{"product_id":"nyquista-johnson-noise","title":"Nyquista – Johnson–Nyquist Noise \/ 4kTR Physics Sticker","description":"\u003cp\u003eNyquista, a grinning goblin of the circuits, holds a striped resistor spitting jagged orange sparks.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eAny resistor at a temperature above absolute zero hisses with voltage noise, because its electrons jiggle thermally. John B. Johnson measured it at Bell Labs and Harry Nyquist explained it, both in 1928 (Phys. Rev. 32, 97 and 32, 110). The noise power per unit bandwidth depends only on temperature and resistance, not on the material.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003e⟨V²⟩ = 4k\u003csub\u003eB\u003c\/sub\u003eTRΔf\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e⟨V²⟩: mean-square noise voltage (V²)\u003c\/li\u003e\n\u003cli\u003ek\u003csub\u003eB\u003c\/sub\u003e: Boltzmann constant, exactly 1.380 649 × 10⁻²³ J\/K since 2019\u003c\/li\u003e\n\u003cli\u003eT: temperature (K)\u003c\/li\u003e\n\u003cli\u003eR: resistance (Ω)\u003c\/li\u003e\n\u003cli\u003eΔf: measurement bandwidth (Hz)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eA 1 kΩ resistor at room temperature gives about 4 nV per √Hz. Because k\u003csub\u003eB\u003c\/sub\u003e is now exact, Johnson noise can be used as a primary thermometer.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The formula is the low-frequency limit; at very high frequency or low temperature quantum corrections (hf ≳ k\u003csub\u003eB\u003c\/sub\u003eT) cut it off.\u003c\/p\u003e\u003ch3\u003eOn the sticker\u003c\/h3\u003e\u003cp\u003eNyquista holds a striped resistor with jagged orange lightning crackling from it. Printed text: \u003cstrong\u003eNYQUISTA\u003c\/strong\u003e with the line \u003cstrong\u003e4kTR\u003c\/strong\u003e. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50964270022759,"sku":"18220938352407663537","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50964270055527,"sku":"13187252428219160049","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50964270088295,"sku":"88588922017894369528","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50964270121063,"sku":"22322011856768034992","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/12247293452936607359_1200.jpg?v=1793663983","url":"https:\/\/pixelatedphysics.com\/de\/products\/nyquista-johnson-noise","provider":"Pixelated Physics","version":"1.0","type":"link"}