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.P1dB_{output} = P1dB_{input} + (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 3rdorder 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 (see table below and resulting graph to the right). The parts represent a crosssection 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 longlived 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. 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 = 10^{P1dB/10} ↔ P1dB (dB) = 10 * log_{10} (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 highorder polynomial that would be very difficult both to ascertain and also to apply mathematically. A wellknown ruleofthumb 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 ruleofthumb. 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 (aboveright). These formulas are used to convert back and forth between input and outputreferenced P1dB values: P1dB_{Output} = P1dB_{Input} + (Gain  1) dBm P1dB_{Input} = P1dB_{Output}  (Gain  1) dBm The following table of values was used to create the chart shown near the top of the page. 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  CMM4000  39  29.5  19   10.5  Amp  Mimix Broadband  CMM1110  31  22  13   9  Amp  M/ACOM  A101  64  36  23  41  13  Amp  M/ACOM  A231  25  22  10  15  12  Amp  M/ACOM  AM050005  55  37  23  32  14  Amp  M/ACOM  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  JCA01301   20  13   7  Amp  JCA  JCS02332   33  23   10  Amp  Mimix Broadband  XL1005   24  16   8  Amp  Technology Distribution  06000007   25  10   15  Amp  Technology Distribution  06000025   20  15   5  Amp  Technology Distribution  06000024A   30  12   18  Amp  Stealth Microwave  SM343634HS   47  34   13  Amp  Stealth Microwave  SM192533   47  33   14  Amp  M/ACOM  MAALSS0045   32  20   12  Mixer  M/ACOM  CSM110   19  6   13  Mixer  M/ACOM  M5T   18  7   11  Mixer  Marki Microwave  M10204L   12  2   10  Mixer  Marki Microwave  M1R0726M   15  5   10  Mixer  Polyphase  SSB2425A   19  8   11  Amp  Triquint  TGA2512SM   16  6   10  Mixer  Triquint  CMY 210   24  14   10  Amp  Miteq  AFS30050020027PCT6   38  27   11  Amp  Milliwave  TMT40601803510P2   20  10   10  Amp  Milliwave  TMT65007501005P5   14  5   9  Amp  Milliwave  AMT40601804010P1   22  15   7  Amp  Skyworks  SKY6501370LF   29  14   15  Amp  Skyworks  SKY6501592LF   35  18   17  Mixer  Synergy  FSM2   40  23   17  Mixer  Synergy  SGM217   18  10   8  Amp  Microwave Technology  MwTA989   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  NBB302   23.5  13.7   9.8  Amp  RFMD  RF2878   29  14.4   14.6  Amp  NuWaves  NILNAGPS   31  17   14  Amp  MCL  AMP15   22  8   14  Amp  MCL  ZFL500HLN   30  16   14  Amp  MCL  ZQL900LNW   35  21   14  Mixer  MCL  MCA19FLH   25  10   15  Mixer  MCL  MCA112GL   9  1   8       Mean  27.1  11.7       StdDev  8.1  2.9       Samples  10  53 
