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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 (see table below). 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 ComponentsCalculating the cascaded values for P1dB for the system budget requires the following operation based upon ratios for gain and P1dB (do not use decibel values). The standard format for indicating decibel values is to use upper case letters, i.e., OP1dB for units of dBm. The standard format for indicating watt values is to use lower case letters, i.e., op1dB for units of mW or W.
A Typical Chain of Cascaded Components
This equation gives the method for calculating cascaded output p1dB (op1dB) values based on the oip3 and gain of each stage. When using the formula in a software program or in a spreadsheet, it is more convenience and efficient to calculate each successive cascaded stage with the one preceding it using the following format:
These formulas are used to convert back and forth between input and out P1dB values:
P1dBoutput = P1dBinput + (Gain - 1) dBm
|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. RF Workbench uses an approximation to model the transition from linear operation through saturation.||