File:Negative resistance vs loop gain.svg
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Summary
Graph of input current-voltage (IV) curve of typical <a href="https://en.wikipedia.org/wiki/amplifier" class="extiw" title="en:amplifier">amplifier</a> with <a href="https://en.wikipedia.org/wiki/positive_feedback" class="extiw" title="en:positive feedback">positive feedback</a> for different values of feedback <a href="https://en.wikipedia.org/wiki/loop_gain" class="extiw" title="en:loop gain">loop gain</a> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f711d987a7bd8cd8e3bddfcea410c127682c5db" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:3.096ex; height:2.676ex;" alt="{\displaystyle A\beta }"> showing it has <a href="https://en.wikipedia.org/wiki/negative_resistance" class="extiw" title="en:negative resistance">negative resistance</a> when
<img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4abff937bb9298363e99c00cc920bfd831fdd652" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:8.668ex; height:2.676ex;" alt="{\displaystyle A\beta \;>\;1}">.
- <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6aaf5ce10d6add44b973e28fb3d95f37abf3721" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:2.141ex; height:2.343ex;" alt="{\displaystyle A\,}"> is the <a href="https://en.wikipedia.org/wiki/voltage_gain" class="extiw" title="en:voltage gain">voltage gain</a> of the amplifier
- <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1ed908f3ddc8a847e2f573e2b559314f017443b" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.838ex; width:5.985ex; height:2.843ex;" alt="{\displaystyle \beta (j\omega )\,}"> is the <a href="https://en.wikipedia.org/wiki/tranfer_function" class="extiw" title="en:tranfer function">tranfer function</a> of the feedback loop
- <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1db3bcc99d41402bdc06bc039076730f38dc491f" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:2.969ex; height:2.509ex;" alt="{\displaystyle R_{i}\,}"> is the input resistance of the amplifier.
The slope of the central linear segment of the graph is
- <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e65c23457c23c967b0a0589eeaf5c518af48463" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -2.505ex; width:14.37ex; height:6.009ex;" alt="{\displaystyle R_{f}={R_{i} \over 1-A\beta }\,}">
In <a href="https://en.wikipedia.org/wiki/electronic_oscillator" class="extiw" title="en:electronic oscillator">electronic oscillator</a> the negative resistance of a feedback amplifier is used to cancel the positive resistance in a <a href="https://en.wikipedia.org/wiki/tuned_circuit" class="extiw" title="en:tuned circuit">tuned circuit</a>, to excite oscillations in the tuned circuit.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 00:59, 16 January 2017 | | 875 × 875 (17 KB) | 127.0.0.1 (talk) | Graph of input current-voltage (<i>IV</i>) curve of typical <a href="https://en.wikipedia.org/wiki/amplifier" class="extiw" title="en:amplifier">amplifier</a> with <a href="https://en.wikipedia.org/wiki/positive_feedback" class="extiw" title="en:positive feedback">positive feedback</a> for different values of feedback <a href="https://en.wikipedia.org/wiki/loop_gain" class="extiw" title="en:loop gain">loop gain</a> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>A</mi><mi>β<!-- β --></mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle A\beta }</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f711d987a7bd8cd8e3bddfcea410c127682c5db" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:3.096ex; height:2.676ex;" alt="{\displaystyle A\beta }"></span> showing it has <a href="https://en.wikipedia.org/wiki/negative_resistance" class="extiw" title="en:negative resistance">negative resistance</a> when <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>A</mi><mi>β<!-- β --></mi><mspace width="thickmathspace"></mspace><mo>></mo><mspace width="thickmathspace"></mspace><mn>1</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle A\beta \;>\;1}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4abff937bb9298363e99c00cc920bfd831fdd652" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:8.668ex; height:2.676ex;" alt="{\displaystyle A\beta \;>\;1}"></span>.<br><ul> <li> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>A</mi><mspace width="thinmathspace"></mspace></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle A\,}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6aaf5ce10d6add44b973e28fb3d95f37abf3721" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:2.141ex; height:2.343ex;" alt="{\displaystyle A\,}"></span> is the <a href="https://en.wikipedia.org/wiki/voltage_gain" class="extiw" title="en:voltage gain">voltage gain</a> of the amplifier<br> </li> <li> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>β<!-- β --></mi><mo stretchy="false">(</mo><mi>j</mi><mi>ω<!-- ω --></mi><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \beta (j\omega )\,}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1ed908f3ddc8a847e2f573e2b559314f017443b" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.838ex; width:5.985ex; height:2.843ex;" alt="{\displaystyle \beta (j\omega )\,}"></span> is the <a href="https://en.wikipedia.org/wiki/tranfer_function" class="extiw" title="en:tranfer function">tranfer function</a> of the feedback loop<br> </li> <li> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>R</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi></mrow></msub><mspace width="thinmathspace"></mspace></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle R_{i}\,}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1db3bcc99d41402bdc06bc039076730f38dc491f" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:2.969ex; height:2.509ex;" alt="{\displaystyle R_{i}\,}"></span> is the input resistance of the amplifier.<br> </li> </ul> <p>The slope of the central linear segment of the graph is </p> <dl><dd><span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>R</mi><mrow class="MJX-TeXAtom-ORD"><mi>f</mi></mrow></msub><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msub><mi>R</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi></mrow></msub><mrow><mn>1</mn><mo>−<!-- − --></mo><mi>A</mi><mi>β<!-- β --></mi></mrow></mfrac></mrow><mspace width="thinmathspace"></mspace></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle R_{f}={R_{i} \over 1-A\beta }\,}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e65c23457c23c967b0a0589eeaf5c518af48463" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -2.505ex; width:14.37ex; height:6.009ex;" alt="{\displaystyle R_{f}={R_{i} \over 1-A\beta }\,}"></span></dd></dl> In <a href="https://en.wikipedia.org/wiki/electronic_oscillator" class="extiw" title="en:electronic oscillator">electronic oscillator</a> the negative resistance of a feedback amplifier is used to cancel the positive resistance in a <a href="https://en.wikipedia.org/wiki/tuned_circuit" class="extiw" title="en:tuned circuit">tuned circuit</a>, to excite oscillations in the tuned circuit. |
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