Homepage - RF Cafe
Webmaster: Kirt Blattenberger | KB3UON | Sitemap | ©1996-2014
Menu below is just a small sample of what is here!
 
Custom Search
More than 10,000 searchable pages indexed.
•−•  ••−•    −•−•  •−  ••−•  •
RF Cafe Morse Code >Hear It<

Spectral (Frequency) Inversion

This description of the phenomenon of spectral inversion was written for the RF Cascade Workbook 2005 user's manual, and provides a unique pictorial representation of what is happening when a frequency mixer multiplies two frequencies together.

 

Mixer + LO - RF Cafe


Mixer output frequency formula - RF Cafe


Click here to use the Frequency Conversion Calculator.

All four combinations of the mixing equation shown next to the mixer above are covered. Figures A and B, below, are equivalent results for both the LO-RF and the RF-LO cases. In case A, the subtraction results in negative frequencies, but the negative terms are said to be “reflected” or “folded” about the 0 Hz (DC) axis. The subtraction in case B does not produce any negative results, so there is no need to mathematically reflect it about the 0 Hz axis. There is no real physical reflection mechanism occurring, it is merely a mathematical convenience. The mixer has no way of determining which frequency is being subtracted from the other, regardless of how you happen to write the equation.

No spectral inversion occurs in either the upper sideband (USB) or the lower sideband (LSB) with a low-side LO injection (cases A and B). However, with a high-side LO injection, the LSB will exhibit spectral inversion while the USB does not (cases C, D and E). An explanation of spectral inversion is provided in the next paragraph. First, though, note that with a high-side LO there is an equivalent subtraction/reflection pair similar to the low-side LO case. Case E is a special case where the LO functions as both a low-side and a high-side signal. There, a portion of the band experiences spectral inversion while the other portion does not (termed "frequency folding").

 Spectral Inversion Low-Side Injection A - RF Cafe

 

 Spectral Inversion Low-Side Injection B - RF Cafe

 

 Spectral Inversion High-Side Injection - RF Cafe

 

 Spectral Inversion High-Side Injection B - RF Cafe

 

 Spectral Inversion - RF Cafe

 


Spectral inversion occurs when the lower sideband of a high-side injected LO is used for the output, like examples C, D and E. The result is the lower frequencies of the input band being translated into the upper frequencies of the output band, and vice versa. Shading and arrow-tipped lines are used to track the relative band edges. A second inversion will cancel out the original, but a third will reintroduce the inversion, and so on. Digital systems can un-invert the spectral inversion in software or firmware if it knows to expect it. However, spectral inversion of analog voice information results in unintelligible garble. If multiple conversions are required, then an even number of inversions will result in no net inversion at the output while an odd number of inversions will always result in a net inversion at the output.
A Disruptive Web Presence

Custom Search
Over 10,000 pages indexed! (none duped or pirated)

Read About RF Cafe
Webmaster: Kirt Blattenberger
    KB3UON

RF Cafe Software

RF Cascade Workbook
RF Cascade Workbook is a very extensive system cascaded component Excel workbook that includes the standard Gain, NF, IP2, IP3, Psat calculations, input & output VSWR, noise BW, min/max tolerance, DC power cauculations, graphing of all RF parameters, and has a graphical block diagram tool. An extensive User's Guide is also included. - Only $35.
RF system analysis including
frequency conversion & filters

RF & EE Symbols Word
RF Stencils for Visio

Product & Service Directory
Personally Selected Manufacturers
RF Cafe T-Shirts & Mugs

RF Cafe Software

Calculator Workbook
RF Workbench
Smith Chart™ for Visio
Smith Chart™ for Excel
Your RF Cafe Progenitor & Webmaster
Click here to read about RF CafeKirt Blattenberger... single-handedly redefining what an
                                 engineering website should be.

View the YouTube RF Cafe Intro Video Carpe Diem! (Seize the Day!)

5CCG (5th MOB): My USAF radar shop

Airplanes and Rockets: My personal hobby website

Equine Kingdom: My daughter Sally's horse riding website