IP2 and IP3: Formulas, Calculations, and Significance in RF Systems

The second-order (IP2) and third-order (IP3) intercept points are crucial parameters in RF systems, defining the levels of nonlinear distortion. Engineers often use input-referenced intercept points, IIP2 and IIP3, to optimize system design.

This guide covers the definitions, formulas, and step-by-step calculations, emphasizing their significance in real-world applications. These intercept points are observed in the saturated amplifier gain response. When an amplifier operates in a nonlinear region or is overdriven, it generates intermodulation products of the input signals. Among these intermodulation products, the second and third-order components are typically larger in magnitude and can interfere with the desired signals.

IP2 (Second-Order Intercept Point) and IP3 (Third-Order Intercept Point) are critical parameters in RF system design, particularly for assessing a receiver’s or amplifier’s linearity and ability to handle interference. While IP2 primarily impacts even-order distortion and is crucial in direct-conversion receivers to mitigate DC offsets and self-mixing effects, IP3 is more relevant in evaluating third-order intermodulation distortion, which affects adjacent channel interference and system dynamic range.

What are Intermodulation Products?

Intermodulation products

As shown, any amplifier or mixing device will produce intermodulation products when two or more signals are fed to the input. The figure illustrates IMD products of the second and third order resulting from two input signals, f1 and f2.

The general formula for the nth order intercept point is:

$IP_n = P + \frac{\Delta P}{n-1}$

Where:

• $IP_n$ is the nth order intercept point
• $P$ is the power in the fundamental frequency/tone in dBm
• $\Delta P$ is the difference between the desired output and undesired nth order output product in dBc

Example: If two amplitude tones have a power of +10dBm and generate a pair of equal amplitude 3rd order IMD products at -20dBm, calculate the 2-tone IP3 of the system.

$IP3 = +10 + \frac{(+10 - (-20))}{(3-1)}$

$IP3 = 25dBm$

Third Order Intercept Point (IP3)

TOI Third Order Intercept Point

The figure shows both the Third Order Input Intercept Point (IIP3) and the Third Order Output Intercept Point (OIP3) with a slope of 3.

$OIP3 = P_o + \frac{1}{2}(P_o - P_{IMD})$

$IIP3 = OIP3 - Gain$

$IIP3 = P_{IN} + \frac{1}{2}(P_o - P_{IMD})$

Second Order Intercept Point (IP2)

IP2 Second Order Intercept Point

The figure shows both the Second Order Input Intercept Point (IIP2) and the Second Order Output Intercept Point (OIP2) with a slope of 2.

$IIP2 = P_{IN} + P_o - P_{IMD}$

$OIP2 = P_o - P_{IMD}$

Third Order Intercept Point in Cascading Stages

cascaded intercept point

$\frac{1}{OIP} = \frac{1}{(G_2 \cdot G_3 \cdot OIP_1)} + \frac{1}{(G_3 \cdot OIP_2)} + \frac{1}{OIP_3}$

$IIP = \frac{OIP}{(G_1 \cdot G_2 \cdot G_3)}$

Second Order Intercept Point in Cascading Stages

$\frac{1}{\sqrt{OIP}} = \frac{1}{\sqrt{G_2 \cdot G_3 \cdot OIP_1}} + \frac{1}{\sqrt{G_3 \cdot OIP_2}} + \frac{1}{\sqrt{OIP_3}}$

$IIP = \frac{OIP}{(G_1 \cdot G_2 \cdot G_3)}$

Conclusion

A higher IP3 value indicates better linearity and reduced intermodulation distortion, making it a key parameter for high performance communication systems. On the other hand, IP2 is crucial in scenarios where even order distortions significantly impact system performance. Understanding the trade-offs between IP2 and IP3 is essential for optimizing RF front end designs, ensuring minimal interference, and maintaining signal integrity in modern wireless communication systems.