# Efficiency of Microwave Devices

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On this page we will define the meaning of efficiency, review some power amplifier efficiency equations, and then speculate on what level of DC-to-RF efficiency you can expect depending on device type, frequency and bandwidth. Maybe we'll even put down some rules of thumb!

### How to Design an RF Power Amplifier: Class F

For April 2016, we have a new video from our friends at Keysight, on designing a Class F amplifier for high efficiency. It has some interesting content on Fourier series, something we will discuss in the near future on this page....

What’s the difference between Class F and Class B? What are their theoretical maximum efficiencies?

How do you shape a sinusoidal waveform into a square wave?

Can you truly get 100% efficiency with Class F?

Learn the answers to these questions, and more in this short video. You will also learn how to:

- Build a nonlinear transistor model to illustrate the mechanism by which a Class F amplifier works
- Analyze and understand an ideal Class F power amplifier design topology
- Demonstrate a practical high frequency Class F power amplifier topology

Check it out, download the example files, and get a jump-start on your own designs!

*How to Design an RF Power Amplifier: Class F *

### Overview of efficiency

Efficiency is a measure of how well a device converts one energy source to another. What doesn't get converted to goes into heat; heat is almost universally a bad by-product of energy conversion.

In different processes that occur in every day life, you can expect different levels of efficiency, usually based on the physics of the devices involved. Automobile internal combustion engines are lucky to convert 20% of your gas tank to measurable work. Of course, there is big difference between "measurable work" and "unnecessary work" when it comes to today's SUV-infested highways, but we'll leave that topic alone for now....

In photo-voltaic (solar) cells, we are interested in converting sunlight to usable electric power, and 10% efficiency is a dream come true for amorphous silicon solar cells. With solar radiation at 1 kilowatt/m^{2}, a 100 megawatt power plant (thanks for the correction, Rob!) will require one square kilometer of PV solar cells, which is unaffordable without a little help from the government but as of the end of 2012 there are 100 GW of PV power installed around the world. Nuclear power plants for all their faults (we made a little joke there) have been built that supply* gigawatts at a single installation*.

In microwave engineering, we are interested in converting DC power to RF power. The higher the power amp efficiency, the longer your cell phone can operate, because it's primarily the transmit amplifier chain that is draining the battery* when you're yacking away. Some Class-E power amplifiers have been known to exceed 80% efficiency.

* But wait, that is not true, according to Mark, who would know.... the receive amplifier is on most of the time, while the power amp is used only sporadically in your cell phone to broadcast your location and those occasional pearls of knowledge you blow out your mouth. Note that "blower" is a slang term for telephone in the UK. So LNA designers are taking the efficiency beating at design reviews just as much or more than power amp designers!

Maximum efficiency of a microwave device is a function of frequency, temperature, input drive level, load impedance, bias point, device geometry, and intrinsic device characteristics. It is truly a multidimensional problem! You can determine the maximum efficiency under different conditions using load pull.

Note that laws of thermodynamics won't allow 100% efficiency, no matter how you calculate it.

Some switching voltage regulators can convert one voltage to another with an amazing 90% efficiency.

Efficiency of power amplifiers can be improved by providing proper terminations at harmonic frequencies for both load and source. The "low-hanging fruit" is the second harmonic load impedance. Merely terminating this frequency in a short circuit can be worth a few efficiency points. The third harmonic wants to see an open circuit. Trying to deal with multiple harmonics in a design is not usually worth the headache unless your devices have significant gain capabilities at the third and higher harmonics

Now let's talk about a Microwave Stupidity topic. Suppose you redesigned an amplifier, and improved its power added efficiency from 20% to 22%. Did you improve the efficiency by 2%? No, you improved it by "2 percentage points". Get that straight, Einstein!

### Five measures of efficiency

In microwave engineering, amplifier efficiency is calculated in at least five ways, which is downright confusing. You'd think that the IEEE would have a standard on "amplifier efficiency terminology" but to our knowledge they don't. Maybe they could adopt our five definitions below for starters. Please don't invite us to that committee meeting....

Update August 2013:three of the following equations were posted way back in 2006. Efficiency is almost always referred to by the Greek letter lower-case eta (η), but we had used delta (δ) by mistake. Karlyn pointed out this discrepancy, so we fixed it. It never did look quite right... thanks!

#### Drain efficiency

Drain efficiency is gets its name from FET devices, where the primary terminal where DC power is supplied is the drain. Drain efficiency is the ratio of output RF power to input DC power:

Drain efficiency is a measure of how much DC power is converted to RF power, for a *single device* (see amplifier efficiency for a chain of devices). The problem with using this measurement as a benchmark is that it doesn't take into account the incident RF power that goes into a device. In the case of a single-stage RF amplifier, RF input power can be substantial, because gain is low. For single devices, drain efficiency is often quoted by cheaters and other marketing types.

Note that while "drain efficiency" applies to FET-based products such as pHEMT, you can substitute "collector efficiency" for bipolar transistor products such as HBT. It is calculated the same way.

#### Power-added efficiency (PAE)

Power added efficiency is similar to drain efficiency, but it takes into account the RF power that is added to the device at its input, in the numerator. PAE is the most-accepted figure-of-merit to use to compare single devices. *It is better to chose the highest PAE rather than the highest drain efficiency, grasshopper...*

Note that PAE is often applied to amplifiers as a figure of merit, as well as devices.

In a theoretical sense, an amplifier with infinite gain will have power added efficiency equal to drain efficiency. For a real amplifier, PAE will always be less than drain efficiency, but once you get to 30 dB gain or so, the two quantities become very close in value because input power will be less than 0.1% of output power (30 dB gain is 1000 in linear scale). You can express PAE in terms of drain efficiency, you will get:

For an amplifier with 30 dB gain, PAE and drain efficiency differ by just 0.1 percent (999/1000).

The maximum possible power-added efficiency of a device always decreases with frequency. This is because the natural tendency for maximum gain of an active device to decrease with frequency.

#### Total efficiency

Total efficiency, sometimes called overall efficiency, gives a more-complete picture of the ratio of output power to both types of input power (DC and RF):

Total efficiency is the measure that makes the most sense from a thermodynamic point of view. But PAE is still the most popular measure in the microwave community. Maybe someday someone will explain that to us!

If you were a mathematician you could prove that total efficiency is always higher than PAE. This will not improve your social life, and it's unimportant, so why bother?

#### Amplifier efficiency

A multi-stage amplifier design should not quote an overall "drain efficiency" number as the efficiency of the various stages are all different and that term should be reserved for single devices (in our opinion). Typically the output stage will be at highest efficiency, with the efficiencies of the other stages decreasing as you go closer to the input. This is necessary as you always want to be sure to have enough drive to saturate the output stage, so the other stages must have some margin to their capabilities.

"Amplifier efficiency" is the ratio of RF output power to DC input power, and is the best FOM for a multi-stage amplifier. You can assume this is a "peak" measurement if you are considering a pulsed amplifier. In practice, for an amplifier with high gain: amplifier efficiency, PAE and total efficiency will be close enough to be equal. Amplifier efficiency is the accepted measurement of an amplifier product.

#### Wall-plug efficiency

A lot of work is done to market efficiency, or should we say a lot of marketing work is done. If you attend a design review for a pulsed power amplifier and someone says efficiency of a transmit chain is 20%, start asking questions. Is this a calculation when the transmitter is on, or is it an average that includes stand-by power when the transmitter is off? Does this include all voltage regulators and DC converters (seeing that some stages are GaAs and some are GaN and operate at very different drain voltages)? What about the modulator voltage drop? How about the gate supply and voltage dividers? Total efficiency often leaves out various dissipaters from the calculation. Put on the spot, the designer might say, "oh, you mean the 'wall-plug efficiency'? That's quite a bit lower..."

By "wall plug efficiency" we mean if you compared average RF output power to exact measured power that is consumed by the product from its AC wall plug, ignoring the effect of RF input power.

Let's offer the following definition for wall-plug efficiency:

Bring a "kill-a-watt" meter to that next design review and put some pressure on the design team!

### Some power amplifier efficiency benchmarks

These examples below are purely hypothetical, and are based on experience but we don't offer and references to back them up. Why's is that? Here's a better question... why don't you offer us some references and we'll build this into a page of content for your company's power amplifier expertise! The data were updated in 2013 in case you were wondering, but some of the numbers could be victim of a "wine accident".

Always consider when someone is talking about PAE, whether it is at the *device level*, or the *amplifier level*. Amplifiers will always have lower PAE than devices because matching networks and ensuring stability always take a toll on gain.

When someone quotes a number for PAE, remember that it only occurred at a specific drive level. Lower or higher drive will almost assuredly mean lower efficiency. Note that communications amplifiers must operate in backed-off condition and are at a disadvantage in terms of efficiency compared to radar amplifiers which can operate in saturated condition.

Unless otherwise noted, assume we are talking about *solid-state* devices here. Also, note that the best solid-state devices (as of 2013) are based on GaN-on-silicon-carbide HEMT.

**L-band**

Silicon LDMOS devices are offered that achieve 60% drain efficiency, with GaN HEMT devices lately looking like they are even better. Run at Class E you can exceed 80% drain efficiency.

**X-band**

MESFET amplifiers with 10% bandwidth can exceed 30% efficiency at X-band. GaAs pHEMT amplifiers can exceed 40% PAE at X-band, GaN HEMT can break 50%. TWTs routinely deliver 60% efficiency.

**Ku-band**

**Wideband**

The more bandwidth, the lower the efficiency, because you just can't hit the best load over that much bandwidth. Distributed amplifiers are notoriously inefficient, because the devices don't all get the same voltage: some are ready to burn out and some are coasting!

A solid-state amplifier that works from 2-18 GHz will have less than 10% PAE.

**Ka-band**

You might read about Ka-band amplifiers that hit 30% efficiency on a good day, but don't expect to beat 20% with a COTS part.

**Q and W-band**

These frequencies, GaN HEMT has already hit 30% PAE at device level and close to 20% amplifier efficiency. COTS parts at these frequencies all suck, don't even go there.

**Author : **Unknown Editor