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Chapter 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
Version 1.11
by Kirt Blattenberger
RF Cafe Website
(www.rfcafe.com)
Chapter 8
8 Mixers + LOs
Ideal mixers use two input signals to generate sum and difference frequencies at
the output. One signal is the input frequency to be converted (commonly referred to as the RF) and the other
is a local oscillator (referred to as the LO) that is higher or lower infrequency than the input signal by an
amount equal to the difference between the input frequency and the desired output frequency. See Figure 14. RF
Cascade Workbook 2005 uses only the sideband (upper or lower) that you specify when calculating results. It
does not account for the unintended sideband (see section 5.2 for discussion on image noise).



Figure 14 Mixer/LO Configuration & Equation 

A unique pictorial presentation of what happens during frequency translation is provided in Figure 15. All four combinations of the mixing equation shown in Figure 14 are covered. Figures A and B are equivalent results for both the LORF and the RFLO 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 is about 0 Hz. 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 you happen to write the equation. 

No spectral inversion occurs in either the upper sideband (USB) or the lower sideband (LSB) with a lowside LO injection (cases A and B). However, with a highside 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 highside LO there is an equivalent subtraction/reflection pair similar to the lowside LO case. Case E is a special case where the LO functions as both a lowside and a highside signal. There, a portion of the band experiences spectral inversion while the other portion does not. 











Figure 15 Frequency Inversion 

Spectral Inversion 

Spectral inversion occurs when the lower sideband of a highside injected LO is used for the output, like the examples in Figure 15 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 arrowtipped 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 uninvert the spectral inversion in software or firmware if it knows to expect it. However, spectral inversion of analog voice information results in unintelligible garble. 

Translated frequencies are calculated and stored for every component at every input frequency (76 frequency as the default value). Refer to Figure 12 to see how the frequency range shifts at the output of the mixer (Mix 1) stage. If more than one mixer is used, then the frequency range s will shift accordingly each time based on the LO frequency and chosen sideband. 

Version 1.11 
Chapter 8 