*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 *f _{1}* = 2 GHz and

*f*= 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 2

_{2}*f*–

_{1}*f*and 2

_{2}*f*–

_{2}*f*, respectively (

_{1}**Figure 1**). The third-order intercept point, abbreviated IP3 or TOI, indicates how well a device limits this interference.

**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) =

*c*

_{1}

*s*+

*c*

_{3}

*s*

^{3}

Here, *c*_{1}*s* is our desired term (representing *f _{1}* and

*f*in Figure 1), and

_{2}*c*

_{3}

*s*

^{3}represents the third-order intermodulation products. Note that the

*c*

_{3}

*s*

^{3}contribution to Po(s) increases linearly as input power increases, whereas the third-order intermodulation products’ contribution increases cubically. Consequently, even if the

*c*

_{3}

*s*

^{3}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

*c*

_{3}

*s*

^{3}term will equal

*c*

_{1}

*s*. 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 *f _{1}* (blue) and 2

*f*–

_{1}*f*(red) until gain compression appears, at input levels of about -6 dBm for

_{2}*f*and -2 dBm for 2

_{1}*f*–

_{1}*f*. (Because

_{2}*f*equals

_{1}*f*in magnitude and the low-side and high-side products equal each other in magnitude, we can ignore

_{2}*f*and the high-side product for this analysis.)

_{2}**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.

**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.

**Where can I learn more?**

These application notes describe how to make intermodulation measurements with specific instruments and software:

*IMD Measurements with IMDView*(Anritsu)*Intermodulation Distortion (IMD) Measurements Using the PNA-X*(Keysight Technologies)*Intermodulation Distortion Measurements on Modern Spectrum Analyzers*(Rohde & Schwarz)

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