# Performing I-Q Measurements Using the PXI-5660

Publish Date: Sep 06, 2006 | 11 Ratings | 3.18 out of 5 |  PDF

### 1. What is I-Q?

A sinusoidal wave of the form f(t) = r*cos(wt +q) can be represented in terms of its In-phase (I) and Quadrature-phase (Q) components, where I(t) = r*cos(q)*cos(wt) and Q(t) = r*sin(q)*sin(wt), and f(t) = I(t) - Q(t). These two components are orthogonal and hence do not interfere with each other.

Figure 1. I-Q Representation of a Sine Wave at Time (t) = 0

Figure 1 shows the I-Q representation of the sinusoidal wave f(t) = r*cos(wt + q) at time t = 0. The magnitude of the vector Q is given by the following equation:

Mag = Sqrt ((I * I )+ (Q * Q)) = r

The phase of the vector Q is given by the following equation:

Phase = arcTan (Q / I) = q

The speed at which the vector rotates around the circle is the frequency of the sine wave. I-Q representations are typically used in digital communications where the amplitude, phase, frequency, or a combination of two of these characteristics, is modulated (varied) to transmit the information signal. I-Q representation provides an effective way to visualize and measure the quality of modulation.

### 2. How Does the PXI-5660 Compute I-Q?

The RF Signal Analyzer (RFSA) consists of the PXI-5600 RF downconverter module, the PXI-5620 IF digitizer module, and the Spectral Measurements Toolkit (SMT) software. The PXI-5620 has an onboard Harris digital downconverter (DDC) chip. The digital downconversion process consists of the following three steps shown in Figure 2 below.

Figure 2. Main Steps in the Digital Downconversion Process
• Modulation: Shifts the spectral region of interest to baseband, where it is centered around DC
• Filtering: Applies a lowpass anti-aliasing filter to remove any higher frequency components
• Decimation: Decimates or downsamples the data by a certain factor M. The effective sample rate is now reduced to fs/M, thus resulting in fewer samples and faster processing.

The SMT provides an efficient software implementation of these three steps. It also performs a Fast Fourier Transform (FFT) on the reduced sample rate data to produce a zoomed spectrum. This process is called the continuous zoom FFT technique.

Figure 3. Conditions Which Determine Hardware or Software Downconversion

Figure 3 shows the conditions in which the hardware or software implementation of the downconversion process is used.

### 3. Configuring the RFSA for I-Q measurements

You can configure the RFSA for I-Q measurements in one of two ways:
• Spectral characteristics: You can configure the RFSA in terms of spectral characteristics, such as center frequency, span and resolution bandwidth (RBW). Other advanced configurable parameters include window type, number of spectral lines and RBW definition. Use these configuration settings if you are interested in the zoomed FFT and the I-Q data corresponding to the FFT. These configuration functions are available in the SMT.
• Time-domain characteristics: You can configure the RFSA by specifying the center frequency, filter bandwidth and time duration for which you want to acquire data. Other advanced parameters that you can specify include stopband attenuation for the filter, and oversampling ratio. The product of the oversampling ratio and the filter bandwidth determine the measurement span. These configuration functions are available in the NI Modulation Toolkit 1.0. Please contact National Instruments for more information.

### 4. Displaying the I-Q data

You can view the I-Q data in rectangular coordinates as I and Q data, or in polar coordinates as magnitude and phase. The phase measurements are with reference to the 10 MHz reference clock. You can either use the 10 MHz clock onboard the PXI-5600 or use an external clock source as the reference clock. If the signal source and clock are locked to each other, you will observe a stable I-Q plot resembling Figure 4.

Figure 4: I-Q plot of a QPSK Signal Measured Using the PXI-5660 RF Signal Analyzer

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