### Introduction

Teledyne LeCroy oscilloscopes include the ability to measure the vector magnitude and phase of a quadrature-modulated signal using an X-Y display of the in-phase (I) and quadrature (Q) components. This is illustrated in Figure 1, where the absolute time cursor is being used to read the vector sum of the I and Q components of a circular 16 QAM signal.

#### Figure 1:

Using the absolute time cursor to measure the vector magnitude (radius=385mV) and phase (angle=44.5°) of a 16 QAM signal state on a vector (state transition) diagram

The cursor readouts of radius (vector magnitude) and angle (vector angle relative to the X-axis) appear below the X-Y display in the polar readout annotation fields. Note that the cursor also simultaneously measures the amplitudes of the I and Q components (shown as the lower reading in the trace descriptor boxes for channels 1 and 2).

Sometimes erroneous states appear in the vector or constellation diagrams and it is necessary to characterize them. Figure 2 shows an example of measuring the magnitude and phase angle of the incorrect state on a constellation diagram.

#### Figure 2:

Measuring the magnitude (218 mV) and phase angle (63.6°) of an error state

Using the relative time cursors, we can also measure the vector difference between the normal and error state. This is shown in Figure 3. This difference represents the error vector from the correct state phase and magnitude to the incorrect state. This direction is set by placing the reference cursor on the correct state location and the difference cursor on the incorrect state location. The magnitude of the error vector is 192 mV and the angle is -155.4°.

#### Figure 3:

Using the relative time cursors to measure the vector difference between the correct state (reference cursor ↓) and the error state (difference cursor ↑)

The same measurement can be made using the relative amplitude cursors. The advantage, in that case, is that the line cursors are often easier to see in complex displays.

Teledyne LeCroy oscilloscopes include cursors that operate in both normal and X-Y displays and include polar as well as Cartesian readouts of cursor locations. This permits direct measurement of vector error in communications systems using quadrature modulation techniques.