IQ Signals and IQ Modulation/Demodulation

The following application note provides an introduction to IQ signals and modulation.

1. On IQ Signals

A complex wave can be represented using two orthogonal value pairs, in the form of IQ signals. These two orthogonal numbers represent a complex waveform with a 90° phase relationship. The I stands for “in-phase” and Q stands for “quadrature”. In fact, a consine and sine wave are quadrature waveforms of each other.

We can say mathematically that our quadrature signal is represented as I*cos(2\pi f t) and Q*sin(2\pi f t), where by convention, the I is the amplitude of the in-phase and Q is the amplitude of the quadrature components. Figure 1 below shows this:

Figure 1: Basic IQ Signal (With I=Q=1)

1.1 Basics of IQ Modulation/Demodulation

The key to IQ modulation and demodulation is how we add quadrature signals for various modulation schemes. The block diagram below shows how adding I and Q works;

Figure 2: Adding Quadrature Signals

As an example, by simply adding the I and Q values together, by superposition, if we were to say I=1 and Q=1, then we’d have a new waveform in black shown below:

Figure 3: Adding the I=1 and Q=1 Signal

Figure 3: Adding the I=1 and Q=3 Signal

In general, if I or Q changes or varies, the result are changes in amplitude, phase and frequency modulation of the sum. Essentially as the I and Q vectors change, the magnitude of the vector sum changes. The GIF below shows how this works using a phasor diagram– another way to visualize IQ signals:

Figure 5: How Adding I (x-axis) and Q (y-axis) Changes with a Phasor Diagram

Now, knowing how the complex plane works, and making our IQ signal a function of time, we can see that IQ pairs can be represented by a famous formula, Euler’s formula:

{e}^{i2\pi f t}= cos(2\pi f t) + isin(2 \pi f t)

= I(t) + iQ(t)

And thus, we say the amplitude vector’s magnitude is given by:

A= \sqrt{(I^2 + Q^2)}

And the angle \theta between the I vector and the A vector is:

\theta= tan^{-1}(Q/I)

1.2 IQ Modulators/Demodulators

To control how the I and Q signals are modulated/demodulated, the use of a IQ modulator and IQ demodulator is needed, which essentially mixes an LO frequency from 0-90° with the I(t) and Q(t) signals, as shown in the following block diagrams:

Figure 6: IQ Modulator and Demodulator

2. Further Reading

For other resources on learning about IQ signals and modulation, see these links:

  1. All About Circuits: Frequnecy Modulation

  2. All About Circuits: Frequency Demodulation

  3. IQ Data for Dummies

3. Further Videos

Videos by user w2aew on Youtube are also very informative, and can be seen in the links below:

  1. #170 Basics of IQ Signals

  2. #171 IQ Signals Part II