# Intercept Point

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The intercept point , abbreviated to IP (dt. Intersection point) is a quantity that cannot be measured directly to characterize the non-linear transmission properties of a two-port , such as an amplifier . The concept is used, among other things, in communications engineering .

## Basis of creation

Frequencies of the third order intermodulation products

The approach is based on the approximation of the non-linear transfer characteristic (e.g. of the amplifier) ​​using the mathematical method of the Taylor series . When the system is excited by several additively superimposed sinusoidal oscillations at the input, the higher orders of the (Taylor) power series result in additional frequencies at the output according to the addition theorems. This process of non-linear signal distortion is used, among other things, in mixer stages , but is usually undesirable in amplifiers.

The newly generated frequencies result from the equation

${\ displaystyle f_ {m + n} = | n \ cdot f_ {1} \ pm m \ cdot f_ {2} |}$

where the sum of and equals the order of the respective term of the power series and thus the order of the intermodulation. ${\ displaystyle | m |}$${\ displaystyle | n |}$

For example, the quadratic term (second order) is responsible for generating the frequencies

${\ displaystyle f = f_ {1} + f_ {2}}$ and ${\ displaystyle f = | f_ {1} -f_ {2} |}$

## definition

Schematic representation of the IP2 (green) and IP3 (red)

The intercept point indicates the power of the stimulating oscillation at which the artificially generated oscillation would achieve the same power at the output. However, this point of intersection does not actually exist, but is determined by extrapolating the two characteristics. The saturation , limitation or compression of the transmission link resulting from the same effects causes the curves to bend before the intercept point is reached.

### Input and output IP3

The intercept point can be related to the input or the output of the transmission link:

• The designation IIP3 stands for Input IP3 and thus relates to the input power.
• The designation OIP3 stands for Output IP3 and thus relates to the output power.

The following also applies:

${\ displaystyle OIP3 = IIP3 + G}$with G = reinforcement of the component; Information in logarithmic measures (dB) .

From a mathematical point of view, the input IP3 (neglecting higher orders) is 9.63 dB above the 1 dB compression point . The term TOI comes from the English term third-order intercept point.

### Higher order intercept points

In addition, different IPs can be specified depending on the order considered. These can be separated by measurement, as the artificially generated frequencies differ.

In practice, the following IPs are usually specified

## Metrological determination of the IP3

To determine the IP3, in addition to the component to be examined (DUT, Device Under Test ), two signal generators and a spectrum analyzer or signal analyzer are required. The frequencies and signal strengths to be set (both test signals have the same amplitude) depend on the respective DUT. It must be ensured that the DUT has not already gone into compression . The sinusoidal signals from the signal generators are fed together to the DUT. The amplitudes of the intermodulation products are then measured with the signal analyzer at the output of the DUT.

The OIP3 is calculated in the logarithmic unit decibel (dB) as follows:

${\ displaystyle OIP3 = P_ {1} + {\ frac {1} {2}} IMA_ {13} = P_ {1} + {\ frac {1} {2}} \ left (P_ {1} -P_ { 3} \ right)}$

with P1 = output level of the useful signal in dBm and P3 = output level on the 3rd order intermodulation product in dBm. IMA 13 is the intermodulation distance between P3 and P1 in dB.

The IIP3 is calculated to

${\ displaystyle IIP3 = OIP3-G}$

in which

${\ displaystyle G = P_ {1_ {out}} - P_ {1_ {in}}}$

with P 1out the power of the excitation signal at the output and P 1in the signal strength of the same signal at the input of the DUT.

All signal levels, OIP and IIP are measured in dBm, gain and intermodulation distance in dB.

## literature

• Ralf Rudersdorfer, with the collaboration of Ulrich Graf and Hans Zahnd: Radio receiver compendium - understanding how it works, areas of application and international assignments, determining and interpreting parameters, optimizing receiving systems . 1st edition. Elektor International Media BV, Aachen 2010, ISBN 978-3-89576-224-6 .
• Peter Vizmuller: RF Design Guide: Systems, Circuits, and Equations . Volume 1, Artech House Inc, Norwood 1995, ISBN 0-89006-754-6 .
• Qizheng Gu: RF System Design of Transceivers for Wireless Communications . Springer Science + Media Inc, New York 2005, ISBN 978-0387-24161-6 .