# Cascaded 1 dB Compression Point (P1dB)

 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.

In order to test the theory, IP3 and P1dB values from 53 randomly chosen amplifiers and mixers were entered into an Excel spreadsheet ). 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

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

 A Typical Chain of Cascaded Components 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).

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 Type Mfg Model IP2 IP3 P1dB P1dB-IP2 P1dB-IP3 Amp Amplifonix 2001 36 32 17 19 15 Amp Amplifonix 8701 47 35 25 22 10 Amp Amplifonix 5404 43 33 22 21 11 Amp Couger/Teledyne A2C5119 46 33 19 27 14 Amp Couger/Teledyne A2C4110 54 34 21.5 32.5 12.5 Amp Couger/Teledyne A2CP14225 54 40 28 26 12 Mixer Couger/Teledyne MC1502 35 12 35 12 Amp Mimix Broadband CMM-4000 39 29.5 19 10.5 Amp Mimix Broadband CMM-1110 31 22 13 9 Amp M/A-COM A101 64 36 23 41 13 Amp M/A-COM A231 25 22 10 15 12 Amp M/A-COM AM05-0005 55 37 23 32 14 Amp M/A-COM SMA411 32 24 10 14 Mixer Polyphase IRM0714B 67 15 7.6 7.4 Mixer Polyphase IRM1925B 68 14 8 6 Mixer Amplifonix M53T 13 3.5 9.5 Amp JCA JCA01-301 20 13 7 Amp JCA JCS02-332 33 23 10 Amp Mimix Broadband XL1005 24 16 8 Amp Technology Distribution 0600-0007 25 10 15 Amp Technology Distribution 0600-0025 20 15 5 Amp Technology Distribution 0600-0024A 30 12 18 Amp Stealth Microwave SM3436-34HS 47 34 13 Amp Stealth Microwave SM1925-33 47 33 14 Amp M/A-COM MAALSS0045 32 20 12 Mixer M/A-COM CSM1-10 19 6 13 Mixer M/A-COM M5T 18 7 11 Mixer Marki Microwave M1-0204L 12 2 10 Mixer Marki Microwave M1R-0726M 15 5 10 Mixer Polyphase SSB2425A 19 8 11 Amp Triquint TGA2512-SM 16 6 10 Mixer Triquint CMY 210 24 14 10 Amp Miteq AFS3-00500200-27P-CT-6 38 27 11 Amp Milliwave TMT4-060-180-35-10P-2 20 10 10 Amp Milliwave TMT6-500-750-100-5P-5 14 5 9 Amp Milliwave AMT4-060-180-40-10P-1 22 15 7 Amp Skyworks SKY65013-70LF 29 14 15 Amp Skyworks SKY65015-92LF 35 18 17 Mixer Synergy FSM-2 40 23 17 Mixer Synergy SGM-2-17 18 10 8 Amp Microwave Technology MwT-A989 39 24 15 Amp Hittite HMC376LP3 36 21.5 14.5 Amp Hittite HMC564 24 12 12 Mixer Hittite HMC399MS8 34 24 10 Amp RFIC RFISLNA01 24 14 10 Amp RFMD NBB-302 23.5 13.7 9.8 Amp RFMD RF2878 29 14.4 14.6 Amp NuWaves NILNA-GPS 31 17 14 Amp MCL AMP-15 22 8 14 Amp MCL ZFL-500HLN 30 16 14 Amp MCL ZQL-900LNW 35 21 14 Mixer MCL MCA-19FLH 25 10 15 Mixer MCL MCA-1-12GL 9 1 8 Mean 27.1 11.7 StdDev 8.1 2.9 Samples 10 53