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. This "Linear Scales Show Mixer Harmonics" article
from a 1964 issue of Electronics magazine got me thinking about it. 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 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
ubersophisticated 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 October 27, 2023 (updated from original
post on 11/15/2018)
