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Cascaded 1 dB Compression Point (P1dB)

3rd-Order Intercept Point (IP3) Graph - RF Cafe

Graph of P1dB, IP2, IP3, and Saturation

See cascade calculations for NF, IP2, IP3, and P1dB.

When operating within the linear region of a component, gain through that component is constant for a given frequency. As the input signal is increased in power, a point is reached where the power of the signal at the output is not amplified by the same amount as the smaller signal. At the point where the input signal is amplified by an amount 1 dB less than the small signal gain, the 1 dB Compression Point has been reached. A rapid decrease in gain will be experienced after the 1 dB compression point is reached. If the input power is increased to an extreme value, the component will be destroyed.

P1dBoutput = P1dBinput + (Gain - 1) dBm

Passive, nonlinear components such as diodes also exhibit 1 dB compression points. Indeed, it is the nonlinear active transistors that cause the 1 dB compression point to exist in amplifiers. Of course, a power level can be reached in any device that will eventually destroy it.

A common rule of thumb for the relationship between the 3rd-order intercept point (IP3) and the 1 dB compression point (P1dB) is 10 to 12 dB. Many software packages allow the user to enter a fixed level for the P1dB to be below the IP3. For instance, if a fixed level of 12 dB below IP3 is used and the IP3 for the device is +30 dBm, then the P1dB would be +18 dBm.

Graph of relationship between IP2, IP3, and P1dB - RF CafeIn order to test the theory, IP3 and P1dB values from 53 randomly chosen amplifiers and mixers were entered into an Excel spreadsheet (see table below and resulting graph to the right). The parts represent a cross-section of silicon and GaAs, FETs, BJTs, and diodes, connectorized and surface mount devices. A mean average and standard deviation was calculated for the sample.

As it turns out, the mean is 11.7 dB with a standard deviation of 2.9 dB, so about 68% of the sample has P1dB values that fall between 8.8 dB and 14.6 dB below the IP3 values. What that means is that the long-lived rule of thumb is a pretty good one. A more useful exercise might be to separate the samples into silicon and GaAs to obtain unique (or maybe not) means and standard deviations for each.

An interesting sidebar is that where available, the IP2 values were also noted. As can be seen in the chart, the relationship between IP2 and P1dB is not nearly as consistent.

Of equal motivation for the investigation was the desire to confirm or discredit the use of the noise figure and IP3 type of cascade formula for use in cascading component P1dB values. As discussed elsewhere, the equation for tracking a component from its linear operating region into its nonlinear region is highly dependent on the entire circuit structure, and one model is not sufficient to cover all instances. Indeed, the more sophisticated (pronounced “very expensive”) system simulators provide the ability to describe a polynomial equation that fits the curve of the measured device. Carrying the calculation through many stages is calculation intensive. Some simulators exploit the rule of thumb of IP3 versus P1dB tracking and simply apply the IP3 cascade equation to P1dB. As with other shortcuts, as long as the user is aware of the approximation and can live with it, it’s a beautiful thing.

 

Cascading P1dB Values in a Chain of Components

Example cascaded system - RF Cafe
Click here to view an example of a cascaded system.
Calculating the cascaded values for 1 dB compression point (P1dB) for the system budget requires use of ratios for gain and power levels for P1dB (do not use dB and dBm values, respectively). The standard format for indicating decibel values is to use upper case letters; i.e., P1dB for units of dBm. The standard format for indicating power values is to use lower case letters; i.e., p1db for units of mW.

Conversions:   p1db = 10P1dB/10  ↔  P1dB (dB) = 10 * log10 (p1db)

where p1db has units of mW and P1dB has units of dBm



Cascaded components for calculating IP2 - RF Cafe

A Typical Chain of Cascaded Components

Cascading receiver transmitter stages two at a time - RF Cafe

Combining 2 Stages at a Time for Calculations

Cascading of 1 dB Compression points is not a straightforward process, since the curve followed from linear operation into saturation is dependent upon the circuit characteristics. A precise calculation requires knowing the equation of the input/output power transfer curve of each device, which is typically a high-order polynomial that would be very difficult both to ascertain and also to apply mathematically. A well-known rule-of-thumb is to subtract 10 to 15 dB to the IP3 value to estimate the P1dB value. To test that theory, I looked at the published values of IP3 and P1dB for some common devices and calculated the difference between IP3 and P1dB (see table below). A sample of 53 devices resulted in a mean difference of 11.7 dB, with a standard deviation of 2.9 dB. That is pretty good agreement with the rule-of-thumb.

Accordingly, a reasonable estimate of the cascaded P1dB value is to either apply the cascaded IP3 equation directly to each device's P1dB value, or to simply calculate the actual cascaded IP3 and subtract 10 to 15 dB to the result and declare that to be the cascaded P1dB. Note that this estimate only holds when none of the stages in the cascade are normally operating outside of the linear region.

This equation gives the method for calculating cascaded output p1db (op1db) values based on the equation for oip3 and gain of each stage. When using the formula in a software program or in a spreadsheet, it is more convenient and efficient to calculate each successive cascaded stage with the one preceding it using the following format, per the drawing (above-right).

Cascaded 1 dB Compression Point (1dB) Equation - RF Cafe     Cascaded receiver transmitter stage notation - RF Cafe

Converting P1db power to dBm - RF Cafe

These formulas are used to convert back and forth between input- and output-referenced P1dB values: 

P1dBOutput = P1dBInput + (Gain - 1) dBm

P1dBInput = P1dBOutput - (Gain - 1) dBm

The following table of values was used to create the chart shown near the top of the page.

Table of IP3, IP2, and P1db Values from Vendor Datasheets
TypeMfgModelIP2IP3P1dBP1dB-IP2P1dB-IP3
AmpAmplifonix20013632171915
AmpAmplifonix87014735252210
AmpAmplifonix54044333222111
AmpCouger/TeledyneA2C51194633192714
AmpCouger/TeledyneA2C4110543421.532.512.5
AmpCouger/TeledyneA2CP142255440282612
MixerCouger/TeledyneMC15023512 3512
AmpMimix BroadbandCMM-40003929.519 10.5
AmpMimix BroadbandCMM-1110312213 9
AmpM/A-COMA1016436234113
AmpM/A-COMA2312522101512
AmpM/A-COMAM05-00055537233214
AmpM/A-COMSMA411322410 14
MixerPolyphaseIRM0714B67157.6 7.4
MixerPolyphaseIRM1925B68148 6
MixerAmplifonixM53T 133.5 9.5
AmpJCAJCA01-301 2013 7
AmpJCAJCS02-332 3323 10
AmpMimix BroadbandXL1005 2416 8
AmpTechnology Distribution0600-0007 2510 15
AmpTechnology Distribution0600-0025 2015 5
AmpTechnology Distribution0600-0024A 3012 18
AmpStealth MicrowaveSM3436-34HS 4734 13
AmpStealth MicrowaveSM1925-33 4733 14
AmpM/A-COMMAALSS0045 3220 12
MixerM/A-COMCSM1-10 196 13
MixerM/A-COMM5T 187 11
MixerMarki MicrowaveM1-0204L 122 10
MixerMarki MicrowaveM1R-0726M 155 10
MixerPolyphaseSSB2425A 198 11
AmpTriquintTGA2512-SM 166 10
MixerTriquintCMY 210 2414 10
AmpMiteqAFS3-00500200-27P-CT-6 3827 11
AmpMilliwaveTMT4-060-180-35-10P-2 2010 10
AmpMilliwaveTMT6-500-750-100-5P-5 145 9
AmpMilliwaveAMT4-060-180-40-10P-1 2215 7
AmpSkyworksSKY65013-70LF 2914 15
AmpSkyworksSKY65015-92LF 3518 17
MixerSynergyFSM-2 4023 17
MixerSynergySGM-2-17 1810 8
AmpMicrowave TechnologyMwT-A989 3924 15
AmpHittiteHMC376LP3 3621.5 14.5
AmpHittiteHMC564 2412 12
MixerHittiteHMC399MS8 3424 10
AmpRFICRFISLNA01 2414 10
AmpRFMDNBB-302 23.513.7 9.8
AmpRFMDRF2878 2914.4 14.6
AmpNuWavesNILNA-GPS 3117 14
AmpMCLAMP-15 228 14
AmpMCLZFL-500HLN 3016 14
AmpMCLZQL-900LNW 3521 14
MixerMCLMCA-19FLH 2510 15
MixerMCLMCA-1-12GL 91 8
    Mean27.111.7
    StdDev8.12.9
    Samples1053


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    BSEE - KB3UON

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The Internet was still largely an unknown entity at the time and not much was available in the form of WYSIWYG ...

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