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<title>Chopper (electronics)</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Chopper (electronics)</span></span>

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<p>In <a href="Electronics" title="Electronics">electronics</a>, a <b>chopper</b> circuit is any of numerous types of electronic switching devices and circuits used in power control and signal applications. A chopper is a device that converts fixed DC input to a variable DC output voltage directly. Essentially, a chopper is an electronic <a href="Switch" title="Switch">switch</a> that is used to interrupt one signal under the control of another.

</p><p>In <a href="Power_electronics" title="Power electronics">power electronics</a> applications, since the switching element is either fully on or fully off, its losses are low and the circuit can provide high efficiency. However, the current supplied to the load is discontinuous and may require smoothing or a high switching frequency to avoid undesirable effects. In signal processing circuits, use of a chopper stabilizes a system against drift of electronic components; the original signal can be recovered after amplification or other processing by a synchronous demodulator that essentially un-does the "chopping" process.

</p>

<div class="mw-heading mw-heading2"><h2 id="Comparison_(step_down_chopper_and_step_up_chopper)">Comparison (step down chopper and step up chopper)</h2></div>

<p>Comparison between step up and step down chopper:

</p>

<th>Step down chopper</th>

<th>Step up chopper

</th></tr>

<tr>

<td>Range of output voltage</td>

<td>0 to V volts</td>

<td>V to +∞ volts

</td></tr>

<tr>

<td>Position of chopper switch</td>

<td>In series with load</td>

<td>In parallel with load

</td></tr>

<tr>

<td>Expression for output voltage</td>

<td>VL dc = D × V volts</td>

<td>V<sub>o</sub> = V/(1 – D) volts

</td></tr>

<tr>

<td>External inductance</td>

<td>Not required</td>

<td>Required for boosting the output voltage

</td></tr>

<tr>

<td>For motoring operation, for motor load</td>

<td>For regenerative braking for motor load.

</td></tr>

<tr>

<td>Type of chopper</td>

<td>Single quadrant</td>

<td>Single quadrant

</td></tr>

<tr>

<td>Quadrant of operation</td>

<td>1st quadrant</td>

<td>1st quadrant

</td></tr>

<tr>

<td>Applications</td>

<td>Motor speed control</td>

<td>Battery charging/voltage boosters

</td></tr></tbody></table>

<div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div>

<p>Chopper circuits are used in multiple applications, including:

</p>

<ul><li><a href="Switched-mode_power_supply" title="Switched-mode power supply">Switched mode power supplies</a>, including <a href="DC_to_DC_converter" class="mw-redirect" title="DC to DC converter">DC to DC converters</a>.</li>

<li>Speed controllers for <a href="DC_motor" title="DC motor">DC motors</a></li>

<li>Driving brushless DC <a href="Torque_motor" title="Torque motor">torque motors</a> or <a href="Stepper_motor" title="Stepper motor">stepper motors</a> in <a href="Actuator" title="Actuator">actuators</a></li>

<li>Class D <a href="Electronic_amplifier" class="mw-redirect" title="Electronic amplifier">electronic amplifiers</a></li>

<li><a href="Switched_capacitor" title="Switched capacitor">Switched capacitor</a> <a href="Electronic_filter" title="Electronic filter">filters</a></li>

<li><a href="Variable-frequency_drive" title="Variable-frequency drive">Variable-frequency drives</a></li>

<li>D.C. voltage boosting</li>

<li>Battery-operated electric cars</li>

<li>Battery chargers</li>

<li><a href="Railway_electric_traction" title="Railway electric traction">Railway traction</a></li>

<li>Lighting and lamp controls</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Control_strategies">Control strategies</h2></div>

<p>For all the chopper configurations operating from a fixed DC input voltage, the average value of the output voltage is controlled by periodic opening and closing of the switches used in the chopper circuit.

The average output voltage can be controlled by different techniques namely:

</p>

<ul><li><a href="Pulse-width_modulation" title="Pulse-width modulation">Pulse-width modulation</a></li>

<li>Frequency modulation</li>

<li>Variable frequency, variable pulse width</li>

<li>CLC control</li></ul>

<p>In pulse-width modulation the switches are turned on at a constant chopping frequency. The total time period of one cycle of output waveform is constant. The average output voltage is directly proportional to the ON time of chopper. The ratio of ON time to total time is defined as duty cycle. It can be varied between 0 and 1 or between 0 and 100%. Pulse-width modulation (PWM), or pulse-duration modulation (PDM), is a technique used to encode a message into a pulsing signal. Although this modulation technique can be used to encode information for transmission, its main use is to allow the control of the power supplied to electrical devices, especially to inertial loads such as motors. The average value of voltage (and current) fed to the load is controlled by turning the switch between supply and load on and off at a fast rate. The longer the switch is on compared to the off periods, the higher the total power supplied to the load. The PWM switching frequency has to be much higher than what would affect the load (the device that uses the power), which is to say that the resultant waveform perceived by the load must be as smooth as possible. Typically switching has to be done several times a minute in an electric stove, 120 Hz in a lamp dimmer, from few kilohertz (kHz) to tens of kHz for a motor drive and well into the tens or hundreds of kHz in audio amplifiers and computer power supplies.

</p><p>In frequency modulation, pulses of a fixed amplitude and duration are generated and the average value of output is adjusted by changing how often the pulses are generated.

</p><p>Variable pulse width and frequency combines both changes in the pulse width and repetition rate.

</p><p>In current limit control (CLC) technique, duty cycle is controlled by controlling the load current between maximum and minimum values. The chopper is switched ON and OFF periodically so that the load current is maintained between predetermined maximum and minimum values.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Chopper_amplifiers">Chopper amplifiers</h2></div>

<p>One classic use for a chopper circuit and where the term is still in use is in <i>chopper amplifiers</i>. These are <a href="Direct_current" title="Direct current">DC</a> amplifiers. Some types of signals that need amplifying can be so small that an incredibly high <a href="Gain_(electronics)" title="Gain (electronics)">gain</a> is required, but very high gain DC amplifiers are much harder to build with low offset and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1/f}">

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</math></span><img src="./e9cd0e60c02ddf533da2abed825389fe5a94b7d0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.603ex; height:2.843ex;" alt="{\displaystyle 1/f}" loading="lazy"></span> noise, and reasonable stability and <a href="Bandwidth_(signal_processing)" title="Bandwidth (signal processing)">bandwidth</a>. It's much easier to build an <a href="Alternating_current" title="Alternating current">AC</a> amplifier instead. A chopper circuit is used to break up the input signal so that it can be processed as if it were an AC signal, then integrated back to a DC signal at the output. In this way, extremely small DC signals can be amplified. This approach is often used in electronic instrumentation where stability and accuracy are essential; for example, it is possible using these techniques to construct <a href="Pico-" class="mw-redirect" title="Pico-">pico-voltmeters</a> and <a href="Hall_effect_sensor" title="Hall effect sensor">Hall sensors</a>.

</p><p>The <a href="Input_offset_voltage" title="Input offset voltage">input offset voltage</a> of amplifiers becomes important when trying to amplify small signals with very high gain. Because this technique creates a very low input offset voltage amplifier, and because this input offset voltage does not change much with time and temperature, these techniques are also called "zero-drift" amplifiers (because there is no drift in input offset voltage with time and temperature). Related techniques that also give these zero-drift advantages are auto-zero and chopper-stabilized amplifiers.

</p><p>Auto-zero amplifiers use a secondary auxiliary amplifier to correct the input offset voltage of a main amplifier. Chopper-stabilized amplifiers use a combination of auto-zero and chopper techniques to give some excellent DC precision specifications.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p><p>Some example chopper and auto-zero amplifiers are LTC2050,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> MAX4238/MAX4239<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and OPA333.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Formulas">Formulas</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Step-up_chopper">Step-up chopper</h3></div>

<p>Take a general step-up chopper with voltage source <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{s}}">

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<annotation encoding="application/x-tex">{\displaystyle V_{s}}</annotation>

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</math></span><img src="./57d5d0bb9d326d015df44456d7c0648f80c0f1f5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.359ex; height:2.509ex;" alt="{\displaystyle V_{s}}" loading="lazy"></span> which is in series with the inductor <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L}">

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<annotation encoding="application/x-tex">{\displaystyle L}</annotation>

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</math></span><img src="./103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}" loading="lazy"></span>, diode and the load with average voltage <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{ave}}">

<msub>

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<annotation encoding="application/x-tex">{\displaystyle V_{ave}}</annotation>

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</math></span><img src="./b0f33e533fc69edf58bd11dda53c94a5e0a32f20.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.021ex; height:2.509ex;" alt="{\displaystyle V_{ave}}" loading="lazy"></span>. The chopper switch would be in parallel with the series diode and load. Whenever the chopper switch is on, the output is shorted. Using <a href="Kirchoff_voltage_law" class="mw-redirect" title="Kirchoff voltage law">Kirchhoff Voltage Law</a> in determining <a href="Inductor" title="Inductor">inductor</a> voltage,

</p><p><span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L{\frac {di}{dt}}=V_{s}}">

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<annotation encoding="application/x-tex">{\displaystyle L{\frac {di}{dt}}=V_{s}}</annotation>

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</p><p>and taking the average current within the turn-off time,

</p><p><span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\Delta i}{T_{ON}}}={\frac {V_{s}}{L}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\frac {\Delta i}{T_{ON}}}={\frac {V_{s}}{L}}}</annotation>

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</p><p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{ON}}">

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<annotation encoding="application/x-tex">{\displaystyle T_{ON}}</annotation>

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</math></span><img src="./191a4301ef891a0a29f17d269faeedda63483393.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.303ex; height:2.509ex;" alt="{\displaystyle T_{ON}}" loading="lazy"></span> is the time were a load voltage is present and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta i}">

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<annotation encoding="application/x-tex">{\displaystyle \Delta i}</annotation>

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</math></span><img src="./af1beae3684adba8f1eca1f373eda6d4cdec3c0b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.738ex; height:2.176ex;" alt="{\displaystyle \Delta i}" loading="lazy"></span> the change current with respect to <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{ON}}">

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<annotation encoding="application/x-tex">{\displaystyle T_{ON}}</annotation>

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</math></span><img src="./191a4301ef891a0a29f17d269faeedda63483393.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.303ex; height:2.509ex;" alt="{\displaystyle T_{ON}}" loading="lazy"></span>. Whenever the chopper switch is off and using <a href="Kirchoff_voltage_law" class="mw-redirect" title="Kirchoff voltage law">Kirchhoff Voltage Law</a> in determining inductor voltage with respect to average current within the turn-on time,

</p><p><span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}L{\frac {di}{dt}}&=V_{ave}-V_{s}\\{\frac {\Delta i}{T_{OFF}}}&={\frac {V_{ave}-V_{s}}{L}}.\\\end{aligned}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}L{\frac {di}{dt}}&=V_{ave}-V_{s}\\{\frac {\Delta i}{T_{OFF}}}&={\frac {V_{ave}-V_{s}}{L}}.\\\end{aligned}}}</annotation>

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</math></span></span>

</p><p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{OFF}}">

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<annotation encoding="application/x-tex">{\displaystyle T_{OFF}}</annotation>

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</math></span><img src="./5a95a5ff6136389a43767a1c1677aacd85586a97.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.306ex; height:2.509ex;" alt="{\displaystyle T_{OFF}}" loading="lazy"></span> is the time were a load voltage is zero. Equating both average current and taking the duty cycle <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ={\frac {T_{ON}}{T_{ON}+T_{OFF}}}}">

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<annotation encoding="application/x-tex">{\displaystyle \alpha ={\frac {T_{ON}}{T_{ON}+T_{OFF}}}}</annotation>

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</math></span><img src="./f0082848f4039246228cb9234d3bef6c74d08e33.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.871ex; height:5.843ex;" alt="{\displaystyle \alpha ={\frac {T_{ON}}{T_{ON}+T_{OFF}}}}" loading="lazy"></span>,<sup id="cite_ref-:1_6-0" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>

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<annotation encoding="application/x-tex">{\displaystyle V_{ave}={\frac {V_{s}}{1-\alpha }}}</annotation>

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</math></span><img src="./f9e6ff5c102f5aa6e15493924a7267b46042033d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.446ex; height:5.343ex;" alt="{\displaystyle V_{ave}={\frac {V_{s}}{1-\alpha }}}" loading="lazy"></span>

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<p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{ave}}">

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<annotation encoding="application/x-tex">{\displaystyle V_{ave}}</annotation>

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</math></span><img src="./b0f33e533fc69edf58bd11dda53c94a5e0a32f20.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.021ex; height:2.509ex;" alt="{\displaystyle V_{ave}}" loading="lazy"></span> is the average output voltage.

</p>

<div class="mw-heading mw-heading3"><h3 id="Step-down_chopper">Step-down chopper</h3></div>

<p>Taking a general step-down chopper with voltage source <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{s}}">

<msub>

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<annotation encoding="application/x-tex">{\displaystyle V_{s}}</annotation>

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</math></span><img src="./57d5d0bb9d326d015df44456d7c0648f80c0f1f5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.359ex; height:2.509ex;" alt="{\displaystyle V_{s}}" loading="lazy"></span> which is in series with the chopper switch, inductor, and the load with voltage <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{o}}">

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<annotation encoding="application/x-tex">{\displaystyle V_{o}}</annotation>

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</math></span><img src="./4373adc7c6ba3ad0a230674368b6a3a2df6cf98d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.385ex; height:2.509ex;" alt="{\displaystyle V_{o}}" loading="lazy"></span>. The diode would be in parallel with the series inductor and load. The same way by equating the average inductor current during the turn-on and turn-off time, we can get the average voltage by <sup id="cite_ref-:1_6-1" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>

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<msub>

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<annotation encoding="application/x-tex">{\displaystyle V_{ave}=\alpha V_{s}}</annotation>

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</math></span><img src="./badf2a997c1ec9ea7aa7fcf7b29c341477370c77.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.965ex; height:2.509ex;" alt="{\displaystyle V_{ave}=\alpha V_{s}}" loading="lazy"></span>

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<p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{ave}}">

<msub>

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<annotation encoding="application/x-tex">{\displaystyle V_{ave}}</annotation>

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</math></span><img src="./b0f33e533fc69edf58bd11dda53c94a5e0a32f20.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.021ex; height:2.509ex;" alt="{\displaystyle V_{ave}}" loading="lazy"></span> is the average output <a href="Voltage" title="Voltage">voltage</a>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }">

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<annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation>

</semantics>

</math></span><img src="./b79333175c8b3f0840bfb4ec41b8072c83ea88d3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" loading="lazy"></span> is the <a href="Duty_cycle" title="Duty cycle">duty cycle</a> and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{s}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle V_{s}}</annotation>

</semantics>

</math></span><img src="./57d5d0bb9d326d015df44456d7c0648f80c0f1f5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.359ex; height:2.509ex;" alt="{\displaystyle V_{s}}" loading="lazy"></span> is the source voltage.

</p>

<div class="mw-heading mw-heading3"><h3 id="Step-up_/_step-down_chopper">Step-up / step-down chopper</h3></div>

<p>Taking a general buck-boost chopper which works as stepup and down chopper, let the voltage source <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{s}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle V_{s}}</annotation>

</semantics>

</math></span><img src="./57d5d0bb9d326d015df44456d7c0648f80c0f1f5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.359ex; height:2.509ex;" alt="{\displaystyle V_{s}}" loading="lazy"></span> be in series with the chopper switch, reverse biased diode, and the load with voltage <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{o}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle V_{o}}</annotation>

</semantics>

</math></span><img src="./4373adc7c6ba3ad0a230674368b6a3a2df6cf98d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.385ex; height:2.509ex;" alt="{\displaystyle V_{o}}" loading="lazy"></span>. The inductor would be in parallel with the series diode and load. The same way by equating the average inductor current during the turn-on and turn-off time, we can get the average voltage by <sup id="cite_ref-:1_6-2" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>

</p>

<msub>

</mrow>

</msub>

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle V_{ave}={\frac {\alpha V_{s}}{1-\alpha V_{s}}}}</annotation>

</semantics>

</math></span><img src="./de87cb9c921058665beb12d98dee316bed3706a9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.804ex; height:5.676ex;" alt="{\displaystyle V_{ave}={\frac {\alpha V_{s}}{1-\alpha V_{s}}}}" loading="lazy"></span>

</p>

</div>

<p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{ave}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle V_{ave}}</annotation>

</semantics>

</math></span><img src="./b0f33e533fc69edf58bd11dda53c94a5e0a32f20.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.021ex; height:2.509ex;" alt="{\displaystyle V_{ave}}" loading="lazy"></span> is the average output <a href="Voltage" title="Voltage">voltage</a>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation>

</semantics>

</math></span><img src="./b79333175c8b3f0840bfb4ec41b8072c83ea88d3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" loading="lazy"></span> is the <a href="Duty_cycle" title="Duty cycle">duty cycle</a> and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{s}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle V_{s}}</annotation>

</semantics>

</math></span><img src="./57d5d0bb9d326d015df44456d7c0648f80c0f1f5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.359ex; height:2.509ex;" alt="{\displaystyle V_{s}}" loading="lazy"></span> is the source voltage.

</p>

<ul><li><a href="Braking_chopper" title="Braking chopper">Braking chopper</a></li>

<li><a href="Vibrator_(electronic)" title="Vibrator (electronic)">Vibrator (electronic)</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

/* start https://en.wikipedia.org/ */

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/* end https://en.wikipedia.org/ */

</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.electronicsmind.com/2022/02/voltage-control-of-chopper.html">"Voltage Control of Chopper - Time Ratio & Current Limit Control"</a>. <i>Electronics Mind</i>. 25 February 2022.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">US Patent 7132883 - Chopper chopper-stabilized instrumentation and operational amplifiers</span>

</li>

</li>

</li>

</li>

<li id="cite_note-:1-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_6-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:1_6-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFSingh2008" class="citation book cs1">Singh, M. D. (2008-07-07). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=0_D6gfUHjcEC&q=page+438"><i>Power Electronics</i></a>. Tata McGraw-Hill Education. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780070583894</bdi>.</cite></span>

</li>

</ol></div>

<div class="mw-heading mw-heading2"><h2 id="Literature">Literature</h2></div>

<ul><li>C. Enz, G. Temes, <a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F5.542410">Circuit techniques for reducing the Effect of Op-Amp Imperfections: Autozeroing, Correlated Double Sampling and Chopper Stabilization</a>  - Proceedings of the <a href="IEEE" class="mw-redirect" title="IEEE">IEEE</a>, vol. 84 No. 11, Nov. 1996</li>

<li>A. Bilotti, G. Monreal, <i>Chopper-Stabilized Amplifiers with a Track-and-hold Signal Demodulator</i> - Allegro Technical Paper STP 99–1</li>

<li>A. Bakker, K. Thiele, J. Huijsing, <a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F4.890300">A CMOS Nested-Chopper Instrumentation Amplifier with 100-nV Offset</a>  - IEEE J. Solid-State Circuits, vol. 35 No. 12, Dec 2000</li></ul></div><div><div class="zim-footer">

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