Search RFCafe.com                           
      More Than 18,000 Unique Pages
Please support my efforts by ADVERTISING!
Serving a Pleasant Blend of Yesterday, Today, and Tomorrow™
Vintage Magazines
Electronics World
Popular Electronics
Radio & TV News
QST | Pop Science
Popular Mechanics
Radio-Craft
Radio-Electronics
Short Wave Craft
Electronics | OFA
Saturday Eve Post
Please Support My Advertisers!
 
  Formulas & Data
Electronics | RF
Mathematics
Mechanics | Physics
 About | Sitemap
Homepage Archive
        Resources
Articles, Forums Calculators, Radar
Magazines, Museum
Radio Service Data
Software, Videos
     Entertainment
Crosswords, Humor Cogitations, Podcast
Quotes, Quizzes
   Parts & Services
1000s of Listings
Software: RF Cascade Workbook | Espresso Engineering Workbook
RF Stencils for Visio | RF Symbols for Visio
RF Symbols for Office | Cafe Press
Aegis Power | Alliance Test | Centric RF | Empower RF | ISOTEC | Reactel | RFCT | San Fran Circuits
Noisecom

Windfreak Technologies Frequency Synthesizers - RF Cafe

Axiom Test Equipment - RF Cafe

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

RF Cascade Workbook for Excel

RF & Electronics Symbols for Visio

RF & Electronics Symbols for Office

RF & Electronics Stencils for Visio

RF Workbench

T-Shirts, Mugs, Cups, Ball Caps, Mouse Pads

These Are Available for Free

Espresso Engineering Workbook™

Smith Chart™ for Excel

RF Cascade Workbook 2018 - RF Cafe

Spectral (Frequency) Inversion

Mixer + LO - RF Cafe

foutput = ±finput ±fLO

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.

Click here to use RF Cafe's 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.

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

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 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.

 

 

Posted October 6, 2004

RF Cascade Workbook 2018 - RF Cafe
Innovative Power Products Passive RF Products - RF Cafe

Windfreak Technologies Frequency Synthesizers - RF Cafe

Innovative Power Products Cool Chip Thermal Dissipation - RF Cafe