# 6.8: Frequency Divider

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$

( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\id}{\mathrm{id}}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\kernel}{\mathrm{null}\,}$$

$$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$

$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$

$$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$

$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$

$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vectorC}[1]{\textbf{#1}}$$

$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$

$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$

$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

A frequency divider is a module that reduces the frequency of a signal. There are three main types of frequency dividers: those that work with square waves and those that work with sinusoidal signals. The square wave dividers are much simpler. A divide-by-$$2$$ square wave divider is shown in Figure $$\PageIndex{1}$$. The square wave input can be produced from a sinusoidal signal using zero-crossing detection or a high-gain circuit with saturating levels.

Figure $$\PageIndex{1}$$: Digital frequency divider with the waveforms shown for a divide-by-$$2$$ divider.

Figure $$\PageIndex{2}$$: Regenerative frequency divider.

One type of analog frequency divider is the regenerative frequency divider shown in Figure $$\PageIndex{2}$$. The key element of this circuit is the mixer, which here produces an output at the difference frequency of the input at frequency $$f_{i}$$ and the signal is fed back at frequency $$f_{x}$$. The output of the mixer is the lowpass filtered difference of $$f_{i}$$ and $$f_{x}$$. The loop stabilizes to produce the divided frequency at the output.

Another analog frequency divider, called a locked-oscillator frequency divider, uses injection locking of an oscillator [35]. It is relatively easy to lock many oscillators by injecting a signal near the $$n$$th harmonic of the free-running oscillation frequency. Then the oscillation frequency shifts and the output has a frequency $$1/n$$th that of the input signal.

Yet another type uses flip-flops dividing the frequency of a microwave-frequency binary clock signal.

6.8: Frequency Divider is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.