Basic Concepts

Warning: info contained below may turn you into a Microwave Good-old Boy! Please check out our compilation of microwave rules of thumb on a separate page. Check out our book recommendation page and also our college page for further study in the awesome field of microwave engineering.

Here are some quick links to the content on this page and other pages with basic microwave engineering info:

What makes a microwave engineer?

What about outsourcing?

The microwave industry

Heating applications (separate page)

Remote sensing and countermeasure applications (such as radar)

Communication applications

Medical applications (separate page)

Directed energy weapons - the fifth application?

RF lighting - the six application?

Microwave spectroscopy - the seventh application? (separate page)

Military versus commercial applications

IEEE Microwave Theory and Techniques Society (separate page)

The microwave frequency spectrum

Frequency letter bands

What's the frequency? (separate page)

Frequency conversion


Transmission lines and characteristic impedance

Characteristic impedance (separate page)

Why fifty ohms? (separate page!)

Impedance of free space

Impedance matching

Dielectric and effective dielectric constants

How to think in dB (separate page)

Greek letter usage in microwave engineering (separate page)

Lumped elements versus distributed elements

VSWR and return loss

The Smith chart (separate page)

Skin depth (separate page)

S-parameters (separate page)

Waveguide (separate page)

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 and don't care what people think of you, become an investment banker and live off everyone else's hard work!

Here in the United States trade unions provide thousands of employees that perform much of the tedious work that engineers would not be good at (and perform it enthusiastically), and we thank them for their daily contributions and wish them luck on their next collective bargainization (if that is a word!) Be respectful of them and they will be nice to you. Thanks to Lyle for reminding us about the union label!

Look for the Union Label!

What about out-sourcing?

Will the U.S. microwave industry be affected by outsourcing to developing nations, like the IT industry was? 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 that microwave engineering is a good field for US college students to consider is that producing complex hardware takes a much higher level of investment than running a call center: initial quality problems can limit the worldwide microwave business of developing countries even if they can offer lower pricing. Below is a picture of a simple wrench the "Pittsburgh Forge" produced in India and sold in the United States. One knuckle-bashing experience with hardware like this will steer the consumer back to Craftsman (made in America) tools. On the other hand, it is just a matter of time before emerging countries develop microwave capabilities that they can be proud of. When we wake up from the current recession, it is a safe bet that many compound semiconductor fabs in the United States will be gone, with Asia aggressively taking a large piece of that part of the microwave industry. And in the not-too distant future you may be driving a Tata!

The microwave industry

Microwaves 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 applications

Here'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 applications

Communications 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 applications

Here'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, in case you wanted to know about its effects on dogs, sunblock, and drunks!

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 applications

We 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 front-end 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 a few more years to run out.

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 spectrum

So 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 bands

This info has been moved to a separate page!

Millimeter-waves versus microwaves

The 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 millimeter-wave 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 millimeter waves, 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:


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?


Bandwidth 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%. There is additional explanation about percentage bandwidth on this page.

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 conversion

A 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 frequencies

A 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 impedance

When 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:


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 self-consistent, 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 120π ohms, which is approximately 377 ohms. Why? This is explained (or should be) on our page on characteristic impedance.

Impedance matching

Impedance 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:



where ε0 is the permittivity of free space (thanks, Maarten!), εR 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 εR, but this induces only a small error in the calculation under most circumstances. ε0 is equal to 8.854x10-12 Farads per meter (you should commit this to memory). Most often it is the dielectric constant εR that is most important in microwaves.

For electromagnetic radiation, the permittivity of the medium that the wave is propagating in is equal to εRε0. In a vacuum or in dry air,ε εR 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 εR is computed by:


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 (εR=12.9) is approximately 6.5.

How to think in dB

This topic now has its own page.

Lumped elements versus distributed elements

Click here to go to our main page on lumped elements.

When the behavior of a resistor, capacitor, or inductor can be fully described by a simple linear equation, microwave engineers refer to it as a lumped element. For example, a 50-ohm resistor at low frequencies will obey Ohm's law (V=IxR). Put five volts across it and it will draw 100 milliamps of current. "Lumped elementhood" is restricted to components that are operate at frequencies where they are physically much smaller than a quarter-wavelength. For example, axial-leaded components perform well up to 10s of MHz, but at one GHz, chances are that an axial-leaded resistor is closer to an open circuit, or a lousy inductor, rather than an ideal resistor. This is why you will rarely be asked the resistor color code as a microwave engineer!

At microwave frequencies, other factors must be considered. To accurately calculate the behavior of that same 50-ohm resistor, you need to consider its length, width, and thickness of metal (due to the skin effect), and its proximity to the ground plane. This is when we must consider it as a distributed element.

By designing really tiny parts, you can often consider them lumped elements, even at microwave frequencies. You must keep the critical dimensions (such as length and width of a thin-film resistor) small compared to an electrical quarter wavelength. For example, if you are designing a 50 ohm microstrip load resistor at X-band, on an alumina substrate (dielectric constant 9.8), a quarter wavelength is approximately 120 mils. You'd better keep both the length and width of the resistor to less than 40 mils, or you else you have to spend some time with a EDA simulation tool such as Agilent ADS or Eagleware Genesis evaluating the performance. Where else but microwave engineering can you make a project out of designing a stupid fifty-ohm resistor?!

 Yet another rule of thumb: to be considered a "lumped element", no feature of the structure can exceed 1/10 of a wavelength at the maximum frequency of it usage.

At low frequencies, the metal that connects components together is treated as an ideal connection, with no loss, no characteristic impedance, and no transmission phase angle. When interconnects become an appreciable fraction of the signal wavelength, these interconnections themselves must be treated as distributed elements or transmission lines. An extreme example of the need to consider the distributed properties of transmission lines is when we are dealing with a quarter-wavelength. At this electrical length (90 degrees), an open circuit is transformed to a short circuit, and a short-circuit is transformed to an open circuit! Think about this: a short-circuited 90 degree "stub" hanging in shunt off of a transmission line will be invisible to signals propagating down the the transmission line, while an open circuited 90 degree stub shunting a transmission line will cause a short circuit and the propagating signal will get hosed! A whole lot of microwave engineering exploits this concept, so you'd better understand it.

One "classic" distributed element is the quarter-wave transformer (we've written an entire chapter on this and other quarterwave tricks! The quarterwave transformer is used to shift the impedance of a circuit by the following simple formula:


where Z2 is the characteristic impedance of the transformer, ZL is the load impedance, and Z0 is the characteristic impedance of the system you are trying to maintain. Do you detect a pattern? Most of the equations on this page use the square-root function... perhaps they put that button on your Casio calculator for a reason!

VSWR and return loss

Click here to go to a more detailed discussion of this topic.

VSWR stands for voltage standing wave ratio. It is a measure of how well a network is matched to it's intended characteristic impedance (Z0), which is almost always 50 ohms in microwave engineering. Return loss is just another way to express the same thing. Both are used in microwave engineering, that's just to keep you on your toes.

VSWR dates back to the days when a "standing wave meter" was an important piece of lab equipment. Long before you could buy a network analyzer for measuring how well a part is impedance matched, the standing wave meter was used by engineers to evaluate the same problem. A small probe was inserted into a waveguide, the output of which was rectified, producing a current or voltage proportional to the electric field with the waveguide. The engineer would pull the probe longitudinally along the waveguide, in search of local maxima and minima readings. These are due to the standing wave within the transmission line. The ratio of the maximum to the minimum voltage recorded was known as the voltage standing wave ratio (VSWR). To this day VSWR is often used to quantify how well a part is impedance matched. Always expressed as a ratio to unity, a VSWR of 1.0:1 indicates perfection (there is no standing wave). A VSWR of 2:1 means the maxima are twice the voltage of the minima. A high VSWR such as 10:1 usually indicates you have a problem, such as a near open or near short circuit.

That's all for now!

Author : Unknown Editor