# Confronting Measurement Uncertainty in Signal Generation - Part 4: I/Q Impairments

2019-05-23  |  9 min read

In previous posts, I discussed the source of errors in a baseband generator and strategies for eliminating these errors such as waveform phase discontinuity, interpolation overshoot, and sampling images. In this post, I will discuss an I/Q modulator and the common errors result from an I/Q modulator.

## I/Q Modulation

The baseband generator output I/Q signals travel to the I/Q modulator and upconvert to an intermediate frequency (IF) and RF signal. Before we combine the I (in-phase) and Q (quadrature) signals, the I and Q signals mix with the same local oscillator (LO) but we place a 90-degree phase-shifter in one of the LO paths, as shown in Figure 1.

Figure 1. A simplified block diagram of a vector signal generator

This 90-degree phase shift makes the I and Q signals orthogonal to each other, so they do not interfere with one another. The I/Q combined signal is a composite output signal. At the receiver side, we can use the same LO and place a 90-degree phase shifter in one of the LO paths to break the composite signal into its original I and Q components.

## What Is I/Q Diagram?

An I/Q diagram is a representation of the I/Q composite output vector signal. Figure 2 represents an I/Q diagram. The vector signal’s (the arrow) projection onto the I axis is its I component and the projection onto the Q axis is its Q component.

Figure 2. I/Q diagram

Figure 3 shows an I waveform (upper-right), a Q waveform (lower-right) and an I/Q diagram (left) for a QPSK modulation. The markers illustrate that the amplitude of I, Q, and the composite vector are 0.70, -0.71, and 1, respectively, at a specific time.

Figure 3. I (upper-right), Q waveform (lower-right), and I/Q diagram (left) of QPSK modulation

You may notice that the amplitude of I, Q, and the composite vector for an ideal QPSK modulation should be 0.707 (root square of 2), -0.707, and 1 which are different from what we measured above. We will discuss the common I/Q modulation errors and how to compensate for these errors.

## Baseband I/Q Impairments

I/Q impairments leading to measurement uncertainty can result from unmatched components in the separate I and Q signal paths.

### I/Q Gain Imbalance

Baseband generator outputs and amplifies I and Q signals independently. Inequality of the gain between the I and Q paths results in incorrect positioning of each symbol in the constellation. I/Q gain imbalance compares the gain of the I signal with the gain of the Q signal, as follows:

IQGain Imb = IGain / QGain

I/Q gain imbalance is usually expressed as a logarithmic value (dB). Figure 4 shows a QPSK I/Q measured constellation diagram (upper-right), and an ideal QPSK constellation diagram (lower-right). The I/Q gain imbalance of this signal is 0.99 dB and error vector magnitude (EVM) is poor at 5.6%.

Figure 4. The signal is impaired due to IQ imbalance

### I/Q Quadrature Skew

If the phase shift between the LO signals that mix with the I and Q baseband signal at a modulator is not 90 degrees, a quadrature error occurs. Figure 5 shows a demodulated QPSK signal which has a 5-degree quadrature error, a result of the I and Q channels not operating orthogonally. The measured I/Q constellation diagram (upper-right) shows the constellation diagram shaped into a parallelogram, either I axis or Q axis shifted by 5 degrees. The error summary (lower-left) reports that the quadrature error is -4.9 degrees and EVM is poor at 4.2%.

Figure 5. The signal is impaired due to IQ quadrature skew error

### I/Q Offset

The I/Q offset (also called I/Q origin offset) indicates the magnitude of RF carrier feedthrough signal or baseband DC offsets. Figure 6 illustrates a QPSK signal without an I/Q offset (left) and with an I/Q offset (right). The red arrow is an I/Q origin offset. The I/Q offset is the ratio of the magnitude of the red vector and green vector in dB.

Figure 6. I/Q origin offset in the constellation diagram

Figure 7 shows a demodulated signal with an I/Q offset. The I/Q measured constellation diagram (upper-right) has removed the I/Q offset, but the I/Q offset measurement reports -22.3 dB in the error summary (lower-right).

Figure 7. The signal is impaired due to IQ offset

### I/Q Timing Skew

The modulator, digital-to-analog converter (DAC), or different electrical lengths in the I and Q paths can all cause an unwanted delay between I and Q signals. The diagram to the far left of Figure 8 shows the QPSK I and Q signals and the constellation diagram. The I and Q signals are timing aligned, and the symbols are at corners. The diagram to the far right of Figure 8 shows the Q signal has a timing shift. The I/Q symbols change their position and the I and Q signals are effectively no longer in quadrature. The effects become serious when the signals have wide bandwidths (high symbol rates).

Figure 8. Example of I/Q timing skew

Learn about how to identify the most common impairments in transmitter designs “Testing and Troubleshooting Digital RF Communications Transmitter Designs

## Baseband I/Q Adjustments

Baseband I/Q impairments can occur in a baseband generator, an I/Q modulator, and an RF section. It is not always necessary or desirable to minimize I/Q impairments. Some applications and tests require a specific amount of impairment to accurately simulate the signal, or for tolerance testing.

Vector signal generators allow you to use I/Q Adjustments to compensate for or add impairments to the I/Q signal. Table 1 is a summary of I/Q effects and impairments available through I/Q Adjustments.

Table 1. Baseband I/Q adjustments

## Baseband I/Q Calibration

I/Q calibration routines compensate for measurement uncertainty resulting from calibration drift related to temperature changes, including I/Q offset, gain, and quadrature skew. When you perform I/Q calibration, that calibration data takes precedence over factory-supplied calibration data.

I/Q calibration routines allow you not only to correct the impairments of the internal baseband generator, but also the external I/Q input signals. You can select the instrument’s entire frequency, or specify the calibration start and stop frequencies to shorten the calibration period.

Run an I/Q calibration when ambient temperature and the latest calibration temperature have changed by more than ±5 degrees Celsius.

## Summary

I/Q offset, gain, quadrature skew, and timing skew are common errors in an I/Q modulator and degrade modulation quality. To simulate a test signal, a signal generator needs to output a clean modulation signal for component and receiver tests and allows you to adjust I/Q impairments in order to characterize the devices under test.

In my next post, I will discuss a key specification – phase noise – which is critical for most test applications.

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