January 10, 1964 Electronics
[Table of Contents]
Wax nostalgic about and learn from the history of early electronics.
See articles from Electronics,
published 1930  1988. All copyrights hereby acknowledged.

Having been out of the RF
system design realm for a few years, I do not have much cause to think about mixer
spurious products anymore. I wonder these days how many designers even do much in the
way of frequency planning in conversion systems? Are the RF, IF, and baseband
frequencies as so well defined for most of what is done in the wireless world that
all the spurious product issues have been solved and there are few people who need to
calculate mixer spurious product frequencies and powers? If there is a need, what
methods are currently being used? Do you still cobble together spreadsheets and/or
MATLAB
worksheets using equations like those presented here, do you have a favorite
smartphone app, a compact program on your computer, or are you using one of the two
or three uber sophisticated and super expensive design engineering programs like
those sold by NIAWR (MWO) and Keysight (ADS)? This inquiring mind wants to know.
Linear Scales Show Mixer Harmonics
Simplified method locates spurious signals generated by the first six harmonics of
two mixed signals: one scale is for the sum, the other for the difference, of input frequencies
By Roger T. Stevens, Sanders Associates, Inc., Nashua, N. H.
When two rf signals are mixed to produce a sum or difference frequency output, the
mixing is inherently a nonlinear process that produces harmonics of the two incoming
signals, resulting in spurious outputs corresponding to these harmonics and the various
combinations of their sums and differences. If the relation of the incoming signals and
local oscillator frequencies is chosen unwisely, some of these spurious signals will
be at the desired output frequency, so that they cannot be filtered out. In many cases,
the resulting distortion of the if signal is intolerable.
Many charts and tables have been published that make it possible to determine where
the spurious frequencies lie, but they all are so general and so complex that they do
not substantially simplify the task of the design engineer. The two linear scales shown
here quickly and easily locate and identify all of the spurious signals generated by
the first six harmonics of the two incoming signals. One scale is for use when the desired
output signal is the sum of the two input signals and the other scale is used when the
output must be the difference of the two input signals. The only other information required
is the ratio of the lower frequency input signal (F_{L}) to the higher frequency
input signal (F_{H}). For example, an input signal of 88 to 108 Mc is mixed with
a local oscillator of 98.7 to 118.7 Mc to produce a 10.7Mc if signal. The ratio F_{L}/F_{H}
varies between 0.893 and 0.911. Looking at scale 2 (since the desired output is the difference
frequency) we see that no spurious signals occur over this range and, therefore, the
choice of local oscillator and if frequencies was satisfactory.
Equations  The derivation of the equations for these spurious signals
is simple. The relation for the case of a desired difference signal output is
± (mF_{H}  nF_{L}) = F_{H}
 F_{L}
where m and n are integers representing the particular harmonics of the desired signal.
This equation can be rewritten in terms of the frequency ratio F_{L}/F_{H}
To make up the scale, all combinations of the first six harmonics of each input were
calculated, but solutions that gave F_{L}/F_{H} > 1 or negative were
discarded since these cases are excluded by definition.
The corresponding equation for the case of the sum frequency being the desired output
is
± (mF_{H}  nF_{L}) = F_{H}
+ F_{L}
This can be reduced to
The scale was calculated from this formula in the same way that the difference frequency
scale was determined.
Reference Sheets
Scale 1: Desired Output = Sum of Input Frequencies
Scale 2: Desired Output = Difference of Input
Frequencies
Posted November 15, 2018
