Editing Counter (digital) (section)

===Stepped sinusoidal waveform generator===

A [[sinusoidal]] voltage waveform can be approximated by cycling through the output states of a Johnson counter and [[Operational amplifier applications#Summing amplifier|summing the output voltages]] through a network of resistors whose weights map each counter state to a point in the cosine function:<ref name="davies" /><blockquote>[[File:A simple sinusoid generator.jpg|550px|border|Sinusoidal voltage generator based on a Johnson counter]]</blockquote>The stepped sinusoid's frequency ''{{Math|{{mvar|F{{sub|out}}}}}}'' equals {{Fraction|{{mvar|F{{sub|in}}}}|(2{{mvar|n}})}} for ''{{Math|{{mvar|n}}}}'' flip-flops and a clock frequency of ''{{Math|{{mvar|F{{sub|in}}}}}}''. Consequently, the sinusoidal waveform frequency can be changed simply by changing the clock frequency.

Harmonic distortion is reduced by increasing <math>n</math>, which gives more steps and smaller step sizes in the waveform; by increasing resistance accuracy; and by adding a capacitor or active filter to [[low-pass filter]] the edges.
{{Multi image
| image1            = Stepped sinusoid.svg
| image2            = Stepped sinusoidal wave.svg
| total_width       = 600
| align             = center
| caption1          = The 8-bit Johnson counter has 16 states and thus completes one period of a stepped sine wave every 16 clock pulses
| caption2          = The counter's bits for each clock pulse over one period of the sine wave
| header            = Stepped sinusoidal waveform using an 8-bit Johnson counter
}}