How can I quantify a device’s nonlinearity? part 1

You can specify nonlinearity in parts per million or, especially for RF components, in terms of the 1-dB compression point or third-order intercept point.

A recent series on intermodulation described how a nonlinear component can introduce frequencies that differ from the frequencies of any input signals. We looked at how intermodulation can be useful or troublesome, and we examined what frequencies get created given specific input frequencies.

What we didn’t do was quantify nonlinearity. Is there a nonlinearity data-sheet spec?
You’ll find several. First, In Figure 1, the blue line represents a circuit’s ideal linear response, while the red line represents measured response. We can draw lines (dotted lines in the figure) parallel to the linear response that bound the actual response and then calculate the nonlinearity as a function of the full-scale output. In this exaggerated representation, the nonlinearity is ±10%. For a high-quality op amp operating in the linear region, nonlinearity would be measured not in percent but parts per million (ppm).

Nonliearilty — Figure 1. Nonlinearity can be expressed in percent or, more likely, ppm.

Amplifier gain shift — Figure 2. Gain gradually shifts from high at low input levels to low at high input levels.

Q: Are there drawbacks to this spec?
A: It leaves out potentially useful information. In Figure 2, the nonlinearity spec remains ±10% as in Figure 1, but the actual response (red curve) looks much different from that of Figure 1. The hint of a staircase in Figure 1 suggests that a digital-to-analog converter might be involved, with quantization error contributing to the nonlinearity. In Figure 2’s response, the gain appears linear at low input levels, but it begins decreasing as the input increases — an effect known as gain compression. These differences might not affect your design, and a ppm spec might be all you need.

1 db compression point — Figure 3. The actual response falls exactly 1 dB below the ideal response at the 1 dB compression point.

Q: When might we care more about the shape of nonlinearity?
A: It’s particularly important in RF devices. Figure 3 shows a typical response for an RF power amplifier, with input and output levels specified in decibels relative to one milliwatt (dBm). The solid blue trace shows the ideal response and the solid red curve shows the actual response. At low input-power levels, the actual output characteristic tracks the ideal linear response, with a gain equaling 12 dB. When the input climbs above about -7 dBm, however, the gain begins decreasing, dropping to about 8.5 dB at the maximum input (that is, a -2 dBm input results in about a 6.5 dBm output) as gain compression occurs. At one input point, just below an input level of -5 dBm in Fig. 3, the actual output falls exactly 1 dB below the expected ideal output. This point is called the 1-dB compression point, abbreviated P1dB, and it serves as a useful figure of merit for RF devices. It can be referenced to either the input (IP1dB) or the output (OP1dB).

IP1dB and OP1dB could be difficult to locate accurately?
If you are using a modern vector network analyzer (VNA), it will probably measure the compression points automatically. If you are doing the measurements manually or are working with previously acquired data, it’s helpful to create a line that represents the ideal response minus one decibel (dashed blue line in Figure 4). That line intersects the red measured response curve right at the P1dB point, helping you quickly locate OP1dB and IP1dB and minimizing the chance of misinterpretation. In Fig. 4, OP1dB is 5.9 dBm and IP1dB -5.1 dBm.

Are there any other figures of merit for device nonlinearity?
The third-order intercept point, abbreviated IP3 or TOI, is an important spec for devices used in systems that have two or more input signals with different frequencies. We’ll take a closer look in part 2 of this series.