Cascaded 1 dB Compression Point (P1dB)

henerychan

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
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

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