Electronics World articles Popular Electronics articles QST articles Radio & TV News articles Radio-Craft articles Radio-Electronics articles Short Wave Craft articles Wireless World articles Google Search of RF Cafe website Sitemap Electronics Equations Mathematics Equations Equations physics Manufacturers & distributors Engineer Jobs LinkedIn Crosswords Engineering Humor Kirt's Cogitations RF Engineering Quizzes Notable Quotes Calculators Education Engineering magazine articles Engineering software Engineering smorgasbord RF Cafe Archives RF Cascade Workbook 2018 RF Symbols for Visio - Word Advertising RF Cafe Forums Magazine USAF Radr Shop Sponsor RF Cafe RF Electronics Symbols for Visio RF Electronics Symbols for Office Word RF Electronics Stencils for Visio Thank you for visiting RF Cafe!
RF Cascade Workbook 2018 by RF Cafe
KR Electronics (RF Filters) - RF Cafe

About RF Cafe

Kirt Blattenberger - RF Cafe Webmaster

Copyright: 1996 - 2024


    Kirt Blattenberger,


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 World Wide Web (Internet) was largely an unknown entity at the time and bandwidth was a scarce commodity. Dial-up modems blazed along at 14.4 kbps while typing up your telephone line, and a nice lady's voice announced "You've Got Mail" when a new message arrived...

All trademarks, copyrights, patents, and other rights of ownership to images and text used on the RF Cafe website are hereby acknowledged.

My Hobby Website:


RF Cascade Workbook 2018 - RF Cafe

Cascaded 2-Tone, 2nd-Order Intercept Point (IP2)

When two or more tones are present in a nonlinear device, intermodulation products are created as a result. A power series describes all of the possible combinations of generated frequencies. 2nd-order products lie far in frequency to the two input tones and are therefore not very likely to fall inband at the output in a narrow band system. As a device is driven farther into its nonlinear region, the amplitudes of the 2nd-order products increase while the powers of the input tones decrease. If the device was not limited in output power, then the powers of the intermodulation products would increase in power until they were eventually equal in power with the input tones at the output.

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

Graph of P1dB, IP2, IP3, and Saturation

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

Example cascaded system - RF Cafe

Click here to view an example of a cascaded system.

Assuming a gain of 1 (0 dB) the slope of the fundamental gain line would be 1:1; the slope of the 2nd-order gain line would be 2:1. Accordingly, the 2nd-order products increase in power at the same rate as the input tones and are always two times farther away from the IP2 than the input tones when not near saturation.

The power of the 2nd-order products can be predicted when the IP2 is known, or the IP2 can be predicted when the relative amplitudes of the 2nd-order tones and the input tones are known.

P2nd-order products = 2 · Pinput tones@output - IP2  {dBm}

IP2 =2 · Pinput tones@output - P2nd-order products  {dBm}

Cascading IP2 Values in a Chain of Components

Calculating the cascaded values for 2nd-order intercept point (IP2) for the system budget requires use of ratios for gain and power levels for IP2 (do not use dB and dBm values, respectively). The standard format for indicating decibel values is to use upper case letters; i.e., IP2 for units of dBm. The standard format for indicating power values is to use lower case letters; i.e., ip2 for units of mW.

Conversions:   ip2 = 10IP2/10 ↔  IP2 = 10 * log10 (ip2)

where ip2 has units of mW and IP2 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

This equation gives the method for calculating cascaded output ip2 (oip2) values based on the oip2 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). Note that the ip2N-1 term in the denominator is the same as the cumulative ip2 up through the previous (N-1) stage.

Cascaded 2nd-Order Intercept Point (IP2) Formula - RF Cafe     Cascaded receiver transmitter stage notation - RF Cafe

Convert IP2 power to dBm - RF Cafe

These formulas are used to convert back and forth between input- and output-referenced IP2 values:

IP2Output = (IP2Input + Gain)  {dBm}

IP2Input = (IP2Output - Gain)  {dBm}

Anatech Electronics - RF Cafe
Axiom Test Equipment - RF Cafe

Please Support RF Cafe by purchasing my  ridiculously low−priced products, all of which I created.

These Are Available for Free