Antenna Performance

Antenna is a pretty huge topic and it would be difficult to describe every aspects of Antenna in a single page, but I would try to give some big pictures of various aspects of antenna mainly for cellular application.

Topics on this page are

What is Antenna ?

As you know, Antenna is a device which convert Electrical Engergy (Electrical Signal) into Electromagnetic Wave which is transmitted into space. That one sentence hides the two problems the rest of this page is about. The conversion is never perfect, so some of the energy is lost on the way out. And the wave does not leave equally in every direction, so where it goes matters as much as how much of it there is.

Dipole element at the centre of a sphere, converting electrical energy into an electromagnetic wave

The whole job in one picture. Electrical energy arrives at the element from below, and what leaves is an electromagnetic wave spreading outward into space.

The coloured sphere is the wave, not the antenna : the shading runs from red at the centre out to green at the edge, which is the energy thinning as it spreads.
The box at the bottom is the input : electrical energy reaches the element along a feed, and the element is the only place where the conversion happens.

There are various types of antenna out there, some of the examples are shown below. These are only some examples and there are a lot of other types as well. Just check how many of these you are familiar with.

Twelve antenna types labelled (a) to (l), from TV aerials and parabolic dishes to whips and cellular sector panels

Twelve antenna types, labelled (a) to (l). They differ enormously in size and shape, and every one of them does the same job.

Directional against omnidirectional shows in the shape : the parabolic dishes at (c) and (d) concentrate energy along one axis, while the whips at (e) and (f) radiate around themselves.
The panels and tower arrays are the cellular case : a sector antenna is built to cover a wedge of ground rather than a full circle, which is why it is flat rather than round.

Now in most of mobile communication devices, antenna are embedded in a small space. In a relatively older type of mobile phone, you might have seen the antenna shown at the left side of the picture (whip antenna). In most of the mobile devices you see these days, the antenna is embedded within the case or right on the PCB as shown below. As a mobile device (e.g, smart phone) gets more and more technologies (e.g, cellular technology with various band/radio access technology, bluetooth, WiFi etc) within a device, it is getting tougher and tougher to design multiple antenna and put them into a smal space).

External whip antennas, internal antenna carriers, and a phone chassis annotated with six internal antennas

The same job, done six times over inside one handset. Panel (c) is annotated with what each internal antenna is for, and that crowding is what this section describes.

Panel (a) is the antenna you can see : two older handsets with an external whip, one extended and one stubby.
Panel (b) is the antenna you cannot : three internal antenna carriers, each a stamped metal pattern on a moulded plastic frame.
Panel (c) names six antennas in one phone : the labels read GPS Antenna Rx Only, 2.6 GHz WiMAX Tx/Rx Ant, 2.6 GHz WiMAX Ant Rx Only, WiFi/BT Tx/Rx Ant, Cell/PCS CDMA/EVDO Ant Rx Only and Cell/PCS CDMA/EVDO Tx/Rx.
Three of the six are receive only : the labels ending in Rx Only are what a diversity receive path or a GPS receiver needs, and neither one requires a transmit chain of its own.

How to represent Antenna Performance ?

There are two major criteria to evaluate Antenna Performance as follows. Both are written from the antenna designer's point of view, and they are not the same question. The first is about loss and the second is about direction, and no single number covers both.

i) I should convert Electrical Engergy into Electromagnetic Energy with as little loss as possible.

ii) I should be able to transmit the converted electromatic engergy as much as possible only to the direction that I want.

There are several indicators to represent the performance of an antenna as follows.

Those four indicators do not each answer both criteria, and knowing which one answers which saves a lot of confusion later on.

Indicator	Criterion	What it measures	What it costs to measure
Radiation Pattern	ii)	The shape of the radiated energy in space. It is a plot rather than a single number.	A chamber, and a measurement at many angles.
Antenna Gain	i) and ii)	Energy in the best direction against an isotropic reference. Efficiency enters through E and direction through D.	A chamber, or a figure taken from the pattern.
Total Radiated Power	i)	How much energy actually leaves the device, summed over the whole sphere.	A chamber, and a measurement at every grid point.
Total Isotropic Sensitivity	i)	The same sum on the receive side, expressed as a sensitivity.	A chamber, and a measurement at every grid point.
S11	i)	How much energy comes back out of the input port instead of going into the antenna.	A network analyser and a minute.

One practical point runs through that table. Answering criterion ii) properly takes the expensive measurements, because they need a chamber and a reading at every point on a sphere. That is why S11 is used so widely even though it answers only criterion i).

Criterion i) is about loss : TRP, TIS and S11 all ask how much energy survives, in one form or another.
Criterion ii) is about direction : only the radiation pattern answers it fully, and gain answers it as a single number.
Gain sits across both : that is what makes it useful and also what makes it easy to misread.

Radiation Pattern

The first step to understand/evaluate the performance of an antenna is to check the radiation pattern of the antenna. Electrical energy flows through a predefined path in most case built in a copper cable or copper trace on PCB, but once the energy is converted into electromagnetic wave, it propagate into the air almost in every direction. Depending on how we design the antenna, the direction in the air in which electromagnetic wave propagate varies. In some direction, the antenna transmit very strong energy and in some direction it transmit small amount of energy and in some direction it transmit the medium range of energy etc. This kind of engergy transmission pattern is called 'Radiation Pattern'. (For more practical example of Radiation Pattern, refer to http://rcexplorer.se/Educational/gain/gain.html )

Following is only some example of possible radiation pattern. In reality, you can think about almost infinite number of different pattern. The goal of antenna design is to make it so that it transmit the energy in the pattern that I want without any energy loss during the conversion from electrical energy to electromagnetic engergy.

In reality, the signal radiate into 3 Dimensional Direction as illustrated (b) in the following figure. However, it is not always easy to represent the propagation patterns in 3D and sometimes it is even harder to estimate the energy propagation quantatively when it is plotted in 3D. So in many case, we cut through the 3D pattern along a specific 2D plane as shown in (c) and (d). This plot came from Ref [7].

Antenna Gain(G)

Gain is the number most often quoted for an antenna, and it is also the one most often misread. Before the definition arrives, it is worth being clear about what the word does not mean here, because it suggests the opposite of what actually happens.

Personally I think the 'Antenna Gain' is a misleading term because

i) When we hear the term 'Gain', we usually think 'this device would amplify a signal to make it bigger energy'. But this is not true for Antenna. Most of Antenna is 'passive device' which does not amplify anything.

ii) When we think about Gain, the higher the gain is, the higher the total amount of energy coming out of the device is. But this may not be the true in Antenna case. Higher gain in Antenna may mean "Higher engergy transmitted in a certain direction', but it may not mean 'Total amount of energy coming out of the device'.

The definition of Antenna gain is the ratio of power transmitted in a certain direction to a certain reference point. This is usually expressed in dB, dBi or dBd. This is indicator to represent 'how well/efficiently the antenna transmit the energy in a specified direction'. Basic concept can be illustrated as follows. (For additional explanation, refer to http://rcexplorer.se/Educational/gain/gain.html )

Multi-lobe radiation pattern drawn over a green isotropic reference circle, with the main lobe reach marked against it

Gain is a comparison, and the green circle is the thing being compared against. The bracket at the bottom measures how much further the main lobe reaches than the isotropic reference does.

The green circle is imaginary : the annotation calls it a radiation pattern assuming the same power in every direction, and it exists only as the reference point for the calculation.
The lobes are the real pattern : one large lobe points right and several smaller ones point elsewhere, which is what a real antenna does with the same total energy.
The bracket is the ratio that matters : the annotation underneath names it as the most important factor in determining antenna gain, and it compares reach in the best direction against the reference.

Following is a rule of thumb propagation pattern for typical Gain values. As you see, as Antenna gain increases the direction of propagation gets more and more focused, it does not mean that the total transmission energy (the area surrounded by the ovals) gets higher.

Three overlapping radiation patterns labelled 3dB, 6dB and 9dB, getting longer and narrower as gain rises

Three gains drawn on the same axes. As the figure goes from 3dB to 9dB the lobe stretches further out and narrows at the same time, which is the point the paragraph makes about total energy.

Higher gain reaches further : the 9dB lobe extends well past the 3dB one along the same axis.
Higher gain is also narrower : the extra reach is paid for by everything the lobe no longer covers.
The enclosed area barely changes : no energy was added between the three curves, which is exactly why gain is not amplification.

If you want to know the methmatical definition for Gain, here you go.

Equations for directivity D, radiated power P_rad, and gain as G equals E times D

Three quantities and one relationship. Directivity comes from the pattern alone, efficiency comes from the losses, and gain is the product of the two.

D is directivity : 4 pi times U_max over P_rad. The figure annotates U_max as the amount of energy transmitted in the direction with the strongest power.
P_rad is the total radiated power : the double integral sums U over the whole sphere, annotated in the figure as the total amount of energy being transmitted in all directions. It is the same quantity TRP measures.
E is the antenna efficiency : the figure calls it a kind of energy conversion ratio, meaning how much of the electrical energy becomes electromagnetic energy.
G = E . D is the part worth keeping : gain folds both criteria of this page into one number. Directivity answers criterion ii) and efficiency answers criterion i).

That relationship explains the complaint at the start of this section. Directivity can be raised without adding any energy at all, simply by narrowing the pattern. So a high gain figure can mean a well made antenna, or it can mean a narrow one, and the number on its own does not say which.

In most case, Antenna Gain is expressed in logarithmic unit as follows.

The units matter as well, because gain is quoted in three of them and they are not interchangeable.

dB on its own is a bare ratio and names no reference. The unit dBi names one, gain relative to an isotropic radiator, and that is what the conversion above produces. The unit dBd names a different reference, a half wave dipole.

A lossless half wave dipole has a directivity of 1.64, which is 2.15 dBi. The two scales therefore differ by a fixed offset, and a figure in dBd becomes a figure in dBi by adding 2.15. A 9 dBd antenna and an 11.15 dBi antenna are the same antenna, described twice.

Gain is not amplification : the equation has no energy source in it. G rises when D rises, and D is only the shape of the pattern.
Efficiency is the only loss term : E is bounded by 1, so gain can never exceed directivity.
Always check the reference letter : dBi and dBd differ by 2.15 dB, and a datasheet that says only dB has not told you which.

Total Radiated Power (TRP)

It means as the term implies. It is 'sum of radiated power measured from all directions'. Simple definition of TRP can be illustrated as follows(Note : The sphere shown here is not the radiation pattern of the antenna. It is a 3 dimensional coordinate which is called 'spherical coordinate). I hope this is intuitive enough for you to get the idea without any further description.

There are two types of TRP, passive TRP and Active TRP. This classification comes from the different ways of measuring TRP. Actually it is related more to how to transmit the signal through the antenna.

In passive TRP, usually the DUT is the isolated antenna and the signal is fed directly to the antenna via the output port of a Network Analyzer (or output port of a signal generator) and measures the transmitted power through the input port of Network analyzer or input port of Spectrum Analyzer.

In active TRP, usually the DUT is the whole device including the antenna. For example, if it is for a mobile phone antenna measurement, we use the whole mobile phone as a DUT. The main purpose of Active TRP measurement is to see the performance of Antenna in real environment. In this case, you cannot use network analyzer or signal generator to transmit the signal through antenna. You have to use what most of people in this area calls a 'call box' which is basically a network simulator (e.g, eNodeB, NodeB, BTS simulator). We send the UE (e.g, mobile phone) a command 'send a signal with power XX dBm or max power' and measure the transmitted power using the 'call box' or 'spectrum analyzer'.

If you are more interested in formal expression, TRP can be represented as follows. If you are interested in how this form is derived, this page would help you.

If you like formal expression but not familiar with the meaning of this expression, following comments may help you a little bit.

Now you might be more interested in TRP measurement as we are getting into 5G/NR. In TR 38.817-9.1.1.1, the TRP in NR is defined as follows. You see the equation is almost same as the one shown above. You see the new terminology called EIRP. In high level concept, you can take EIRP is a kind of power (not exactly same value as power, but it can directly derived from the measured power). Refer to EIRP page for further details.

In real measurement, the measurement is made at specific points across the whole surface of a spherical coordinate. So we need to convert this equation to a discrete form to get TRP from the real measurement.

If we do the measurement in a unitform grid on the coordinate, the equation can be as simple as follows :

If the measurement is made on the non-uniform grid on the coordinate system, the equation would be as follows :

The scaling factor in this case can be derived from the area of small rectangle at the measurement point and can be expressed as shown below.

If you want go even deeper into the details, then you would need to refer to your Calculus textbook or refer to my note on Surface Integral example. I strongly recommend you to try to understand the details of this equation and how this is derived. It would help you a lot to understand various mathematical expressions related to antenna theory.

For further reference of TRP. Refer to http://www.antenna-theory.com/definitions/trp.php

Total Isotropic Sensitivity (TIS)

First you may ask "What does 'Isotropic'mean ?" If you look into a dictionary or google it, you would find a definition like "Identical in all direction". TIS means "Sensitivity at every direction based on assumption that the antenna is Isotropic(radiate/receive in the same strength in all direction)". In reality, there is no such an antenna that is purely isotropic. More practical meaning of TIS can be illustrated as below(Note : The sphere shown here is not the radiation pattern of the antenna. It is a 3 dimensional coordinate which is called 'spherical coordinate). As you see, you measure the sensitivity at every point at the intersection of a spherical grid. you wille have the different measurement result at all of those points in reality. If you take the average of those measured value, you will get a single value which indicate the TIS

Spherical measurement grid with sensitivity measured at each intersection and averaged to give TIS

TIS is an average taken on the receive side. The sensitivity is measured at every intersection of the spherical grid, and the single TIS figure is the average of all of them.

The sphere is a coordinate grid, not a pattern : the note in the paragraph above says the same thing, and it bears repeating because the picture invites the opposite reading.
The red dots are measurement points : each is labelled Sensitivity Measurement at this point, and the vertical dots stand for all the intersections that are not drawn.
Take Average is the whole operation : the brace at the bottom collapses every measured value into the single number marked TIS in red.

Two properties follow from that average, and both surprise people the first time.

The first is the direction of goodness. TIS is a sensitivity, so it is a power level in dBm and a lower number is the better one. A TIS of -100 dBm beats a TIS of -95 dBm. That is the opposite of TRP, where higher is better, and the two figures usually sit next to each other on the same test report.

The second is that TIS is the receive counterpart of TRP, measured the same way and in the same chamber. TRP asks how much energy the device manages to get out. TIS asks how weak a signal it can still hear, averaged over every direction the signal might arrive from. A device can pass one and fail the other, because the transmit and receive paths do not share all of their hardware.

Lower TIS is better : it is a sensitivity in dBm, so the more negative figure wins.
TIS and TRP are a pair : same chamber, same grid, opposite direction of travel.
The average hides the worst angle : a single bad direction is diluted by every good one, which is why the radiation pattern is still worth having.

For further reference of TIS. Refer to http://www.antenna-theory.com/definitions/tis.php

Effective Isotropic Radiated Power/Equivalent Isotropic Radiated Power(EIRP)

As you see the descriptions above, most of the antenna performance parameters like Gain / TRP / TIS are based on the measurement across the whole surface and some additional processing afterwards, but EIRP is a measurment showing a performance at a specific point only (i.e, the measurement at a specific angle (Phi, Theta).

NOTE : When I say the Measured Power in above figure, it does not mean the absolute power (in dBm), it is a kind of relative power with reference to istropic power. That's why is is called Equivalent Isotropic Radiated Power. This is calculated from a couple of different parameters that can directly be measured or just given. As you see in the above figure, to accurately specify a EIRP you need to indicates the specific measurement angle. However, in many cases the term EIRP is used without specifying any specific measurement angle. In this case, it is assumed that the measurement angle is the angle where the maximum EIRP is obtained. For example, if we say EIRP of the antenna shown above without specifying any specific angle, it would me the EIRP measured at theta = 0, phy = 0. When we assume the EIRP at the max value, it can be calculated as follows :

EIRP = Tx RF Power(dBm) + G(dB) - L(dB)

Tx RF Power :RF power measured at RF connector of the unit

G :Antenna gain

L : Feeder loss(cable loss or any other loss)

S11

S11 is the cheap measurement on this page, and that is why it is used everywhere. It answers only one of the two criteria, but it answers that one in seconds with a network analyser instead of in hours in a chamber.

In order to evaluate the antenna performance, we need to exactly measure the following items.

i) How much power (energy) is transmitted through the antenna without bouncing back to the input port.

ii) How much power (energy) is transmitted in the direction that I want

iii) How much weak power can be received by the antenna

Actually if you get the exact measurement for item ii) and iii), you don't need to measure item i), but to get accurate assessment for item ii) and iii), you have to perform TRP and TIS measurement as explained above. However, Measuring TRP and TIS is very expensive and time consuming. Therefore, we need some quick and simple method to evaluate the antenna performance which is to measure item i) listed above. The most common method for item i) would be to measure S11.

Since S11 shows how much energy is bounced back at the input port, the low S11 means that less energy is bounced back, implying that higher energy gets transmitted through the antenna. (Note : S11 just give you an idea of how much energy gets transmitted, but it does not give you any information on which direction the energy is transmitted. )

The number itself needs some explanation, because three different quantities describe the same reflection, and RF datasheets move between them without warning.

S11 is a reflection coefficient. As a magnitude it is the fraction of the voltage wave that comes back, and in dB it is negative, because less comes back than went in. Return loss is the same figure with the sign flipped, so an S11 of -10 dB is a return loss of 10 dB. VSWR writes it a third way, as a ratio that starts at 1 for a perfect match and grows as the reflection grows.

What matters in practice is the power, and the reflected power fraction is the square of the reflection coefficient magnitude. The numbers work out as follows.

S11 (dB)	Return loss (dB)	VSWR	Power reflected	Power delivered
-3	3	5.85	50.1 %	49.9 %
-6	6	3.01	25.1 %	74.9 %
-10	10	1.92	10.0 %	90.0 %
-14	14	1.50	4.0 %	96.0 %
-20	20	1.22	1.0 %	99.0 %

The -10 dB row is the one most often used as a working pass mark for a handset antenna. It is not a specification, and different programmes set the bar in different places, but it is a useful anchor. At -10 dB a tenth of the power is coming back and nine tenths is getting through.

Two warnings belong with that table. S11 says nothing about where the energy goes once it has left the port, which is the point the paragraph on direction already makes. And a low S11 does not by itself prove a good antenna, because a lossy structure can absorb the energy as heat, and heat does not come back either. A 50 ohm resistor has an excellent S11 and radiates nothing at all.

S11, return loss and VSWR are one measurement : the same reflection written three ways, so convert rather than measure again.
Power goes as the square : an S11 of -6 dB sounds close to -10 dB, and it reflects two and a half times as much power.
A good match is not a good antenna : a perfectly matched load radiates nothing, and S11 cannot tell the difference.

Dynamic Antenna Matching

(As of Apr, 2013) I think Automatic tunning of Antenna Matching circuit is becoming a hot topic especially in mobile phone industry and think it will be a pretty common technology in near future. If you google the keywords like "Automatic Antenna Tuner","Dynamic Antenna Tuning" etc, you will find various articles, papers and patents about various tuning technology.

Basic Idea on this technology is pretty simple. (It does not tune th antennna itself, it tunes the matching circuit of the antenna).

For example, let's suppose that we have a simple Pi network type of matching circuit as shown below. (In real implementation, the matching circuit would be more complex.. but I wanted to use the simplest structure for easy understanding).

In conventional implementation, you would build as shown below. Build a circuit as follows, keep changing the values for each component until you get the best transmission of the antenna. You may find the proper values in a couple of hours if you are lucky. If you are in bad luck, you would have to spent several day-and-nights to find the proper value. If the target frequency of the antenna changes, you would have to repeat this process. and the predefined value may not always work best for all the individual antenna mass produced in the factory.

To solve the problems mentioned above, they came out with the concept of automatic (dynamic) tuning of the matching circuit. The baisc idea is as follows. Let's assume that we built a matching circuit with variable Inductors and variable capacitors. These variable components should not be one of those variable component you can purchase from local radio shack and set the value by rotating a knob by hand. They all should be set in electronic control to make this circuit work without human intervention. Now the tricky thing would be to find (or develope) the variable inductor and capacitors. And these variable device should operate with minimum energy (voltage, current) consumption. Currently, it would be a little bit easier to find variable capacitors than variable inductors.

Mainly due to availability of components and some other reasons, in most auto tuning circuit we use variable capacitors as shown below. Once you build a circuit, you may have to find proper values for these components for various situations and store those values in a lookup table and the control reflash the values from the lookup table according to the situation. In this case, how to construct the proper look up table for each situation would be a critical issue.

So far so good ?

May be, or may be not.

One of the problems for the technique described above would be that you cannot guarantee the predefined look up table would work for all the possible situations. The situation may change in a little bit different way than expected and the look up table cannot do any good job. One of the common solution for this kind of situation would be to apply a value and check the result and feedback the result to the tuning algorithm so that the algorithm can do more tunings. This approach (closed loop approach) can be illustrated as shown below.

References

[1] Wiki : Antenna

[2] AntennaTheory.com

[3] Effective Isotropic Radiated Power (EIRP)

[4] 3GPP TSG-RAN WG4 #80bis R4-167503 : BS Output power for NR

[5] EIRP Calculator

[6] Guidelines for Determining the Effective Radiated Power (ERP) and Equivalent Isotropically Radiated Power (EIRP) of a RF Transmitting System

[7] Some Common Antenna Radiation Patterns