Topics: Circulators and isolators Circulators and isolators Updated December 18, 2005 Why are circulators and isolators relatively expensive in the world of cheap microelectronics? Because for the most part they are hand assembled, tuned and tested. Tolerances on material properties of the ferrite and magnet as well as mechanical tolerances mean that invariably someone must make at least minimum wage tweaking the product. Tuning methods are different at different manufacturers. One method is to design the part so that the ports are all greater than 50 ohms, then tweak the impedance down by squeezing RTV over the traces to increase their capacitance while watching the result in real time on a network analyzer. Circulators A circulator is a ferrite device (ferrite is a class of materials with strange magnetic properties) with usually three ports. The beautiful thing about circulators is that they are non-reciprocal. That is, energy into port 1 predominantly exits port 2, energy into port 2 exits port 3, and energy into port 3 exits port 1. In a reciprocal device the same fraction of energy that flows from port 1 to port 2 would occur to energy flowing the opposite direction, from port 2 to port 1. The selection of ports is arbitrary, and circulators can be made to "circulate" either clockwise (CW) or counterclockwise (CCW). A circulator is sometimes called a "duplexer", meaning that is duplexes two signals into one channel (e.g. transmit and receive into an antenna). This is not to be confused with the term "diplexer" which is refers to a filter arrangement where two frequency bands are separated into two channels from a single three-terminal device. A lot of people mix up these terms. You can remember the correct definitions because "filter" and "diplexer" both have an "i" in them, and "circulator" and "duplexer" both have a "u". What are circulators good for? The make a great antenna interface for a transmit/receive system. Energy can be made to flow from the transmitter

(port 1) to the antenna (port 2) during transmit, and from the antenna (port 2) to the receiver (port 3) during receive. Circulators have low electrical losses and can be made to handle huge powers, well into kilowatts. They usually operate over no more than an octave bandwidth, and are purely an RF component (they don't work at DC). Circulator rule of thumb!

A circulator's isolation is roughly equal to its return loss, and should always be specified to the same requirement. A circulator with 20 dB isolation will need to have a return loss of 20 dB. Think about it, if you terminate the third arm in a perfect 50 ohms, the clockwise isolation you will measure in a CCW circulator won't be better than the stray signal that is bouncing off the loaded port due to the reflected signal due to its mismatch to 50 ohms. Isolators By terminating one port, a circulator becomes an isolator, which has the property that energy flows on one direction only. This is an extremely useful device for "isolating" components in a chain, so that bad VSWRs don't contribute to gain ripple. Circulators and isolators can be made from 100's of MHz to through Wband (110 GHz). They can be packaged as planar microstrip components, coaxial components or as waveguide components. Waveguide circulators and isolators have by far the best electrical characteristics. You can specify insertion loss down to less than 0.2 dB in some cases! Microstrip and coax circulators and isolators might have losses between 0.5 and 1.0 dB. Note that the more bandwidth you ask for, the crummier the insertion loss and isolation will be. Circulator vendors There are probably 100 garage shops around the country that claim to be circulator manufacturers, be careful who you buy from. There are many reputable circulator vendors for circulators. But from now on, we are NOT going to give them any free advertising! If you want some advice on which vendors to look at, contact us by email and we'll help you out. Better still, tell your favorite circulator vendor to get in touch with us to sponsor this page!

Switchable circulators A really cool type of circulator is a switchable circulator, in which an electrical signal is used to switch the orientation of the circulator from CW to CCW and vice versa. The way the circulator is constructed it latches into a particular orientation and will stay there in the absence of the electrical signal, say, for instance your power supply goes off. The means for switching the orientation is a single high-current DC pulse that is provided by the driver circuit. This in an expensive technology, but it makes an unbelievably low-loss RF switch with high power handling.

Got any good material on circulators and isolators? drop us a line, we want to expand this page into a more useful tutorial! Rat-race couplers Revised February 21, 2006 Click here to go to our main page on couplers and splitters Click here to go to our page on magic tees (a waveguide network with similar properties to the rat-race) Applications of rat-race couplers are numerous, and include mixers and phase shifters. The rat-race gets its name from its circular shape, shown below. The circumference is 1.5 wavelengths. For an equal-split rat-race coupler, the impedance of the entire ring is fixed at 1.41xZ0, or 70.7 ohms for a 50 ohm system. For an input signal Vin, the outputs at ports 2 and 4 (thanks, Tom!) are equal in magnitude, but 180 degrees out of phase.

Rat-race coupler (equal power split) The coupling of the two arms is shown in the figure below, for an ideal rat-race coupler centered at 10 GHz (10,000 MHz). An equal power split of 3 dB occurs at only the center frequency. The 1-dB bandwidth of the coupled port (S41) is shown by the markers to be 3760 MHz, or 37.6 percent.

Power split of ideal rat-race coupler The graph below illustrates the impedance match of the same ideal ratrace coupler, at ports 1 and 4. By symmetry, the impedance match at port 3 is the same as at port 1 (S11=S33). For better than 2.0:1 VSWR (14 dB return loss), a bandwidth of 4280 MHz (42.8%) is obtained.

Impedance match of ideal rat-race coupler The next graph shows the isolation between port 1 and port 3 (S31). In the ideal case, it is infinite at the center frequency. The bandwidth over which greater than 20 dB isolation is obtained is 3140 MHz, or 31.4%.

Isolation of ideal rat-race coupler Below the phase difference between arms 2 and 4 is plotted. At the center frequency. a perfect 180 degree difference is observed. The bandwidth that better than +/- 10 degrees is maintained is 3200 MHz, or 32%.

Unequal-split rat-race couplers In order to provide an unequal split, the impedances of the four arms are varied in pairs, as shown below.

Unequal-split rat-race power divider Equations for the Z0A and Z0B line impedances, as a function of the power split PA/PB, are given below:

Z0A and Z0B are graphed below versus the power split express in dB (coupling ratio) for a 50-0hm system. Click here for info on how to think in dB.

The graph below shows the frequency response for a rat-race coupler where PA/PB=0.25. This corresponds to a 50-ohm power divider where the power out of port 2 (PA) is six dB below the power out of port 4 (PB). Solving the above equations for the line impedances yields Z0A=111.6 ohms, and Z0B=55.9 ohms. Note that in many real-life cases, this coupler may prove impractical because a line impedance as high as 111.6 ohms may be difficult to accurately achieve in a 50-ohm system.

Unequal-split rat-race frequency response, PA/PB=0.25 The graph below shows the frequency response for a rat-race coupler where PA/PB=4.0. This corresponds to a power divider where the power out of port 2 (PA)is six dB higher than the power out of port 4 (PB). The line impedances are opposite to the case where PA/PB=0.25; here Z0A=55.9 ohms, and Z0B= 111.6 ohms.

Unequal-split rat-race frequency response, PA/PB=4.0 Check out our all-new unequal-split power divider calculator, it handles Wilkinsons, rat-races and branch-line couplers!

Waveguide Flanges

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IL-WNonCommercial Flang MIL-SPEC MIL-SPEC 85E E.I.A. Waveguide Contact Pressure I.E.C. Cover Choke Nonveguide Equiv. Material Flange Contact Pressure Flange Flange pressu Type Flange Copper UG1348/U UG1724 G48/U WR284 R32 UG53/U UG54B/U CMR284 Bronze CPR284G CPR28 Copper UG1352/U UG1728 G49/U WR187 R48 UG149A/U UG148C/U CMR187 Bronze CPR187G CPR18 Copper UG1356/U UG1732 G50/U WR137 R70 UG344/U UG343B/U CMR137 Bronze CPR137G CPR13 Copper UG1358/U UG1734 G51/U WR112 R84 UG51/U UG52B/U CMR112 Bronze CPR112/G CPR11 Copper UG1360/U UG1736 G52/U WR90 R100 UG39/U UG40B/U CMR90 Bronze CPR90G CPR90 Copper G53/U WR42 R220 UG595/U UG596A/U UG425/U Bronze

G66/U

WR42 R220 WR90 R100

G67/U

G68/U WR112 R84

G75/U WR284 R32 WR62 R140

G91/U

G95/U WR187 R48

G95/U WR187 R48 avy Wall G96/U WR28 R320 G97/U WR22 G98/U WR15 G99/U WR12

G103/U WR650 R14

G104/U WR430 R22

G105/U WR430 R22

G106/U WR137 R70

G107/U WR62 R140

G109/U WR284 R32

G110/U WR137 R70

G112/U WR340 R26

G113/U WR340 R26

G121/U WR42 R220

G271/U WR28 R320

Silver 6061 Al 1100 Al 6061 Al 1100 Al 6061 Al 1100 Al Copper Bronze 6061 Al 1100 Al 6061 Al 1100 Al Silver Silver Silver Silver 6061 Al 1100 Al Copper Bronze 6061 Al 1100 Al 6061 Al 1100 Al Silver Copper Bronze Copper Bronze Copper Bronze 6061 Al 1100 Al 6061 Al 1100 Al Copper

UG595/U UG596A/U UG425/U UG135/U UG136B/U UG138/U UG137B/U UG584/U UG585A/U UG419/U UG541A/U UG407/U UG406B/U UG407/U UG406B/U Modified Modified UG599/U UG600A/U UG381/U UG383/U UG385/U UG387/U UG418A/U UG418B/U CMR187 UG1361/U CPR90G UG1359/U CMR112 CPR112G UG1349/U CMR284 CPR284G CMR90

UG1737 CPR90 UG1735 CPR11 UG1725 CPR28

UG1353/U UG1729 CPR187G CPR18

UG1343/U UG1720

UG1344/U UG1716

UG1345/U UG1711 UG441/U UG440B/U UG419/U UG541A/U UG509/U UG510/U UG512/U CMR137

UG1357/U UG1733 CPR137G CPR13

UG1346/U UG1712

UG1347/U UG1713 UG597/U UG598A/U UG599/U UG600A/U

G272/U WR22

G273/U WR15

G274/U WR12 WR5 WR6 WR4 WR8 WR3

G275/U

G276/U

G277/U

G278/U

G279/U

G320/U WR102

G337/U WR510 R18

G338/U WR510 R18

G340/U WR229 R40

G341/U WR229 R40

G343/U WR159 R58

G344/U WR159 R58

G346/U WR75 R120

G347/U WR75 R120

G349/U WR62 R140

G351/U WR51 R180

Bronze Copper Bronze Copper Bronze Copper Bronze Copper Bronze Copper Bronze Copper Bronze Copper Bronze Copper Bronze Bronze 6061 Al Copper Bronze 6061 Al 1100 Al Copper Bronze 6061 Al 1100 Al Copper Bronze 6061 Al 1100 Al Copper Bronze 6061 Al 1100 Al 6061 Al 1100 Al 6061 Al

UG383/U UG385/U UG387/U UG1524/U UG1525/U UG1526/U UG387/U Modified UG1527/U

UG1493/U UG1494/U

CMR229 UG1350/U UG1726 CMR229 UG1351 UG1354/U CPR159/G UG1355/U CMR159 CPR159/G CMR159 WR75 WR75 WR75 WR75 CPR75G CPR75G

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UG1655/U UG1666/U WR51 WR51

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G353/U WR51 R180

G354/U WR34 R260

G355/U WR34 R260

G357/U WR34 R260

G358/U WR19

G359/U WR10

G375/U WR284 R32 avy Wall

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ITT 17137

CHAPTER 5 LOOPS Before I began my study of duplexers, the coupling loops in the filters were the most mysterious part. It was not obvious from the published designs how one goes about designing them. There seemed to be so many variations. There were fat loops and thin loops, wire loops and strap loops, side loops and top loops. Why had the designers made these choices? Which was best for my designs? I couldn't see any consistency. That's why I devoted a great deal of time to loops in my early experiments. That's what we are going to talk about in this chapter. We'll discuss loop shape. Is that critical? We'll do the same for the placement of loops in the cavity. Does this require great precision? We'll also discuss loop materials. How important is that? My intention in answering these questions will be to take you through the experiments that gave me the answers. They all add up to a practical picture of loop design and permformance.

Loop Shape My first question was, is there a magic shape for a loop? As I mentioned, I had inspected many duplexers, and the loops came in a baffling veriety. I wanted to know what effect loop shape has on duplexer performance. So I built a moderate sized cavity and began to experiment. Fortunately I had a spectrum analyzer available with a tracking signal generator. The generator sweeps over an adjustable range of frequencies and the spectrum analyzer follows it. The result is an instantaneous display of the performance of a cavity, plotted against frequency. One of the biggest difficulty one has in studying duplexers is isolating a single factor of their design. With every experimental adjustment you make, you usually unwittingly change more than just one thing. After seeing this phenomenon time and time again, in every duplexer parameter I studied, it occurred to me that this is probably one of the main reasons why duplexers are accused of being black magic. Simple intuitive understanding is difficult to extract. Loop shape is a perfect example. When I first began making experimental changes in loop shape, I was changing more than just the shape of the loop. For examples, two loops of different geometry may have a different inductance even if you use the same amount of wire. They also have a different geometric center. Since the magnetic field in the cavity is not the same everywhere, the two loops would couple differently to the field. The complete list of differences caused by just one simple change is quite large. What I needed was a yardstick for testing, some way to isolate individual factors, if I was going to arrive at intuitive understanding. As you may appreciate, it took me some time to find the answer. It is not a perfect answer -- there isn't one, but it works. It eventually occurred to me that performance is a good yardstick. I figured that if two loops differing in only one characteristic were made to perform the same, then the effect of the single difference would be more visible. I have found that this idea works well for studying almost any duplexer chactersitic. To determine the effect of loop shape, I adjusted each pair of different loops to yield equal bandwidth and equal loss. Both were installed, one at a time, in the same cavity, in roughly the same position. I tested circular loops, rectangular loops and loops of irregular shape. What I discovered was that the shape of the loop makes very little difference, once is is made equal in performance to another shape.

This led me to see that only the area of the loop matters. To be precise, coupling is proportional to the square root of the area. But if two loops have the same area, they will perform almost identically in the cavity even if their shape and the amount of wire is quite different. This simple generalization has limits of course, but for practical purposes, loop shape is not a significant factor in duplexer design. Loop area alone determines how well a loop will couple to the magnetic field. Where to Put the Connectors? Another factor, that I wanted to know about, is where do you put the connector that feeds the loop? Also what is the best way to ground the loop?. I had seen a lot of variations in both of these in commercial and amateur-built duplexers. Two locations seemed to be common. The connectors were either installed directly in the shorted end of the cavity or a short distance down the side wall from the shorted end. Loop Construction Materials Next I wanted to know if the size and shape of the conductor in a loop matters. I knew for example that when used as a transmission line, conductors of different dimensions have different characteristic impedances. Is this important in a cavity? Since the loop is fed with a 50 transmission line, perhaps the loop itself had to be constructed to also look like a 50 ohm line section. So again, I began experimenting. I tired wires of widely differing diameters. As before, I adjusted all factors until the performance of each loop was equal to the others under comparison. I also tried strip conductors. I had noticed that in some commercial cavities that loops made of flat strap are used. After trying all these variations, while keeping performance equal, I came to the conclusion that conductor size and shape has almost no effect of loop performance. Ordinary wire is perfectly acceptable. In fact, it is probably the best choice. The only factor that does matter in the type of material used in loop construction is current handling capacity. Notice figure xx. It shows RF current at corresponding output powers.

1 watt 3 watts 10 watts 30 watts 100 watts 300 watts 1000 watts

.14 Amps .25 Amps .44 Amps .77 Amps 1.4 Amps 2.5 Amps 4.4 Amps

Figure xx Current vs. Power at 50 Ohms These values may not seem high if you think of them in DC terms, but RF needs much larger conductors due to skin effect. We will go into the problems caused by skin effect in a later chapter, but as a general principle here, above about 100 watts, loops should be built with heavy wire. Below that power level, 16 AWG wire is completely adequate. Flat strap is not as good a choice. It has worse skin effect problems. It is just a little easier to bend into loops for cavities used at higher power levels. Loop Placement In the last chapter I stated how a loop must be placed to couple most effectively to the magnetic field. The H field, as you will recall, lies in concentric circles around the center conductor of the cavity. To couple best to it, the loop must be perpendicular to the field. This would be parallel to the length and parallel to the diameter of the cavity. Also, for maximum coupling a loop needs to be at a point where the magnetic field is strongest. As we learned, this is near the shorted end of the cavity near the center conductor. If the loop is moved, or rotated in any way, coupling will be less. The question is, does that matter? Must loops always be at a maximum field spot for the cavity to work well? I spent a lot of time researching this point, and concluded that the answer is no. Again using performance as a comparison guide, I experimented with loops at all possible locations, near the shorted end, away from the shorted end, near the center conductor, away from the center conductor. I also experimented with rotated loops.

With every different location, if I merely changed the area of the loop, I could get it to perform just as well as at any other location. Insertion loss and bandwidth do not suffer. Loop Grounding Armed with the knowledge above of how tolerant loops are, it then came as no surprise to me to discover that it also does not matterhow or where you ground a loop. That's probably why you see many variations in commercial and amateur designs. Three common configurations are: a. Side of Cavity b. End of Cavity c. To the Connector As we have learned, only the loop's area matters. For side grounding, a section of the loop is actually a part of the cavity's wall. The area contained by the wall and the remainder of the loop performs the coupling. My personal favorite for loop grounding is to the connector. If you ground the loop on the body of the connector that feeds the loop, the loop and the connector become a removable and rotatable assembly. The convenience of this method makes it a common loop grounding configuration, even in commercial cavities. Chapter Summary Loop shape is not critical. Only the area of the loop determines how much it will couple to the magnetic field. The location of the connectors is not critical. The side or the top works equally well. Round wire is best for loop construction. 16 AWG is suitable for all power levels up to 100 watts. Above this, larger wire is needed to handle the RF current, due to skin effect. Loop placement is not critical. Equal performance can be obtained from a wide range of positions in a cavity. Loop grounding is also not critical. Grounding to the connector is the most convenient method. All this leads to a Golden Rule. Nothing about a loop matters significantly. All you must do is to change the area and orientation of the loop until it couples to the magnetic field to the desired degree. At this point it will work almost identically to any other loop configuration.

From Wikipedia, the free encyclopedia (Redirected from Directional coupler) Jump to: navigation, search

Power dividers and directional couplers are passive devices used in the field of radio technology. They couple part of the transmission power in a transmission line by a known amount out through another port, often by using two transmission lines set close enough together such that energy passing through one is coupled to the other. As shown in Figure 1, the device has four ports: input, transmitted, coupled, and isolated. The term "main line" refers to the section between ports 1 and 2. On some directional couplers, the main line is designed for high power operation (large connectors), while the coupled port may use a small SMA connector. Often the isolated port is terminated with an internal or external matched load (typically 50 ohms). It should be pointed out that since the directional coupler is a linear device, the notations on Figure 1 are arbitrary. Any port can be the input, (as in Figure 3) which will result in the directly connected port being the transmitted port, the adjacent port being the coupled port, and the diagonal port being the isolated port. Physical considerations such as internal load on the isolated port will limit port operation. The coupled output from the directional coupler can be used to obtain the information (i.e., frequency and power level) on the signal without interrupting the main power flow in the system (except for a power reduction - see Figure 2). When the power coupled out to port three is half the input power (i.e. 3 dB below the input power level), the power on the main transmission line is also 3 dB below the input power and equals the coupled power. Such a coupler is referred to as a 90 degree hybrid, hybrid, or 3 dB coupler. The frequency range for coaxial couplers specified by manufacturers is that of the coupling arm. The main arm response is much wider (i.e. if the spec is 2-4 GHz, the main arm could operate at 1 or 5 GHz - see Figure 3). However it should be recognized

that the coupled response is periodic with frequency. For example, a /4 coupled line coupler will have responses at n/4 where n is an odd integer. Common properties desired for all directional couplers are wide operational bandwidth, high directivity, and a good impedance match at all ports when the other ports are terminated in matched loads. These performance characteristics of hybrid or non-hybrid directional couplers are self-explanatory. Some other general characteristics will be discussed below. Contents [hide]

1 Coupling factor 2 Loss 3 Isolation 4 Directivity 5 Hybrids 6 Amplitude balance 7 Phase balance 8 Other power dividers 9 Power combiners 10 Sample Problem 11 Low frequency directional couplers 12 See also 13 External links 14 References

[edit] Coupling factor

The coupling factor is defined as: where P1 is the input power at port 1 and P3 is the output power from the coupled port (see Figure 1) The coupling factor represents the primary property of a directional coupler. Coupling is not constant, but varies with frequency. While different designs may reduce the variance, a perfectly flat coupler theoretically cannot be built. Directional couplers are specified in terms

of the coupling accuracy at the frequency band center. For example, a 10 dB coupling +/- 0.5 dB means that the directional coupler can have 9.5 dB to 10.5 dB coupling at the frequency band center. The accuracy is due to dimensional tolerances that can be held for the spacing of the two coupled lines. Another coupling specification is frequency sensitivity. A larger frequency sensitivity will allow a larger frequency band of operation. Multiple quarter-wavelength coupling sections are used to obtain wide frequency bandwidth directional couplers. Typically this type of directional coupler is designed to a frequency bandwidth ratio and a maximum coupling ripple within the frequency band. For example a typical 2:1 frequency bandwidth coupler design that produces a 10 dB coupling with a +/- 0.1 dB ripple would, using the previous accuracy specification, be said to have 9.6 +/- 0.1 dB to 10.4 +/- 0.1 dB of coupling across the frequency range. [edit] Loss In an ideal directional coupler, the main line loss from port 1 to port 2 (P1 - P2) due to power coupled to the coupled output port is:

The actual directional coupler loss will be a combination of coupling loss, dielectric loss, conductor loss, and VSWR loss. Depending on the frequency range, coupling loss becomes less significant above 15 dB coupling where the other losses constitute the majority of the total loss. A graph of the theoretical insertion loss (dB) vs coupling (dB) for a dissipationless coupler is shown in Figure 2.

[edit] Isolation Isolation of a directional coupler can be defined as the difference in signal levels in dB between the input port and the isolated port when the two output ports are terminated by matched loads, or:

Isolation can also be defined between the two output ports. In this case, one of the output ports is used as the input; the other is considered the output port while the other two ports (input and isolated) are terminated by matched loads.

Consequently: The isolation between the input and the isolated ports may be different from the isolation between the two output ports. For example, the isolation between ports 1 and 4 can be 30 dB while the isolation between ports 2 and 3 can be a different value such as 25 dB. If both isolation measurements are not available, they can be assumed to be equal. If neither are available, an estimate of the isolation is the coupling plus return loss (Standing wave ratio). The isolation should be as high as possible. In actual couplers the isolated port is never completely isolated. Some RF power will always be present. Waveguide directional couplers will have the best isolation.

If isolation is high, directional couplers are excellent for combining signals to feed a single line to a receiver for two-tone receiver tests. In Figure 3, one signal enters port P3 and one enters port P2, while both exit port P1. The signal from port P3 to port P1 will experience 10 dB of loss, and the signal from port P2 to port P1 will have 0.5 dB loss. The internal load on the isolated port will dissipate the signal losses from port P3 and port P2. If the isolators in Figure 3 are neglected, the isolation measurement (port P2 to port P3) determines the amount of power from the signal generator F2 that will be injected into the signal generator F1. As the injection level increases, it may cause modulation of signal generator F1, or even injection phase locking. Because of the symmetry of the directional coupler, the reverse injection will happen with the same possible modulation problems of signal generator F2 by F1. Therefore the isolators are used in Figure 3 to effectively increase the isolation (or directivity) of the directional coupler. Consequently the injection loss will be the isolation of the directional coupler plus the reverse isolation of the isolator. [edit] Directivity Directivity is directly related to isolation. It is defined as:

where: P3 is the output power from the coupled port and P4 is the power output from the isolated port. The directivity should be as high as possible. Waveguide directional couplers will have the best directivity. Directivity is not directly measurable, and is calculated from the isolation and coupling measurements as:

Directivity (dB) = Isolation (dB) - Coupling (dB) [edit] Hybrids The hybrid coupler, or 3 dB directional coupler, in which the two outputs are of equal amplitude takes many forms. Not too long ago the quadrature (90 degree) 3 dB coupler with outputs 90 degrees out of phase was what came to mind when a hybrid coupler was mentioned. Now any matched 4-port with isolated arms and equal power division is called a hybrid or hybrid coupler. Today the characterizing feature is the phase difference of the outputs. If 90 degrees, it is a 90 degree hybrid. If 180 degrees, it is a 180 degree hybrid. Even the Wilkinson power divider which has 0 degrees phase difference is actually a hybrid although the fourth arm is normally imbedded. Applications of the hybrid include monopulse comparators, mixers, power combiners, dividers, modulators, and phased array radar antenna systems. [edit] Amplitude balance This terminology defines the power difference in dB between the two output ports of a 3 dB hybrid. In an ideal hybrid circuit, the difference should be 0 dB. However, in a practical device the amplitude balance is frequency dependent and departs from the ideal 0 dB difference. [edit] Phase balance The phase difference between the two output ports of a hybrid coupler should be 0, 90, or 180 degrees depending on the type used. However, like amplitude balance, the phase difference is sensitive to the input frequency and typically will vary a few degrees.

The phase properties of a 90 degree hybrid coupler can be used to great advantage in microwave circuits. For example in a balanced microwave amplifier the two input stages are fed through a hybrid coupler. The FET device normally has a very poor match and reflects much of the incident energy. However, since the devices are essentially identical the reflection coefficients from each device are equal. The reflected voltage from the FETs are in phase at the isolated port and are 180 degrees different at the input port. Therefore, all of the reflected power from the FETs goes to the load at the isolated port and no power goes to the input port. This results in a good input match (low VSWR). If phase matched lines are used for an antenna input to a 180 hybrid coupler as shown in Figure 4, a null will occur directly between the antennas. If you want to receive a signal in that position, you would have to either change the hybrid type or line length. If you want to reject a signal from a given direction, or create the difference pattern for a monopulse radar, this is a good approach. [edit] Other power dividers Both in-phase (Wilkinson) and quadrature (90) hybrid couplers may be used for coherent power divider applications. The Wilkinson power divider has low VSWR at all ports and high isolation between output ports. The input and output impedances at each port are designed to be equal to the characteristic impedance of the microwave system.

A typical power divider is shown in Figure 5. Ideally, input power would be divided equally between the output ports. Dividers are made up of multiple couplers and, like couplers, may be reversed and used as multiplexers. The drawback is that for a four channel multiplexer, the output consists of only 1/4 the power from each, and is relatively inefficient. Lossless multiplexing can only be done with filter networks. Coherent power division was first accomplished by means of simple Tee junctions. At microwave frequencies, waveguide tees have two possible

forms - the H-Plane or the E-Plane. These two junctions split power equally, but because of the different field configurations at the junction, the electric fields at the output arms are in-phase for the H-Plane tee and are anti-phase for the E-Plane tee. The combination of these two tees to form a hybrid tee allowed the realization of a four-port component which could perform the vector sum () and difference () of two coherent microwave signals. This device is known as the magic tee. [edit] Power combiners Since hybrid circuits are bi-directional, they can be used to split up a signal to feed multiple low power amplifiers, then recombine to feed a single antenna with high power as shown in Figure 6.

This approach allows the use of numerous less expensive and lower power amplifiers in the circuitry instead of a single high power TWT. Yet another approach is to have each solid state amplifier (SSA) feed an antenna and let the power be combined in space or be used to feed a lens which is attached to an antenna. (See [1])

[edit] Sample Problem If two 1 watt peak unmodulated RF carrier signals at 10 GHz are received, how much peak power could one measure? 1. 2. 3. 4. 5. 0 watts 0.5 watts 1 watt 2 watts All of these

The answer is all of these as shown in Figure 7.

[edit] Low frequency directional couplers For lower frequencies a compact broadband implementation by means of unidirectional couplers (transformers) is possible. In the figure a circuit is shown which is meant for weak coupling and can be understood along these lines: A signal is coming in one line pair. One transformer reduces the voltage of the signal the other reduces the current. Therefore the impedance is matched. The same argument holds for every other direction of a signal through the coupler. The relative sign of the induced voltage and current determines the direction of the outgoing signal.

For a 3 dB coupling, that is equal splitting of the signal, another view might be more appropriate: Two of the line pairs are combined into a polyphase line. A polyphase_transformer can be used to redistribute the signal onto a set of 45 rotated lines. Although many wavemeters are used in performing various functions, the cavity-type wavemeter is the type most commonly used. Only this type is discussed in some detail. Cavity Wavemeter Figure 2-12 shows a typical CAVITY WAVEMETER. The wavemeter is of the type commonly used for the measurement of microwave frequencies. The device uses a resonant cavity. The resonant frequency of the cavity is varied by means of a plunger, which is mechanically connected to a micrometer mechanism. Movement of the plunger into the cavity reduces the cavity size and increases the resonant frequency. Conversely, an increase in the size of the cavity (made by withdrawing the plunger) lowers the resonant frequency. The microwave energy from the equipment being tested is fed into the wavemeter through one of two inputs, A or B. The crystal rectifier then detects (rectifies) the signal. The rectified current is indicated on current meter M.

Figure 2-12.Typical cavity wavemeter. Electronic Frequency Counters Another device used to measure frequencies above the audio range is the ELECTRONIC FREQUENCY COUNTER. Since this instrument will be covered in detail in a later chapter, only a brief description is provided at this time. The electronic frequency counter is a high-speed electronic counter with an accurate, crystal- controlled time base. This combination provides a frequency counter that automatically counts and displays the number of events occurring in a precise time interval. The frequency counter itself does not generate any signal; it merely counts the recurring pulses fed to it.

Transmission Line There appears to be some controversy, disagreement, or lack of understanding surrounding the term "transmission line". While most engineers familiar with transmission lines understand two-conductor transmission lines are fed differentially at one end by a source and have a

termination placed differentially across the far end, a few seem to disagree. Let's go through this and see if we can sort transmission line mode operation from other forms of energy transfer parallel or concentric conductors can sustain. Conventional Use of Transmission Line We all know a traditional transmission line system appears like this:

Fig 1. In each of these cases, the line will not radiate or contain substantial electric or magnetic fields external to the line area. The lack of external fields, even at a very small distances, is rooted in two conditions: 1.) All outgoing currents on one conductor are matched by equal level and exactly opposite phase currents on a return conductor at any given point along the line. This causes an exactly equal and opposite magnetic field along each conductor. The opposing magnetic

fields caused by equal currents flowing opposite directions cancel magnetic fields outside the general area of the two conductors. 2.) All voltages from each conductor of the line to the outside environment surrounding the line are either contained within a closed shield, or are exactly equal and opposite an imaginary neutral reference point representing the environment around the line (balanced lines). We always have a constant differential voltage across the line (between the conductors) and that voltage changes only with standing wave ratio as we move along the line. 3.) The vector product of differential current flowing in conductors and voltage between line conductors at any point along the line always equals the power transmitted in transmission line mode. (Number two and three above are very important. They indicate a TEM wave. To understand it think about how your rig connects to your feedline. Everyone knows the alternating current coming from our radios has voltage across the output jack. At any instant of time when energy is being transferred to the load ((except when zero is being crossed)) the voltage polarity of the two conductors is of opposite signs. Except for zero crossing or when the transmitter is off the potential difference is always there, and the vector product of voltage across the line and current flowing through the line always equals applied power.) The conditions above are required to support energy flow through a transmission line. That mode is called TEM mode, or transverse electromagnetic mode. All two conductor transmission lines, either coaxial or balanced, transfer energy down the line by TEM mode. Here is what Edward Jordan and Keith Balmain say about TEM mode operation of transmission lines in the classic Prentice-Hall Electrical Engineering Series textbook "Electromagnetic Waves and Radiating Systems":

To make a long story short, classic transmission line theory (called "ordinary transmission line theory" in the text above) requires the wave to be launched from one end of the two parallel conductors forming our transmission line. If we do not do that, we simply have two parallel conductors magnetically and electrically coupled. Energy will not be confined to the "transmission line", and can radiate out into the surroundings freely. This is a very important distinction when dealing with feedlines and antennas! In transmission line mode (transverse electromagnetic mode) we can sleeve the line with ferrites and properties inside the line do not change. The electrical length does not change, losses do not change, and the frequency response is very wide as it is with any transmission line of similar design. This occurs because energy in a two-conductor transmission line is transferred via TEM mode; fields are confined to the general area between the conductors. Things outside that energy path, such as ferrite beads, metallic conduit, and other conductors or cables do not affect TEM mode or transmission line mode energy flowing through the transmission line. Except for very low levels caused by slight flaws in the lines, signals don't leak in and signals don't leak out when we have a transmission line operated in transmission line mode. Balance Unbalanced lines (coaxial cables) actually have equal and opposite currents in the shield and center conductor at any place along the transmission line. So do balanced lines. This leaves us with a question. What makes one line or system balanced and the other unbalanced? Currents behave the same way and are always balanced in a properly working transmission line, its source, or its load regardless of line type, so what's the difference? The thing separating balanced from unbalanced lines or systems, including antenna feedpoints, is voltage from each conductor or terminal with respect to a physical or imaginary reference point representing the world around the source, feedline, or load. In the case where the feedline does not radiate both systems have equal and opposite currents at every point. These points include the source, the entire length of transmission line, and the load. It is the voltage that actually makes sources or loads "balanced" or "unbalanced", and the containment of fields inside a shield that causes a coaxial transmission line to be considered "unbalanced".

Common Mode Excitation We can make a transmission line become a conventional radiating conductor if we apply energy in a non-TEM mode. This can be useful when we wish to use a feedline as an antenna or as a conventional conductor. When we excite a cable like this:

or like this:

The cable freely radiates. Things outside the line influence the line. Adding a ferrite core will add loss and make the line electrically longer. The SWR will change. This is true even when currents are equal in the two conductors, and can even be true when currents are equal and opposite as long as the line was excited from end-to-end! The key to having a line behave like a transmission line is feeding it differentially at one end, and not applying voltage across the length of one or both conductors. This is a transmission line as we generally know it, and as dozens of reputable engineering textbooks define it:

The above configuration shows a direct wire connection from source to load, and cannot transform voltage, current, or impedance based on turns ratio. This fits the definition of classic transmission line, which requires TEM mode in coaxial or parallel wire lines. Jordan and Balmain cover this extensively in "Electromagnetic Waves and Radiating Systems" (Guided Waves, p215, 2nd ed). Kraus also covers this in "Antennas" in various sections dealing with transmission lines and wave propagation, as does Terman in his "Radio Engineers Handbook" Circuit Theory chapter under the subheading "Transmission Lines". Most engineering text I have clearly state parallel conductor transmission lines employ TEM mode of energy transfer. If not, they are not considered transmission lines. Cutoff frequencies Waveguide can support many modes of transmission. All microwave textbooks will tell you about this, but we don't really care. The usual mode of transmission in rectangular waveguide is called TE01. The lower cutoff wavelength (and frequency) for this mode is very simply:

The upper cutoff frequency is exactly one octave above the lower. We'll let you do the math on this (multiply lower cutoff frequency by two...) now it's time for another Microwaves101 rule of thumb:

Waveguide operating band The accepted limits of operation for rectangular waveguide are

(approximately) between 125% and 189% of the lower cutoff frequency. Thus for WR-90, the cut-off is 6.557 GHz, and the accepted band of operation is 8.2 to 12.4 GHz. Remember, at the lower cutoff the guide simply stops working. See our page on waveguide loss for more information. Guide wavelength Guide wavelength is defined as the distance between two equal phase planes along the waveguide. The guide wavelength is a function of operating wavelength (or frequency) and the lower cutoff wavelength, and is always longer than the wavelength would be in free-space. Here's the equation for guide wavelength:

Guide wavelength is used when you design distributed structures in waveguide. For example, if you are making a PIN diode switch with two shunt diodes spaces 3/4 wavelength apart, use the 3/4 of a guide wavelength in your design. The guide wavelength in waveguide is longer than wavelength in free space. This isn't intuitive, it seems like the dielectric constant in waveguide must be less than unity for this to happen... don't think about this too hard you will get a headache. Here is a way to imagine why this is... picture yourself at Zuma Beach in Malibu. The waves are coming in at an angle to the beach.... check out the intersection of the wavefront with the beach, it is zipping along faster than you can run... yes, it's apparently faster than the waves are moving if you look straight at them. Maybe it's time for us all to go to the beach and check this out... send us an

good mpg video of this and we'll send you $100!

Phase velocity and group velocity Phase velocity is an almost useless piece of information you'll find in waveguide mathematics; here you multiply frequency times guide wavelength, and come up with a number that exceeds the speed of light!

Be assured that the energy in your wave is not exceeding the speed of light, because it travels at what is called the group velocity of the waveguide:

The group velocity is always less than the speed of light, we like to think of that this is because the EM wave is ping-ponging back and forth as it travels down the guide. Note that group velocity x phase velocity = c2. Group velocity in a waveguide is speed at which EM energy travels

in the guide. Plotted below as a percentage of the speed of light (c), we see how group velocity varies across the band for WR-90 (Xband) waveguide. Note that the recommended operating band of WR-90 is from 8.2 to 12.4 GHz. At 8.2 GHz the signal is slowed to 60% of the free-space speed of light. At the lower cutoff (6.56 GHz), the wave is slowed to zero, and you can outrun it without breathing hard.

Group delay in waveguide Click here to check out our page on group delay! Now that we know the group velocity, we can calculate the group delay of any piece of waveguide, noting that time is distance divided by velocity:

The group delay of rectangular waveguide components is a function of the frequency you are applying. Near the lower cutoff, the group delay gets longer and longer, as the EM wave ping-pongs down the

guide, and can easily be 10X the free-space group delay. But at the upper end of a waveguide's band, the group delay approaches the free-space group delay, which follows the rule-of-thumb, approximately one foot per nanosecond, independent of frequency. To compare with the one nanosecond/foot rule of thumb, below is a plot of the group delay of one foot of WR-90 waveguide. At the upper end of the band you will see that very nearly the free-space group delay is achieved.

The problem of electromagnetic energy traveling at different speeds over frequency is commonly called dispersion. Soon we will have a page on this topic as well.

Frequency meters Updated June 18, 2006 Click here to go to our page on historic test equipment Click here to go to our main page on test equipment

Click here to go to our main page on waveguide Click here to go to our page on resonant cavities Frequency meters, also called "wavemeters", are what your grandparents used to determine the frequency of an unknown signal source. Sometimes called "gumball machines", (thanks, John!) now frequency meters just take up space in one of the lab cabinets that no one opens. Engineers will fight tooth and nail to get the $100,000 spectrum analyzer in their setup. But you can obtain similar accuracy with a frequency meter, and if you use one in your next setup, people will think you really know what you are doing. And they'll probably ask "where do you plug it in?" Here's one we saw on Ebay recently, it probably sold for $10 or less. In this case the frequency meter is for X-band, and uses WR-90 waveguide. The scale reads out in MHz.

How does a frequency meter work? The cylindrical cavity forms a resonator that produces a suck-out in the frequency response of the unit. This you would turn the knob until a dip in the response is observed. The graduations will tell you what frequency you are at. Waveguide frequency meters use a short circuit resonant cavity, which resonates at half-wavelength. Most wavemeters are waveguide, however, coaxial types are possible. Waveguide wavemeters can only measure frequency over their respective frequency band.

Here is a view of the above wavemeter taken apart. You can see the hole in the E-plane that couples out to the cavity. At the bottom of the cavity is the piston that changes the resonant frequency.

Wavemeters are affected by temperature changes, which slightly change the dimensions of the cavity.

This page is about waveguides for electromagnetic wave propagation at microwave and radio wave frequencies. For optical waveguides, see Waveguide (optics). For other types of waveguide, see Waveguide. In electromagnetics and communications engineering, the term waveguide may refer to any linear structure that guides electromagnetic waves. However, the original and most common meaning is a hollow metal pipe used for this purpose. A dielectric waveguide employs a solid dielectric rod rather than a hollow pipe. An optical fibre is a dielectric guide designed to work at optical frequencies. Transmission lines such as microstrip, coplanar waveguide, stripline or coax may also be considered to be waveguides. The electromagnetic waves in (metal-pipe) waveguide may be imagined as travelling down the guide in a zig-zag path, being repeatedly reflected

between opposite walls of the guide. For the particular case of rectangular waveguide, it is possible to base an exact analysis on this view. Propagation in dielectric waveguide, may be viewed in the same way, with the waves confined to the dielectric by total internal reflection at its surface. Some structures, such as nonradiative dielectric waveguide [NRD], and the Goubau line, use both metal walls and dielectric surfaces to confine the wave.

Short length of rectangular waveguide (WG17 with UBR120 connection-flanges)

Section of flexible waveguide Contents [hide]

1 History 2 Principles of operation 3 Analysis 4 Hollow metallic waveguides 5 Dielectric rods for microwaves 6 Applications 7 See also 8 References 9 Further reading 10 External links

[edit] History The first waveguide was proposed by J. J. Thomson in 1893 and experimentally verified by O. J. Lodge in 1894; the mathematical analysis of the propagating modes within a hollow metal cylinder was first performed by Lord Rayleigh in 1897. (McLachan, 1947.)

[edit] Principles of operation Depending on the frequency, waveguides can be constructed from either conductive or dielectric materials. Generally, the lower the frequency to be passed the larger the waveguide is. For example the natural waveguide[1] the earth forms given by the dimensions between the conductive Ionosphere and the ground as well as the circumference at the median altitude of the earth is resonant at 7.83 Hz. This is also known as Schumann resonance. Waveguides can also be less than a millimeter in width. An example might be those that are used in extremely high frequency (EHF) Satellite Communications(SATCOM). There is a formula for calculating waveguide dimensions, more information may be found at this website[2]. [edit] Analysis Electromagnetic waveguides are analyzed by solving Maxwell's equations, or their reduced form, the electromagnetic wave equation, with boundary conditions determined by the properties of the materials and their interfaces. These equations have multiple solutions, or modes, which are eigenfunctions of the equation system. Each mode is therefore characterized by an eigenvalue, which corresponds to the axial propagation velocity of the wave in the guide. Waveguide propagation modes depend on the operating wavelength and polarization and the shape and size of the guide. The longitudinal mode of a waveguide is a particular standing wave pattern formed by waves confined in the cavity. The transverse modes are classified into different types:

TE modes (Transverse Electric) have no electric field in the direction of propagation. TM modes (Transverse Magnetic) have no magnetic field in the direction of propagation. TEM modes (Transverse ElectroMagnetic) have no electric nor magnetic field in the direction of propagation. Hybrid modes are those which have both electric and magnetic field components in the direction of propagation.

In hollow metallic waveguides, the fundamental modes are derived from the transverse electric TE1,0 mode for rectangular and TE1,1 for circular waveguides. Also, in hollow waveguides, TEM waves are not possible, since Maxwell's Equations will give that the electric field must then have zero divergence and zero curl and be equal to zero at boundaries,

resulting in a zero field. (or, equivalently, with boundary conditions guaranteeing only the trivial solution). However, TEM waves can propagate in coaxial cable.

TE1,0 mode of a rectangular hollow metallic waveguide. [edit] Hollow metallic waveguides

TE1,1 mode of a circular hollow metallic waveguide.

In the microwave region of the electromagnetic spectrum, a waveguide normally consists of a hollow metallic conductor. Hollow waveguides must be one-half wavelength or more in diameter in order to support one or more transverse wave modes. Waveguides are often pressurized to inhibit arcing/multipaction, allowing higher power. Conversely, waveguides may be required to be evacuated as part of evacuated systems. (e.g. electron beam systems) A slotted waveguide is generally used for radar and other similar applications. The waveguide structure has the capability of confining and supporting the energy of an electromagnetic wave to a specific relatively narrow and controllable path. A closed waveguide is an electromagnetic waveguide (a) that is tubular, usually with a circular or rectangular cross section, (b) that has electrically conducting walls, (c) that may be hollow or filled with a dielectric material, (d) that can support a large number of discrete propagating modes, though only a few may be practical, (e) in which each discrete mode defines the propagation constant for that mode, (f) in which the field at any point is describable in terms of the supported modes, (g) in which there is no radiation field, and (h) in which discontinuities and bends cause mode conversion but not radiation. Hollow metallic waveguides are far narrower than the wavelength of operation. They can take the form of single conductors with or without a dielectric coating, e.g. the Goubou line and helical waveguides.

VSWR measurements may be taken to ensure that a waveguide is contiguous and has no leaks or sharp bends. If such bends or holes in the waveguide surface are present, this may diminish the performance of both TX and RX equipment strings. Arcing may occur if there is a hole, if transmitting at high power, usually 200 watts or more. Waveguide plumbing[3] is crucial for proper waveguide performance. Reflected power may occur and damage equipment as well. Another cause for a bad VSWR in a waveguide is moisture build up and can typically be prevented with silica gel which is a desiccant. Due to the negative effect of moisture buildup within the waveguide desiccant silica gel canisters may attached with screw-on nibs. [edit] Dielectric rods for microwaves Dielectric rod waveguides, in linear arrays of short transverse conductors, and planar resistive conductors use the same principle as optical waveguides. These function via a refractive index effect where the waveguide slows the EM wave velocity below the free space velocity, continuously bending the relatively wide EM wavefronts towards the narrow waveguide and keeping them entrained. Helical waveguides and linear arrays of short conductors are used as part of "end-fire" antennas such as the helical antenna and Yagi antenna. Planar resistive waveguides are used in Over-The-Horizon radar and the Ground Wave Emergency Network, where the resistive surface of the Earth or ocean serves to slow the waves below free space velocity; entraining them and forcing them to follow the curvature of the Earth. Several waveguides based on entrainment of EM waves also exist. [edit] Applications Waveguides can be constructed to carry waves over a wide portion of the electromagnetic spectrum, but are especially useful in the microwave and optical frequency ranges. Waveguides are used for transferring both power and communication signals, usually for short distances. Bell Labs in the 1970s built a waveguide line several miles long, to study possible use for intercity communication, but advances in optical fiber disrupted the plan.

2-6 Figure 2-3.Moving electron losing energy and velocity. The operation of a velocity-modulated tube depends on a change in the velocity of the electrons passing through its electrostatic field. A change in electron velocity causes the tube to produce BUNCHES of electrons. These bunches are separated by spaces in which there are relatively few electrons. Velocity modulation is then defined as that variation in the velocity of a beam of electrons caused by the alternate speeding up and slowing down of the electrons in the beam. This variation is usually caused by a voltage signal applied between the grids through which the beam must pass. The first requirement in obtaining velocity modulation is to produce a stream of electrons which are all traveling at the same speed. The electron stream is produced by an electron gun. A simplified version of an electron gun is shown in figure 2-4A. Electrons emitted from the cathode are attracted toward the positive accelerator grid and all but a few of the electrons pass through the grid and form a beam. The electron beam then passes through a pair of closely spaced grids, called BUNCHER GRIDS. Each grid is connected to one side of a tuned circuit. The parallel-resonant tuned circuit (figure 2-4A) in the illustration represents the doughnut-shaped resonant cavity surrounding the electron stream (figure 2-4B). The buncher grids are the dashed lines at the center of the cavity and are at the same dc potential as the accelerator grid. The alternating voltage which exists across the resonant circuit causes the velocity of the electrons leaving the buncher grids to differ from the velocity of the electrons arriving at the buncher grids. The amount of difference depends on the strength and direction of the electrostatic field within the resonant cavity as the electrons pass through the grids.

Fi Electron gun with buncher grids.

gure 2-4A.

Velocity Modulation The microwave tube was developed when the use of the frequency spectrum went beyond 1,000 megahertz and into the microwave range. The microwave tube uses transit time in the conversion of dc power to radio-frequency (rf) power. The interchange of power is accomplished by using the principle of electron VELOCITY MODULATION and low-loss resonant cavities in the microwave tube. A clear understanding of microwave tubes must start with an understanding of how electrons and electric fields interact. An electron has mass and thus exhibits kinetic energy when in motion. The amount of kinetic energy in an electron is directly proportional to its velocity; that is, the higher the velocity, the higher the energy level. The basic concept of the electron energy level being directly related to electron velocity is the key principle of energy transfer and amplification in microwave tubes. An electron can be accelerated or decelerated by an electrostatic field. Figure 2-2 shows an electron moving in an electrostatic field. The direction of travel (shown by the heavy arrow) is against the electrostatic lines of force which are from positive to negative. The negatively charged electron will be attracted to the positively charged body and will increase in velocity. As its velocity increases, the energy level of the electron will also increase. Where does the electron acquire its additional energy? The only logical source is from the electrostatic field. Thus, the conclusion is clear. An electron traveling in a direction opposite to electrostatic lines of force will absorb energy and increase in velocity (accelerate).

Figure 2-2.Moving electron gaining velocity and energy.

As figure 2-3 illustrates, the opposite condition is also true. An electron traveling in the same direction as the electrostatic lines of force will decelerate by giving up energy to the field. The negatively charged body will repel the electron and cause it to decrease in velocity. When the velocity is reduced, the energy level is also reduced. The energy lost by the electron is gained by the electrostatic field.

What makes a microwave engineer?First off, let's remind everyone that microwave electronics are by and large an analog science, as opposed to most other electrical engineering, which has mostly gone digital. We think of analog as real life, and digital as the "reality TV" of electronics. No one really listens to digital music or sees digital television, your senses are analog. Digital communications must be carried on an analog radio signal. Analog engineering will never go away. If we had to summarize what sets a microwave engineer apart from a "normal" electrical engineer, we'd say that knowledge of just a few simple concepts is required to fit in with microwave geeks. These are S-parameters, the Smith chart, decibels, transmission lines (including waveguide, which really isn't a transmission line but performs the same function) and skin depth. Notice that we didn't mention antennas, because we consider that almost a separate subject from microwave engineering! The funny thing is that you can be expert on all of these without any advanced math or even a college education, but without a college degree it will be difficult to ever land a job as an engineer in this industry. Here's a great list of colleges that offer education in microwave engineering! You'll learn about all of these concepts and more, starting here on this page. Thankfully, there is a ton of electronic design analysis software out there that does all of the heavy lifting for you. Here's a Microwaves101 piece of advice: if you want to succeed in this field (or any other) the most important thing is to love your work. Nothing trumps enthusiasm, not even large brains. If you don't find microwaves particularly interesting, go do something else. If you don't find any type of work interesting, join a trade union, buy some four-wheeled off road vehicles so you can share a "sport" with your fat kids, drink lots of beer and watch more television while the rest of us invent the future. And don't forget to complain about everything, especially during your impoverished retirement years!

What about out-sourcing?

Will the U.S. microwave industry be devastated by outsourcing to India, like the IT industry? We don't think so, for two reasons. A vast part of the microwave industry is related to defense work and infrastructure (think towers). Outsourcing these would make as much sense as outsourcing your local fire department. The second reason is that third-world countries picked the IT industry to grab because it doesn't take near the level of investment that developing hardware does, and quality problems will kill your business. Below is a picture of a simple wrench the "Pittsburgh Forge" outsourced to India. The results speak for themselves, that is why you should buy Craftsman (made in America) tools!

The microwave industryMicrowaves components and systems are a multi-10-billion dollar industry, how's that for a vague data point? The design community is small, perhaps only about 50,000 to 100,000 people in the US consider themselves in the microwave field (this estimate is based on observed attendance at the annual IEEE IMS symposium, factored for how many of us have to stay home and do real work). What are the "big three" applications of microwaves in everyday life?

Heating Remote sensing and countermeasures Communications

Heating applicationsHere's a page on microwave use of heating.

Remote sensing and countermeasures applications

The most well-known remote sensing systems are radars (radio direction and ranging), which use a transmitter to illuminate an object, and a receiver to detect its position or velocity (or both). Another class of remote sensing is radiometry. Radiometric systems need no transmitter, they merely collect naturally-occurring electromagnetic energy and process its to form images. Terahertz radiometric receivers will soon be employed as security systems in airports, provided that the ACLU will permit us all to be seen in the nude by quarter-inch-brow security guards. Another excellent example of remote sensing is the new "T-ray" imaging being done at terahertz frequencies, by companies such as Teraview. Radio astronomy uses uses huge dishes to capture incredibly weak RF signals from space to reconstruct the origins of the universe starting with the big bang. We now have a page on this topic! Let's lump in global-positioning systems into remote sensing, because a GPS unit "senses" where it is. Countermeasures to remote sensing include all types of jamming equipment, usually associated with military applications. Interested in electronic countermeasures? Consider becoming an Old Crow! We will also lump RFID in as a use of microwaves to perform sensing.

Communications applicationsCommunications systems include satellite, radio, television, wireless phone and data transmission applications, and all combinations of these. We'll get into these later... or sooner, if someone sends us some material!

Medical applicationsHere's a page on medical applications of microwaves.

The fifth application?Directed energy weapons will eventually make up a new category of microwave applications. This includes the Pentagon's new pain ray, as well as high-power microwave (HPM) systems that can be used to defeat weapons such as missiles and even disable ground vehicles (with the exception of diesel engines which have no ignition system). Here's some great info on the pain ray from wired.com, in case you wanted to know about its effects on dogs, sunblock, and drunks!

http://www.wired.com/news/technology/0,72134-0.html? tw=rss.index http://www.wired.com/news/technology/0,72236-0.html? tw=rss.index Speaking of using microwaves as a weapon, here's a page on the biological effects of electromagnetic radiation. Relax and enjoy your microwaved popcorn!

The sixth application?RF lighting is a relatively new topic for microwave engineering. The sulfur lamp uses a 2.45 GHz magnetron to excite sulfur to give up an eye-pleasing spectrum of light. We've started a page on this topic here.

Military versus commercial applicationsWe often divide microwave technology based on commercial or military/aerospace applications. The mix of people in microwaves is roughly half in commercial applications, and half in military/aerospace. Everyone knows that people who work in military/aerospace microwaves generally are more manly than their commercial brothers. Commercial applications of microwave technology include the frontend of much of the wireless stuff you use everyday, such as cell phones, pagers, wireless LANs, satellite television, XM Radio, and that cool GPS playtoy you received on Father's Day. Unfortunately the boom years of commercial microwave technology seem to be behind us, as the telecom infrastructure was overbuilt, while competition drove the price of wireless phone services into unprofitable territory. Who knows, videophone and Bluetooth tricks may eventually bring some real money back to this industry. Doesn't everyone want to be able to buy a pack of gum from a vending machine by clicking a few buttons on their cell phone? You can do this in Finland right now thanks to Nokia! We're not holding our breath for a lot of new gadgets to take hold here in the USA, the Second Bush Recession still has two more years to go. Military, aerospace applications probably account for more research dollars than commercial stuff. It's arguably a lot more fun to work in this arena, where cost is often NOT as big a consideration as performance. How would you rather spend your career, with a team of 100 engineers trying to shave the cost of a $20 cell phone by one buck in six weeks, or with a team of four engineers designing a million-dollar electronic warfare pod in six years?

Perhaps the coolest microwave development programs are sponsored by DARPA, the Defense Advanced Research Projects Agency. Here's a page that reviews some of their current work. Here's a separate page that discusses MIL-Specs for microwave hardware. If you want to get into the U. S. defense industry, chances are your employer will need to get you a security clearance, granted from the Defense Security Agency (DSS). This takes some time (perhaps six months), and if you were born outside the country, or have been convicted of a crime, or have declared bankruptcy, it might be better to rethink your career choice. Although the DSS might ask you to sign something that will permit them to use a polygraph to check out your background, we've never heard of it being used. They will certainly ask you if you have used illegal drugs, but chances are they will overlook your use of weed during college, or the defense industry would lose 47% of all candidates. They don't care about your sexual orientation, and won't ask about your religious preference. Publishing the results of research for defense work has the added restriction of the International Traffic in Arms (ITAR) regulations.

The microwave frequency spectrumSo what's a microwave? There is some controversy about the exact frequency limits. We define it as an electromagnetic wave between 300 MHz and 300 GHz, in agreement with Pozar's Microwave Engineering, which allows microwave engineers as broad a stake as possible in the EM spectrum. Below 300 MHz is called very high frequency (VHF, thanks, Chris!), above 300 GHz you are into the sub-millimeter-wave spectrum. Terahertz frequency means 1012 cycles per second, approaching infrared radiation. Yikes! Here's a separate Microwaves101 page that provides a table of frequencies used by different systems, such as police radar, XM radio, automotive radar, etc. Check it out! Speaking of frequencies, you will often encounter frequency-band letter designations within the microwave field. Although the letter bands are considered obsolete, you should memorize some of the more common designators (such as the IEEE standards shown below) if you ever want to be a Microwave Good-old Boy.

Frequency letter bandsThis info has been moved to a separate page!

Millimeter-waves versus microwavesThe following distinction between millimeter-waves and microwaves is almost universally accepted: frequencies with free-space wavelengths less than one centimeter but greater than one millimeter are referred to as millimeter-waves. Thus, the millimeterwave spectrum starts at 30 GHz, and runs to 300 GHz, where the wavelength in free-space is less than one millimeter. Welcome to the sub-millimeter-wave band, you are on your way to infrared radiation and terahertz frequencies. Some microwave engineers have a fear of millimeterwaves, thinking that solving problems is harder at higher frequency. This is irrational thinking, millimeter-wave hardware requires nothing new, the components are just smaller. Let's illustrate the concept by comparing the rock group Kiss, versus the midget tribute band Tiny Kiss:

Kiss

Tiny Kiss

Yes, they serve the same purpose, but one is smaller. The details are all there, even the guy who plays Chaim Witz (a.k.a, everyone's favorite band member. Gene Simmons) is the tallest. Got it?

BandwidthBandwidth is a measure of how much spectrum your microwave system can respond to. Bandwidth is often given in megahertz or gigahertz, calculated from from a low frequency FL to an high frequency FH, the bandwidth is given by (FU-FL). Bandwidth is expressed a number of other ways, which we will define here: Three-dB bandwidth: for a network that has a non-ideal frequency response (which includes all physical networks), the three-dB bandwidth is where the transmission coefficient S21 falls off from its

highest peak by three dB. Similarly, you could describe a network by its two-dB or one-dB bandwidths. Percentage bandwidth: for a system that works from a low frequency FL to an high frequency FH, the percentage bandwidth is given by 100%x(FH-FL)/FC. FC is the center frequency, equal to (FH+FL)/2. Note that it is possible to have more than 100% bandwidth by this definition; an amplifier that works from 100 MHz to 10 GHz has a bandwidth of 200%. Instantaneous bandwidth: this is a measure of how wide a spectrum a system can respond to, without any type tuning. Using the analogy of radio, the IF bandwidth in an American FM receiver is about 200 kHz, which is necessary to pass the full spectrum of a broadcast FM signal. The demodulator processes this bandwidth to obtain the approximately 18 kHz baseband bandwidth. The "despreading" effect of this processing results in the superior signal to noise ratio enjoyed by FM transmission. (Thanks for the correction, Miles!) Tunable bandwidth: tunable bandwidth is a measure of how wide a spectrum a system can respond to with the user allowed to change settings such as local oscillator frequency. For a receiver, the tunable bandwidth is almost always more than the instantaneous bandwidth. An AM radio has a tunable bandwidth of 540 kHz to 1600 kHz, or over one MHz of bandwidth. This is about 100X its instantaneous bandwidth. What does octave bandwidth mean? It implies that the the upper frequency of operation is double the lower frequency of operation, for example, an amplifier that works from 2 to 4 GHz has one octave bandwidth. The origin of the word octave goes back to music theory, where an octave is an interval of eight notes in the major scale. For reference, the interval from middle C to high C on a piano is an octave; high C is double the audio frequency of middle C. A device with an octave bandwidth always has 67% bandwidth (do the math for homework!)

Frequency conversionA fundamental problem in electromagnetics is that for a signal to be radiated into free space, an antenna must be on the order of 1/10 or more of a wavelength. Thus transmitting voice without some type of upconversion would require a 30 kilometer antenna for a 10 kHz signal! Thus, baseband signals need to ride on carrier waves, which are at RF and microwave frequencies. Mixers are the devices that are used to convert from one frequency to another. Upconversion

means you are increasing the frequency of your signal, and downconversion means you are decreasing it.

Harmonic frequenciesA harmonic frequency is 2X, 3X, 4X, etc. the frequency of a signal. Why is it called a harmonic? Because in music, harmonic frequencies of 2X, 3X, 4X sound good together (they are harmonious, like the Del Vikings). 2X and 4X frequencies are octaves, 3X is an octave plus a perfect fifth. A subharmonic frequency is one that is 1/2, 1/3, 1/4 of a signal.

Transmission lines and characteristic impedanceWhen your done looking at the paragraph below, check out our page on characteristic impedance! What is a transmission line? Here's our definition: it's any conducting structure that supports an electromagnetic wave "in captivity". Most transmission lines use two conductors, where one is considered ground. This includes coax (the outer conductor is ground), microstrip and stripline. The transmission line that does not use a pair of conductors is waveguide. By the way, we are talking about lossless transmission lines here, or at least near-lossless. We have an entire chapter devoted to transmission lines, click here and we'll take you there. What's a "substrate?" It is the insulating material that support the the transmission lines. In microstrip and stripline, the substrate is the dielectric slab onto which the strip conductors and groundplanes are plated and etched. When microwave engineers talk about a "fifty-ohm system", what does that mean? A common misconception is that if you placed an ohmmeter across the ground and conductor of a fifty-ohm coax cable, you would always read 50 ohms. This is not the case, here's what we're talking about: transmission lines have two important properties that depend on their geometry, their inductance per unit length, and their capacitance per unit length. The "characteristic impedance" of a system is calculated from the ratio of these two: Z=sqrt(L'/C') where L' is the inductance per unit length and C' is the capacitance per unit length. Note that higher inductance translates to higher impedance, and higher capacitance translates to lower impedance. Notice also that the units of length don't matter, since they are "lost

in the sauce". The units of inductance and capacitance must be selfconsistent, such as pico-henries/foot and pico-farads/foot. How do you know the inductance and capacitance per unit length of a particular transmission line? Who cares, when this has all been calculated for you about a million times already and plenty of software exists that will calculate it for you. The thing you should care about is what parameters within a transmission line geometry control the relative capacitance and inductance per unit length, so you get a feeling for what controls the impedance. Let's start with coax cable. The inductance per unit length is mainly attributed to the diameter of the center conductor. Decrease this diameter (keeping everything else the same) and you will increase the inductance. This also raises the characteristic impedance, referring to the equation above. Filling the cable with a material of higher relative dielectric raises the unit capacitance, and lowers the line impedance. Another example: microstrip. Here unit capacitance and inductance are inexorably linked together; widening the microstrip line decreases its inductance while it increases it capacitance. Hence, wide lines are always lower in impedance than narrow lines for a given substrate height. As with coax, the dielectric constant of the substrate has a big effect on capacitance; using a higher dielectric substrate will yield a lower impedance line, all other things being equal. So it is important not to mix up your Rogers Duroid materials, once your circuit is etched it is pretty hard to judge the dielectric constant from color and texture alone! Why fifty ohms? Now moved to a separate page for more in-depth discussion! Impedance of free space The exact characteristic impedance of free space is 120 ohms, which is approximately 377 ohms. Why? This is explained (or should be) on our page on characteristic impedance.

Impedance matchingImpedance matching of source and load is important to get maximum power transfer. If you have a 75 ohm load, you don't want to drive it with a 50 ohm source, because it is inefficient. You can learn more about the simple math behind maximum power transfer by clicking here.

Simple impedance transformation can be done using quarterwave transformers. Click here to go to our main page on quarter-wave tricks!

Dielectric constant and effective dielectric constant"Dielectric constant" is another way to say "relative permittivity". Check out our separate page on permittivity for more info on this subject. Although some people use the phrase "relative dielectric constant", this is incorrect, akin to saying "deja vu again". Remember back to your physics class, when you learned that dielectric constant is used to calculate the value of a capacitor? The higher the dielectric constant, the higher the capacitor value. For an ideal parallel plate capacitor, the capacitance is calculated by: C=( 0xR

xA)/D

where 0 is the permittivity of free space (thanks, Maarten!), R is the relative permittivity (the dielectric constant) of the material between the plates, A is the area of the parallel plates, and D is the distance they are separated. Technically for this expression to be 100% accurate, the material surrounding the plates must be of the same relative dielectric constant R, but this induces only a small error in the calculation under most circumstances. 0 is equal to 8.854x10-12 Farads per meter (you should commit this to memory). Most often it is the dielectric constant R that is most important in microwaves. For electromagnetic radiation, the permittivity of the medium that the wave is propagating in is equal to R 0. In a vacuum or in dry air, R is equal to unity, and the signal travels at the speed of light. All electromagnetic energy, from 60 Hertz power that your electric company sells you, to signals that the latest Mars satellite returns to earth, travels really, really fast. In a vacuum, the speed of light, denoted "c" in textbooks, is 2.998 x 1010 centimeters/second (thanks, Jared!) , or 2.998 x 108 meters per second, or about 186,000 miles per second, which puts the moon about 1.5 seconds away by radio. The dielectric constant of a material can be used to quantify how much a material "slows" an electromagnetic signal. The velocity of the signal within any transmission line that is 100% filled with a material of dielectric constant R is computed by: v=c/sqrt(R

)

So if your stripline or coax transmission line is fabricated on a material with dielectric constant 2.2, the velocity of propagation is

only 67% of the speed of light in free space. Similarly, because wavelength is proportional to velocity, the length of a quarter-wave transformer is also 67% of what it would be in free space. Thus one of the tricks of reducing the size of microwave components is revealed; by using materials of higher dielectric constant, distributed structures can be made smaller. One of the advantages of using GaAs for microwave ICs (known in the industry as MMICs) is its dielectric constant of 12.9, which is appreciably higher than ceramics such as alumina, and most soft substrates.

A very good rule of thumb is that electromagnetic radiation in free space travels about one foot in one nanosecond; a more exact value is 0.983571 feet per nanosecond. This slows to about 8 inches per nanosecond for coax cables filled with PTFE (almost all coax cables are filled with PTFE, or a combination of PTFE and air.) For more information please see our discussion of group delay. This brings us to the subject of "effective dielectric constant". In transmission lines realized in microstrip media, most of the electric fields are constrained within the substrate, but a fraction of the total energy exists within the air above the board. The effective dielectric constant takes this into account. The effective dielectric constant of a fifty-ohm transmission line on ten mil alumina is a number somewhere around 7, which is less than the dielectric constant of the substrate bulk material (9.8). Another example of an effective dielectric constant is if you were to create a stripline circuit using two sheets of substrates with different dielectric constants. To a first order, the effective dielectric constant would be the average of the two materials' dielectric constants. A third example is coplanar waveguide transmission lines with air above the substrate. Here the effective dielectric constant is very nearly the average of the substrate dielectric constant and one (the dielectric constant of air=1). Thus the effective dielectric constant of CPW circuits on GaAs ( R=12.9) is approximately 6.5.

How to think in dBEvery time you talk to a microwave engineer it's dB-this and dBthat. What are they talking about? A decibel is a convenient logarithmic ratio of two RF power or RF voltage levels (usually input and output levels). If you are asking "why are logarithmic ratios convenient?", you are too young to have owned a slide rule. The beautiful thing about log ratios is that multiplication of "linear" numbers becomes addition, and division becomes subtraction. The conversion of linear ratios to dB is:

10xlog(power level2/power level1), or 20xlog(voltage level2/voltage level1) Bear in mind that in microwaves we are most often referring to power levels, not voltage levels. That's because microwave signals are usually measured in milliwatts, not millivolts. You can easily convert from power to voltage and vice-versa if you know the system characteristic impedance (usually 50 ohms). Decibels are very useful for talking about increases (gains) or decreases (losses) without talking about the actual power or voltage levels. Remember, though, that dB by itself isn't a unit like millimeters or inch, it's all relative. A negative number of dB indicates loss or reduction in signal strength, while a positive number indicates gain or increase in signal strength. When you refer to a loss in dB, it is customary to eliminate the negative sign. For example, a ten-dB attenuator has 10 dB loss, while it has -10 dB gain. By the way, the decibel is actually a tenth of a Bel, a unit named after (you guessed it) Alexander Graham himself! You'll also see the term dBm in the field of microwaves (decibels referenced to milliwatts), or sometimes dBW (decibels referenced to watts). This is simply the same logarithmic calculation but instead of comparing two power levels to each other, you are comparing one power level to 1 milliwatt. 10 dBm is the same at 10 mW, 20 dBm is the same as 100 mw, 30 dBm is the same as 1000 mw (or one watt). How do you "think" in decibels compared to linear units? Just remember a few key conversions and you will be all set to impress your friends with quick approximations of some heavy multiplication and division (that is, if they are easily impressed). By the way, we rounded these off so they will be easier to remember, if you need an exact answer, get a calculator! 30 dB is an increase of 1000X in power 20 dB is an increase of 100X in power 10 dB is an increase of 10X in power 6 dB is an increase of 4X in power 3 dB is an increase of 2X in power 2 dB is an increase of 1.6X in power

1 dB is an increase of 1.25X in power 0 dB is no increase or decrease in power -1 dB is a decrease of 20% in power -2 dB is a decrease of 37% in power (roughly a decrease of 1/3) -3 dB is a decrease of 50% in power -6 dB is a decrease of 75% in power -10 dB is a decrease of 90% in power -20 dB is a decrease of 99% in power -30 dB is a decrease of 99.9% in power When you input a 5 milliwatt signal into a power amplifier that has 12 dB of gain, the output is 80mW. You can easily do the math in your head. Break down the 12 dB into 6 dB + 6 dB, and remember that each 6 dB increases power by 4X, so you have an increase of 16X ( equal to 4x4). Sixteen times five is eighty. Let's try a harder laboratory calculation. Your signal source has an adjustable power output from 0 to 27 dBm (one milliwatt to half a watt). You have an isolator on the source output (always a good idea) with one dB loss. Then you are coupling off a sample of the signal through a ten dB coupler, attenuating it with a six dB pad before reading the signal strength in decibels with a power meter. The "through" port of the coupler is known to have one dB of loss with respect to its input port, and your device under test (DUT) resides right on the output port of the coupler. When Power meter A reads 6 dBm, how much power does the DUT see?

Working backwards from the "known" power (Power meter A), you have 17 dB loss between it and the source (the 6 dB pad, the 10 dB coupler, and the isolator at one dB). Therefore the source is generating a power of 23 dBm, which is 200 milliwatts (remember that 20 dBm is 100 milliwatts, and you are 3 dB above that). Then working toward the DUT, you have two dB loss total (one dB in the isolator, one dB in the coupler), so the DUT sees 21 dBm, or 15 dB higher than the power meter reading. 21 dBm is 25% more than 100 milliwatts, or 125 milliwatts. Note that once you know the 15 dB difference between the DUT and the power meter, you can apply it to any power meter reading A; this is your calibration factor for input power. With a little practice you will be able to do decibel calculations in your sleep, it's easier than balancing your checkbook. For homework, try the previous calculation using "normal" math... let's see, the pad loses 75% of the signal power, the coupler loses another 90% on top of that and the circulator loses another 10%... forget about it!

Lumped elements versus distributed elementsClick here to go to our main page on lumped elements. When the behavior of a resistor, capacit