{"product_id":"vco-gain-and-injection-locking-to-measure-inductor-coupling-on-ics-von-peter-popplewell","title":"VCO Gain and Injection-Locking to Measure Inductor Coupling on ICs","description":"\u003cp\u003eThe theoretical behavior of oscillators is explored using the ¿gm model. Mathematical derivations based on the model show that the frequency response of an LC oscillator resembles that of a high-Q bandpass filter with exceptionally high, but finite, pass-band gain. The linear derivations predict a 20 dB\/decade roll-off beyond the loaded 3 dB corner frequency which is consistent with the accepted phase noise model of the oscillator. The demonstrated oscillator gain shows how oscillators can be used in non-traditional roles such as active filters or amplifiers. As an oscillator has gain within a determinable bandwidth and an injection-locked oscillator has the same output power as an identical oscillator operated free-running, on-chip inductor coupling can easily be measured using oscillators. The design, implementation, and measurements of a unique experimental test chip and PCB for measuring on-chip inductor coupling easily and accurately are presented. The experiment requires no calibration, matching, or probe de-embedding and makes use of an injection-locked bipolar oscillator acting as a transmitter and a free-running bipolar oscillator behaving as a receiver.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783843367011\"\u003e\u003ch3\u003eUsing Oscillator Gain and Injection-Locking to Measure On-Chip Inductor Coupling\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783843367011","offer_id":39497082077277,"sku":"9783843367011","price":59.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/3fb9dee8-0fe8-4d13-8999-d11d97f38127.jpg?v=1769236351","url":"https:\/\/shop.autorenwelt.de\/en\/products\/vco-gain-and-injection-locking-to-measure-inductor-coupling-on-ics-von-peter-popplewell","provider":"Autorenwelt Shop","version":"1.0","type":"link"}