be seen as a open circuit. Q1. You specify an equation for waveguide wavelength for the dominant TE01 mode. However on the previous page you say the dominant mode is TE10. Why is there a discrepancy between the two pages? Is this a mistake? What is the dominant mode and if there are conditions in which it is different what are they? Q2. You discuss how to get the input impedance once you know the slot admittance: but how can you determine the slot admittance? Is there an analytical way to calculate this based on antenna dimensions or other parameters? Or is it expected that you simply find the value from some simulation software? Q3. Assuming you have the slot admittance and thus the input impedance, how can you use that to actually calculate losses in the antenna? As it's purely resistive the only losses associated with this resistance should be conductive heating losses in the material itself right (ignoring possible reflection from the transmission line feeding the waveguide)? How can you determine this resistive loss? Even if you somehow determined a voltage and current as the input to the circuit(doing so may be another question entirely) what would this circuit model tell you about the losses? It would simply show all the power being consumed by the N number of slots, each slot consuming 1/N of the total power, right? Thanks.

Q1 The dominant mode in rectangular waveguide is TE10. The presence of the slots excite other modes but they are in cut-off and don't propagate along the waveguide.

Q2 The admittance of a slot in an infinite conductive plane is
Ys = 2.09*(a/b) * (lambdag/lambda) * (sin(pi*x1/a))^2 * (cos(betaz*lambda/4))^2 * Y0
where Y0 is the characteristic admittance of the equivalent line of the waveguide [for TE10 mode it is equal to w*mu/kz with kz = sqrt(beta^2-(pi/a)^2)]
x1 is the distance of the slot from the edge of the waveguide
This formula comes from considerations about Babinet's principle and the admittance of a simple dipole and can be used for the case of your interest if x1 is not too small

Q3 If you are interested only in attenuation due to non perfect conductor, there is a formula that can help you but it involves some integrals. With some (heavy ) calculation I found an analytic formula. For TE10 mode it is
alfa = (Y0/(sigma*d*a*b)) * (a^3 + (a+b)*lambda^2/(4a^2-lambda^2))
where sigma is the conductivity of the metal and d is the penetration thickness
d = sqrt(2/(sigma*w*mu0))
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