How can I quantify a device’s nonlinearity? part 3

A higher third-order intercept point results in lower intermodulation products at any given input power level below compression.

In part 1 of this series, we discussed the 1-dB compression point as a figure of merit for device linearity. In part 2, we examined a circuit that adds two fundamental input signals of frequencies f₁ = 2 GHz and f₂ = 2.5 GHz. Because of nonlinearities, the circuit generates interference, predominantly in the form of low-side and high-side third-order intermodulation products at 2f₁ – f₂ and 2f₂ – f₁, respectively (Figure 1). The third-order intercept point, abbreviated IP3 or TOI, indicates how well a device limits this interference.

Figure 1. Third-order intermodulation products are predominant contributors to interference in this example, which represents an amplifier that adds two signals.

What exactly is IP3?

In part 2, we introduced an infinite power series that describes a nonlinear device output PO as a function of the input s. For Figure 1, the relevant terms are as follows:

P_O (S) = c₁s + c₃s³

Here, c₁s is our desired term (representing f₁ and f₂ in Figure 1), and c₃s³ represents the third-order intermodulation products. Note that the c₃s³ contribution to Po(s) increases linearly as input power increases, whereas the third-order intermodulation products’ contribution increases cubically. Consequently, even if the c₃s³ term is very small relative to c1¬s at low input-power levels, it will grow much faster as power increases. At some theoretical point, the c₃s³ term will equal c₁s. That point is IP3. Of course, we can’t reach IP3 in real life—the amplifier would go into compression first.

If we can’t reach IP3, how can we measure it?

We’ll extrapolate from the linear portions of the response curves. We can begin with a series of snapshots of the output spectrum at various input power levels, as shown in Figure 2. The trend lines connect the peaks of f₁ (blue) and 2f₁ – f₂ (red) until gain compression appears, at input levels of about -6 dBm for f₁ and -2 dBm for 2f₁ – f₂. (Because f₁ equals f₂ in magnitude and the low-side and high-side products equal each other in magnitude, we can ignore f₂ and the high-side product for this analysis.)

Figure 2. Six snapshots at successively increasing input power levels show increases in fundamental and intermodulation products.

Is IP3 where the blue and red lines intersect?

Right. If we’re working manually, we can read data off our signal source and spectrum analyzer and create a table such as the simplified version in Table 1.

Plotting the Table 1 data gives us the curves shown in Figure 3 on the left, where IP3 appears at the intersection of the extrapolation of the linear portions of the two curves. Figure 3 on the right zooms in on the region representing input power levels from 0 dBm to 12 dBm, showing IP3 as well as the 1-dB compression point P1dB. Like P1dB, IP3 can be referred to either the input (IIP3) or the output (OIP3). Here, IIP3 equals -2 dBm, and OIP3 equals 10 dBm.

Figure 3. IP3 occurs at the intersection of extrapolated dotted lines representing the first-order (blue) and third-order (red) curves.

Just to be clear, a high value of IP3 is good, right?

Right. Note that in Figure 4, the red line indicates an OIP3 of 10 dBm, while the orange line represents an OIP3 of 14 dBm. At any given input power level below compression, the higher OIP3 rating results in lower intermodulation products — for example, -22 dBm for the orange line vs. -14 dBm for the red line within the blue oval at an input power level of -10 dBm.