# Compression point

The compression point is used for the quantitative description of the non-linear behavior of an active element ( e.g. an amplifier ) e.g. B. in audio components or in high frequency technology . It indicates the greatest amplitude of the input signal at which the distortions caused by non-linearity do not yet exceed a specified level.

The cause of the non-linear behavior is the saturation that occurs in every amplifying component ( transistor , electron tube ) above a certain input amplitude. The designation compression point indicates that the saturation always leads to a smaller, ie "compressed" (compressed) output signal compared to the linear case.

## definition

The 1 dB compression point , often referred to as P1dB , is that value of the input amplitude at which the power of the output signal at the fundamental frequency deviates by 1 decibel from the ideal linearly extrapolated characteristic of the component

${\ displaystyle P_ {1 \ mathrm {dB}} = 10 \ log \ left ({\ frac {P _ {\ mathrm {real}}} {P _ {\ mathrm {ideal}}}} \ right) = - 1. }$

( and are linear quantities here.) ${\ displaystyle P _ {\ mathrm {real}}}$${\ displaystyle P _ {\ mathrm {ideal}}}$

In data sheets the P1dB is given as input power in dBm . In addition to the 1 dB compression point, you can also use any other compression point, e.g. B. Define P3dB for a deviation of 3 dB.

## Calculation of the amplitude

Schematic representation of the P1dB

The characteristic of a non-linear amplifier can be expressed in a Taylor series

${\ displaystyle U _ {\ mathrm {out}} = U_ {0} + \ alpha \ cdot U _ {\ mathrm {in}} + \ beta \ cdot {U _ {\ mathrm {in}}} ^ {2} + \ gamma \ cdot {U _ {\ mathrm {in}}} ^ {3} + ...}$

describe.

In the 1 dB compression point, the following applies

${\ displaystyle -1 = 20 \ log {\ frac {\ alpha \ cdot U _ {\ mathrm {1dB}} + {\ frac {3} {4}} \ gamma \ cdot {U _ {\ mathrm {1dB}}} ^ {3}} {\ alpha \ cdot U _ {\ mathrm {1dB}}}}.}$

${\ displaystyle U _ {\ mathrm {1dB}}}$ is the amplitude at the 1 dB compression point

The following results are changed:

${\ displaystyle U _ {\ mathrm {1dB}} = {\ sqrt {(10 ^ {- {\ frac {1} {20}}} - 1) \ cdot {\ frac {4 \ alpha} {3 \ gamma} }}}}$

or logarithmic:

${\ displaystyle A _ {\ mathrm {1dB}} = 20 \ log \ left ({\ sqrt {(10 ^ {- {\ frac {1} {20}}} - 1) \ cdot {\ frac {4 \ alpha } {3 \ gamma}}}} \ right) = 10 \ log \ left ({(10 ^ {- {\ frac {1} {20}}} - 1) \ cdot {\ frac {4 \ alpha} { 3 \ gamma}}} \ right)}$

## literature

• Otto Mildenberger (Ed.): Information technology compact. Theoretical foundations. Friedrich Vieweg & Sohn Verlag, Wiesbaden 1999, ISBN 3-528-03871-3 .
• Hans Dodel, René Wörfel: Satellite frequency coordination . Regulations - link design - system technology. Springer Verlag, Berlin / Heidelberg 2012, ISBN 978-3-642-29202-6 .
• Johann Siegl, Edgar Zocher: Circuit technology - analog and mixed analog / digital. 5th edition. Springer Verlag, Berlin / Heidelberg 2014, ISBN 978-3-642-29559-1 .
• H. Meinke, FW Gundlach: Pocket book of high frequency technology. Volume 3: Systems. 5th edition. Springer Verlag, Berlin / Heidelberg 1992, ISBN 3-540-54716-9 .
• Frieder Strauss: Basic course in high frequency technology. An introduction. 2nd Edition. Springer Verlag, Berlin / Heidelberg 2016, ISBN 978-3-658-11899-0 .
• Manfred Thumm, Werner Wiesbeck, Stefan Kern: high frequency measurement technology. Procedures and measuring systems. 2nd Edition. Springer Fachmedien, Wiesbaden 2008, ISBN 978-3-519-16360-2 .