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Download this article in PDF format. (91 KB) Multipliers vs. Modulators By James Bryant Although many descriptions of modulation describe it as a multiplication process, the truth is a bit more complex. First, to be quite clear, if the two inputs of a perfect V If the carrier, A V But, in most cases, a modulator is a better circuit to perform this function. A modulator (also called a
We use modulators rather than multipliers for several reasons. Both ports of a multiplier are linear, so any noise or modulation on the carrier input multiplies the signal input and degrades the output, while amplitude variation on the carrier input of a modulator can mostly be ignored. Second-order mechanisms can cause amplitude noise on the carrier input to affect the output, but these are minimized in the best modulators and will not be discussed here. A simple model of a modulator uses switches driven by the carrier. An (perfect) open switch has infinite resistance and zero thermal noise current, and a (perfect) closed switch has zero resistance and zero thermal noise voltage, so modulators, even though their switches are less than perfect, tend to have less internal noise than multipliers. Also, it is easier to design and manufacture a high-performance, high-frequency modulator than a similar multiplier. Like analog multipliers, modulators multiply two signals, but, unlike analog multipliers, the multiplication is not linear. Instead, the signal input is multiplied by +1 when the polarity of the carrier input is positive, and by –1 when it is negative. In other words, the signal is multiplied by a square wave at the carrier frequency. A square wave with a frequency of ω K[cos(ω The sum of the series: [+1, –1/3, +1/5, –1/7 + ...] is π/4. Therefore, the value of K is 4/π, such that a balanced modulator acts as a unity gain amplifier when a positive dc signal is applied to its carrier input. The carrier amplitude is unimportant as long as it is large enough to drive the limiting amplifier, so a modulator driven by a signal, A 2As/π[cos(ω 1/3{cos(ω 1/5{cos(ω 1/7{cos(ω This output contains sum and difference frequencies of the signal and carrier, and of the signal and each of the odd harmonics of the carrier. In an ideal, perfectly balanced modulator, products of even harmonics are not present. In a real modulator, however, residual offsets on the carrier port result in low-level, even harmonic products. In many applications, a low-pass filter (LPF) removes the products of the higher harmonics. Remember that cos(A) = cos(–A), so cos(ω 2As/π[cos(ω This is the same expression as the output of a multiplier, except for a slightly different gain. In practical systems, the gain is normalized by amplifiers or attenuators, so we won’t consider the theoretical gains of various systems here. In simple cases, it’s obviously better to use a modulator than a multiplier, but how do we define simple? When a modulator is used as a mixer, the signal and carrier inputs are simple sine waves at frequencies If ( If we assume that the signal contains a single frequency, Figure 2 shows the inputs—a signal in the
Figure 3 shows the output of a multiplier, or a modulator, and LPF with a cutoff frequency of 2
Figure 4 shows the output of an unfiltered modulator (but not harmonic products above 7
If the signal band, Figure 5 shows what happens when the signal band is just below
Figure 6 shows that as the signal band passes through Thus, although modulators are better than linear multipliers for most frequency changing applications, it is important to consider their harmonic products when designing real systems.
Analog DialogueBrandon, David. “Multichannel DDS Enables Phase-Coherent FSK Modulation.” Analog Dialogue, Volume 44, Number 4, 2010.Gilbert, Barrie. “Considering Multipliers (Part 1).”
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