Waveguides, cavities and circuits

[RedX]

Can you make a microwave oven by taking a microwave generator and attaching one lead to one side of a metal box, and the other lead to the other side of the metal box, and putting food in the box and flipping the switch on? If this is possible, can you take a can of food and put two leads across it to heat the food? At such high frequencies, the can, can be modeled as a capacitor whose plates are the top and bottom of the can, and the sides of the can, can be modeled as inductors in parallel with the capacitor. So it's an ordinary LC circuit whose resonant frequency is also the frequency of the electromagnetic fields inside the can/cavity (the capacitor has its voltage and hence electric fields changing at the frequency of the microwave generator, as do the magnetic fields from the inductor sides).

Or do you have to feed a microwave cavity by a waveguide? Why is there a waveguide at all - can't you just put the antenna inside the cavity, with direction the same as the electric field of the preferred standing wave patterns? Microwaves have small wavelength, so the antennas are short enough to not take any space. Also, with a waveguide don't you have to match the impedance at the end of the cavity, so as to not have waves reflected back, while you don't have that problem if the fields are antenna fed without guidance?

Also, can one view a waveguide as basically just saying that you don't want to deal with having to have a return wire to your generator, so you're just going to beam alternating voltages with an antenna, and you deliver this voltage to a load by connecting the load to a receiving antenna? For some reason I have hard time believing this is efficient - can you really beam large amounts of energy like this to efficiently power a neighborhood, or are these things only used for communications and not for power?

 

[Born2bwire]

You cannot support a microwave on two leads as you describe it. For microwaves at the typical size scales that we work with you always need waveguides. You wouldn't be able to model the can as a capacitor regardless. The can is a closed metallic surface and as such would effectively block any radiation from penetrating the can. The surface of the can would heat up due to the ohmic losses but I doubt it would be significant enough to serve as a practical method of heating food.

Using antennas to generate microwaves is a rather low powered solution for the most part. Not only is it low powered, it would give poor heating of the food. You do not want to excite selected standing wave patterns. Standing waves give rise to nodes and antinodes which correlate to cold and hot spots when cooking. To get around this, we make a chamber that is large with respect to the wavelength so that there are many modes supported. In addition, we attempt to excite as many of these modes as possible so that the superposition of the fields has few hot/cold spots. This is done by making the mixed mode chamber through the use of a stirrer. The metal fan that runs in your microwave acts as a stirrer to constantly change the boundary conditions of the chamber and thus continually excite different modes. The use of a stirrer means that you could use a single source, but not every microwave has a stirrer (for some reason). In addition, just to get the amount of power comparable to a magnetron I would imagine you would need many antennas offset from the walls of your microwave. Too many would be needed to be practical or feasible.

 

[RedX]

You cannot support a microwave on two leads as you describe it. For microwaves at the typical size scales that we work with you always need waveguides.

If the two leads were exactly the same length, wouldn't the voltages arrive at their respective points in phase? So couldn't it work?

I know there would be huge radiation losses, but what if you shielded each wire that is connected to each lead with a conducting sheath?

You wouldn't be able to model the can as a capacitor regardless. The can is a closed metallic surface and as such would effectively block any radiation from penetrating the can.

If you connect a microwave AC generator to just a capacitor, then there will be alternating electric fields between the capacitors, and also alternating magnetic fields caused by induction from these electric fields. So there is a space between the plates of the capacitor that has microwaves. If you short the capacitor with a wire, then you won't get infinite flow of electrons through the short because wires have inductance, and at high frequency these wires will have high impedance. Now if you short the plates by putting wires all around the perimeter of the plates, then you'll eventually get a can whose sides are the shorting wire. So the can represents a capacitor in parallel with a lot of inductors, and inductors in parallel add like resistors in parallel, so the total inductance will get small. The radiation from the can would come from the fields created by the capacitor and the inductor, created by the changing voltage and current through them from the two leads.

I know the way that it's typically done is to feed the cavity via a waveguide, but I'm wondering whether you can feed the cavity by putting a circuit across it.

 

[Born2bwire]

But you cannot transmit microwaves using a twisted pair unless you are talking about a set of leads that are less than one centimeter in length. A twisted pair does not support high frequency electromagnetic waves, you need a purposely designed waveguide to direct microwaves even in a circuit.

You cannot model a can like a circuit in the manner that you would like. Electromagnetic waves cannot penetrate an ideal Faraday Cage. Your metal can, because it is a closed surface and is made of a decent conductor, will behave as a very good Faraday Cage at microwave frequencies. Your waves will just bounce off of the can and will not penetrate it.

 

[RedX]

But you cannot transmit microwaves using a twisted pair unless you are talking about a set of leads that are less than one centimeter in length. A twisted pair does not support high frequency electromagnetic waves, you need a purposely designed waveguide to direct microwaves even in a circuit.

You cannot model a can like a circuit in the manner that you would like. Electromagnetic waves cannot penetrate an ideal Faraday Cage. Your metal can, because it is a closed surface and is made of a decent conductor, will behave as a very good Faraday Cage at microwave frequencies. Your waves will just bounce off of the can and will not penetrate it.

With a twisted pair or coax, the hot and neutral connections have to be close together (since the hot wire is always close to the neutral wire). Wouldn't a pair of shielded lines be better?

Why would the leads have to be less than one centimeter in length?

I agree with you that waves cannot penetrate the can. If you put a hole in the side of the can however, would waves go from the lid of the can, to the outer surface of the can, into the hole, and flow through the inside of the can, and come out again through that same hole and go towards the opposite lid? Then could you get waves into the cavity of the can without using an antenna guided by a waveguide, but by direct metallic connection of the lids of the can with a microwave AC generator?

 

[Born2bwire]

With a twisted pair or coax, the hot and neutral connections have to be close together (since the hot wire is always close to the neutral wire). Wouldn't a pair of shielded lines be better?

Why would the leads have to be less than one centimeter in length?

I agree with you that waves cannot penetrate the can. If you put a hole in the side of the can however, would waves go from the lid of the can, to the outer surface of the can, into the hole, and flow through the inside of the can, and come out again through that same hole and go towards the opposite lid? Then could you get waves into the cavity of the can without using an antenna guided by a waveguide, but by direct metallic connection of the lids of the can with a microwave AC generator?

Whenever you are talking about AC you have to use waveguides, you cannot assume that circuit theory is directly applicable. So anytime you have a signal operating in AC, you have to consider its frequency, bandwidth, distance of transmission, and impedances when you wish to transmit it along a line. At very low frequencies, let's say typically below 1 MHz, you can largely ignore these factors without any great detriment to the performance of your circuit. You can use twisted pair as your transmission line, you can mix and match connectors without regard to impedances and so forth without too much noticeable adverse effects.

However, you are discussing microwaves, which have a frequency of around 2.54 GHz. Wires cannot support the electromagnetic waves at such a frequency and any attempts to transmit them using wires will result in evanescent modes. This means that the power transmitted will be lost over the span of a wavelength or two. So if you wish to use wires to transmit microwaves you need them to be of lengths less than a wavelength. Hence, a centimeter or two.

As for connecting the leads to the can, what are the waves going to see? Let's say you are using an appropriate transmission line like a coax. You cut the coax cable at the end, butt it up agains the side of the can and you solder the inner and outer conductors to the side. But now all you have done is presented a short termination to the transmission line. The waves travel down the coax and then see a solid wall of conductor and thus they will just reflect back. If you want the waves to go into the can, sure, cut a hole in the side and then stick the coax cable into it. But now you have a regular microwave again. You have a cavity that is being fed microwaves by an attached waveguide.