What is I/Q Data?

This tutorial is part of the National Instruments Measurement Fundamentals series. Each tutorial in this series, will teach you a specific topic of common measurement applications, by explaining the theory and giving practical examples. This tutorial covers brief overview and introduction to IQ Data as it relates to RF and wireless systems.

For the complete list of tutorials, return to the NI Measurement Fundamentals Main page or for more RF tutorials refer to the NI RF Fundamentals Main subpage.

Put in its simplest form, IQ data shows the changes in magnitude and phase of a sine wave. If changes in magnitude and phase of a sine wave are made in an orderly, predetermined fashion, one can use these magnitude/phase changes to encode information upon a sine wave, a process known as modulation.

Modulation is the process of changing a higher frequency signal in proportion to a lower frequency signal. The higher frequency signal is referred to as the carrier signal and the lower frequency signal is referred to as the message signal, information signal, or modulating signal. IQ data is highly prevalent in RF communications systems, and more generally in signal modulation, because of the convenience it provides in dealing with modulating signals. This discussion will cover the theoretical background of IQ data as well as practical considerations which make the use of IQ data in communication so desirable.

Background on Signals

Signal modulation involves changes made to sine waves in order to encode information. The mathematical equation representing a sine wave is as follows:

Figure 1: Equation of a Sine

If we think about possible parameters of a sine wave which we can manipulate, the equation above makes it clear we are limited to making changes to the amplitude, frequency, and phase of a sine wave to encode information. Frequency is simply the rate of change of phase of a sine wave (frequency is the first derivative of phase), so these components of the sine wave equation can be collectively referred to as the phase angle. Therefore, we can represent the instantaneous state of a sine wave with a vector in the complex plane containing magnitude (amplitude) and phase coordinates in a polar coordinate system.

Figure 2. Polar Representation of a Sine Wave

In the graphic above, the distance from the origin to the black point represents the magnitude of the sine wave, and the angle from the horizontal axis represents the phase.  Thus, the distance from the origin to the point will remain fixed as long as the amplitude of the sine wave is not changing (modulating). The phase of the point will change according to the current state of the sine wave. For example, a sine wave with a frequency of 1 Hz (2π radians/sec) will rotate counter-clockwise around the origin at a rate of one revolution per second. If the amplitude is unchanged during this time, you can imagine a circle around the origin with radius = Magnitude along which the point will travel at a rate of one cycle per second.

Since phase is a relative measurement, imagine for a second if the phase reference used is a sine wave of frequency equal to the sine wave that is being represented by the magnitude and phase points. If the frequencies of the reference sine wave and the sine wave being plotted are the same, then the rate of change the phase of the two signals experience will be the same, and the rotation of the sine wave around the origin will become stationary. In this case, a single magnitude/phase point can be used to represent a sine wave of frequency equal to the frequency of the reference. Any phase rotation around the origin would indicate a frequency difference between the reference sine wave and sine wave being plotted. We will return to this point later.

Up to this point, we have been talking about magnitude and phase data in a polar coordinate system. All the concepts discussed above apply to IQ data, and in fact, IQ data is merely a translation of magnitude and phase data from a polar coordinate system to a Cartesian (X,Y) coordinate system. Using simple trigonometry, we convert our polar coordinate sine wave information into Cartesian I,Q sine wave data. These two representations are equivalent and contain the exact same information, just in different forms.

Figure 3. I and Q Represented in Polar Form

Here is a screenshot of a LabVIEW example showing the relationship.

[+] Enlarge Image

Figure 4: Screenshot of IQ Data in LabVIEW Example

IQ Data in Communication Systems

At this point, we have covered technically what IQ data is, but this does not explain anything about why IQ data is used. In order to help explain this, let us first cover some basics about modulation.

RF communication systems use advanced forms of modulation to increase the amount of data that can be transmitted in a given amount of frequency spectrum. Modulation of signals can be broken down into two broad categories: analog modulation and digital modulation. In these terms, the word 'analog' or 'digital' refers to the data being modulated onto a sine wave. If analog audio data is modulated onto a carrier sine wave, then this is referred to as analog modulation. If analog audio data is sampled by an Analog to Digital Converter (ADC) with the resulting digital bits modulated onto a carrier sine wave, this is digital modulation since digital data is being encoded. Both analog modulation and digital modulation are performed by changing the amplitude, frequency, or phase (or combination of amplitude and phase simultaneously) of a carrier sine wave according to the message data.

AM (amplitude modulation), FM (frequency modulation), or PM (phase modulation) are all examples of analog modulation.  With amplitude modulation, the amplitude of the carrier sine wave is modulated according to the message signal. The same goes for frequency and phase modulation.

Figure 5. Time Domain of AM, FM, and PM Signals

Figure 5 represents various analog modulation techniques being applied to a carrier signal. In the AM case, the message signal is the dashed sine wave that forms the 'envelope' of the higher frequency carrier sine wave. In the FM case, the message data is the dashed square wave.  As the figure illustrates, the resulting carrier signal changes between two distinct frequency states.  Each of these represents the high and low state of the message signal. If the message signal were a sine wave in this case, there would be a more gradual change in frequency much more difficult to see with the naked eye. In the PM case, notice the distinct phase change at the edges of the dashed square wave message signal.

Applying this to the earlier discussion, if only the magnitude of the carrier sine wave is changing with respect to time (proportional to the message signal) as is the case with AM modulation, we should see changes in the IQ plane only with respect to the distance from the origin of the IQ points. This is evidenced by the following image:

Figure 6. IQ Data in the Complex Domain

Here we see the IQ data points varying in magnitude only, with the phase fixed of 45 degrees. We cannot tell from this plot the nature of the message signal - only that it is amplitude modulated. However, if we can see how the IQ data points vary in magnitude with respect to time, we can essentially see a representation of the message signal. Using LabVIEW's 3D graph control, we can show the third axis of time to illustrate this.

Figure 7. Representation of Magnitude vs. Time

The image above is the same data as the 2D I vs. Q plot above it. The magnitude of the signal trace is modulating in a sinusoidal pattern indicating that the message signal is a sine wave. The green trace represents the magnitude and phase data in a polar coordinate system, while the red traces represent the projections of this waveform onto the I and Q axes, representing the individual I and Q waveforms.

We can show the same type of example using PM. Here is an image of the same message signal sine wave using PM modulation instead of AM modulation.

Figure 8. Polar Representation of Phase vs. Time

Once again, we can tell that the message signal is PM modulated as the magnitude is constant but the phase is changing (modulating). We cannot tell what the shape of the message signal is with respect to time, but we can tell the minimum and maximum signal levels of the message signal are represented by phase deviations of -45 degrees and +45 degrees respectively.

Once again, let us pull out the time axis to better understand this concept.

Figure 9. 3D Representation of Phase Modulation

The image above shown in the LabVIEW 3D graph shows the green trace varying in a sinusoidal fashion with respect to time. The projections onto the I and Q axes represent the individual I and Q waveforms corresponding to the PM modulated sine wave with fixed magnitude and oscillating phase.

In essence, the IQ data represents the message signal. Since the IQ data waveforms are Cartesian translations of the polar magnitude and phase waveforms, it is not easy to visually tell what the nature of the message signal is from the IQ data. To illustrate this, compare the red I and Q traces on the 3D I vs. Q plots above to the green trace. If we plotted magnitude vs. time for the AM modulated sine wave, we would be displaying the message signal. If we plotted the phase data vs. time for the AM modulated sine wave, we would have a straight line. We would see sine waves for the I vs. time and Q vs. time waveforms as well, but the scale would be off, and this would not necessarily be the case for more complex digital modulation schemes where both magnitude and phase are modulated simultaneously.

So Why Use IQ Data?

Thus far we have discussed what IQ data is, but not why it is used. Since magnitude and phase data seem more intuitive, it would seem that we should use polar magnitude and phase data instead of Cartesian I and Q data. However, practical hardware design concerns make I and Q data the clear cut choice in this matter.

It is difficult to precisely vary the phase of a high frequency carrier sine wave in a hardware circuit according to an input message signal. A hardware signal modulator that manipulated the magnitude and phase of a carrier sine wave would therefore be expensive and difficult to design and build, and as it turns out not as flexible as a circuit that uses I and Q waveforms. To understand how we can avoid having to manipulate the phase of an RF carrier directly, we first return to trigonometry.

Figure 9. Mathematical Background of IQ Modulation

With the trig identity shown in line 1 above, we can multiply both sides of the equation by A and substitute 2πfct in place of alpha and Φ in place of beta to arrive at the equation shown in line 2. By then substituting I in place of A Cos (Φ) and Q in place of A Sin (Φ), we can represent a sine wave with the equation shown on line 3. One final observation to be made is to remember that a sine wave and a cosine wave of the same frequency are exactly the same, except for a 90 degree phase offset between them. The implications of this are very important. What this essentially means is that we can control the amplitude, frequency and phase of a modulating RF carrier sine wave by simply manipulating the amplitudes of separate I and Q input signals! With this method, we no longer have to try to directly vary the phase of an RF carrier sine wave. We can achieve the same effect by manipulating the amplitudes of input I and Q signals. Of course, the second half of the equation is a sine wave and the first half is a cosine wave, so we must include a device in the hardware circuit to induce a 90 degree phase shift between the carrier signals used for the I and Q mixers, but this is a much simpler design issue than the aforementioned direct phase manipulation.

Figure 9. Hardware Diagram of an IQ Modulator

Here is a block diagram of an IQ modulator. The circles with an 'X' in them represent mixers, devices that perform frequency multiplication and either upconvert or downconvert signals (upconverting here). The IQ modulator mixes the I waveform with the RF carrier sine wave, and mixes the Q signal with the same RF carrier sine wave offset by 90 degrees in phase. The Q signal is subtracted from the I signal (just as in the equation shown in line 3 above) producing the final RF modulated waveform. In fact, the shifting of the carrier by 90 degrees is the source of the names for the I and Q data - I refers to in-phase data (since the carrier is in phase) and Q refers to quadrature data (since the carrier is offset by 90 degrees). This technique is known as quadrature upconversion and the same IQ modulator can be used for any modulation scheme. This is because the IQ modulator is merely reacting to changes in I and Q waveform amplitudes, and I and Q data can be used to represent any changes in magnitude and phase of a message signal. The flexibility and simplicity (relative to other options) of the design of an IQ modulator is the reason for its widespread use and popularity.

Related NI Hardware

Customers interested in this topic were also interested in the following NI products:

• NI RF & Communications Platform
• NI Signal Generators
• NI High-Speed Digitizers
• NI RF Switch Hardware
• NI Spectral Measurements Toolkit Software
• NI Modulation Toolkit Software 
   

Conclusions

This document is meant to provide a brief overview and introduction to IQ Data as it relates to RF and wireless systems. For the complete list of tutorials, return to the NI Measurement Fundamentals Main page or for more RF tutorials refer to the NI RF Fundamentals Main subpage.

Reader Comments | Submit a comment »

Simple and clever
I'm a telecoms engineer who almost forgot where the hell the I/Q come from! With this simple and clever explanation its better to remember.
- Jun 18, 2008

Excellent!
Great explanation...better than most texts!
- Andy Knitt, Caterpillar, Inc.. knitt_andrew_a@cat.com - Apr 16, 2008

Wow, finally I understand
Great explanation! As a mechanical engineer, I've been trying to understand this EE principle forever. Now I do.
- Trey, Northrop Grumman. - Mar 22, 2008

Excellent easy to understand
I train electronic technicians for the AF and trying to explain many concepts like !/Q, FFT, and digital mod types is often difficult at best. Your text and supporting images are thorough yet simple enough that even I can understand. Now I have some great basics to use in describing these principles to new technicians.
- Feb 21, 2008

I am a student of Texas A & M ,very simple to understand.
- saikrishna. saikrishna1985@tamu.edu - Feb 9, 2008

IQ is now clear for me!
Many thanks for the clear explanation of IQ signals! Rudolf
- Rudolf, hb9ari. hb9ari@bluewin.ch - Jun 27, 2007

Concise
I enjoyed the clarity, simplicity and lack of vocab words. This is the first clear explanation of IQ I have seen. RF engineering need not be "black magic".
- Garry Garrett, IntelliServ. garry.garrett@intelliserv.net - Jun 21, 2007

Perfect explaination with practical application
This is very good explaination of pratical concern..why it is used.. no jorgan in understanding this
- Murali, CDOT. muralipv@cdotb.ernet.in - Apr 27, 2007

Perfect explaination with practical application
This is very good explaination of pratical concern..why it is used.. no jorgan in understanding this
- Murali, CDOT. muralipv@cdotb.ernet.in - Apr 27, 2007

Extremely good explanation. Thank you
- sinnagiri@yahoo.com - Apr 8, 2007

Very clear, useful and helpful
It just saved my day.... and night~!
- Evean, University of Toronto. - Apr 3, 2007

Keep up the Good Work..
very simple and intuitive...
- Rudheesh - Feb 24, 2007

Very clear explanation.
- Jan 24, 2007

Trig identity omitted
Minor quibble: In Figure 9, you omitted the trig identity referred to as "line 1" in the text, i.e. cos(alpha+beta)=cos(alpha) cos(beta) - sin(alpha)sin(beta). Also, you didn't number the lines referred to in the text as lines 2 and 3. But very enlightening all the same!
- leland.j.moody@l-3com.com - Jan 18, 2007

EXCELLENT!!!!!!!
It took me 30 minutes only to understand IQ !!! And before that I wasted one complete week .
- sandeep_csc@yahoo.com - Dec 7, 2006

Clear, Consise, perfect summary
Pictures / graphs always help better your understanding. I am a novice on RF principles. This tutorial on I/Q mod/demod is as good as one can make for a beginner.
- Prakash, NEC. pmanivanan@yahoo.com - Dec 7, 2006

Finally any excellent and simple description of what I/Q data is!
For the first time, i finally understood what I/Q means!
- Nov 19, 2006