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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: Cursitor Doom Newsgroups: sci.electronics.design Subject: Re: AI Date: Fri, 10 Jan 2025 22:41:53 -0000 (UTC) Organization: A noiseless patient Spider Lines: 106 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Injection-Date: Fri, 10 Jan 2025 23:41:54 +0100 (CET) Injection-Info: dont-email.me; posting-host="642a4d287d172f98fabb3fb39cedc5e5"; logging-data="287144"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+eiohDx0RjR4ibPHAkxTmpqljHd7aEPtg=" User-Agent: Pan/0.149 (Bellevue; 4c157ba) Cancel-Lock: sha1:rC0y3Q7KbeINSCmNu/G3WMzaTk4= Bytes: 5556 On Fri, 10 Jan 2025 22:28:40 +0100, Jeroen Belleman wrote: > On 1/10/25 20:37, Cursitor Doom wrote: >> Gentlemen, >> >> I've just been goofing around with X's AI assistant, Grok. After >> feeding in a few straightforward questions and getting surprisingly >> impressive answers, I decided to try something a bit more subjective to >> see how it would cope. Here's what happened... >> >> >> My question: >> >> Which of the common 'classic' oscillator designs is the most impressive >> or ingenious from a technical standpoint? >> >> Grok's Answer: >> >> From a technical standpoint, several classic oscillator designs stand >> out >> for their ingenuity, but one that is often highlighted for its elegance >> and versatility is the Colpitts oscillator. Here's why: >> >> Design Ingenuity: >> >> Simplicity and Efficiency: >> The Colpitts oscillator uses a simple configuration with a >> transistor (or vacuum tube in older versions) and a combination of >> capacitors and an inductor to create a feedback loop. Despite its >> simplicity, it achieves stable oscillation with just a few components. >> Feedback Mechanism: >> It employs a capacitive voltage divider for feedback, which is >> particularly ingenious. The two capacitors in series (C1 and C2) form a >> voltage divider that provides the necessary phase shift for >> oscillation. This method naturally provides the correct phase without >> additional complex circuitry, making it both efficient and reliable. >> Frequency Stability: >> The frequency of oscillation in a Colpitts oscillator is >> determined primarily by the LC tank circuit's resonant frequency, which >> can be calculated as f=12πL(C1⋅C2)/(C1+C2) >> . This formula highlights how the design inherently stabilizes >> frequency through the interaction of inductance and capacitance. The >> use of capacitors in the feedback loop also helps in reducing the >> impact of transistor parameter variations on frequency stability. >> Versatility: >> The Colpitts oscillator can be adapted for use across a wide >> range >> of frequencies from audio to RF. By changing the values of L, C1, and >> C2, one can easily tune the oscillator to different frequencies, making >> it adaptable for various applications from radio transmitters to clock >> generators. >> Low Noise and High Purity: >> When designed correctly, the Colpitts oscillator can offer low >> phase noise, which is critical for applications like communication >> devices where signal purity is paramount. The design inherently >> minimizes noise by reducing the number of components in the feedback >> path. >> Ease of Adjustment: >> Adjusting the frequency is relatively straightforward with >> minor >> changes to the capacitor or inductor values, making it practical for >> both prototyping and production environments. >> >> >> Historical Context: >> >> Invented by Edwin H. Colpitts in 1918, this oscillator was a >> breakthrough in the era of vacuum tubes, which were later adapted for >> transistor use. Its principles have stood the test of time, still being >> taught and used today in various forms. >> >> >> Comparison: >> >> While other oscillators like the Hartley oscillator (which uses an >> inductive voltage divider) or the Clapp oscillator (a variation of >> Colpitts with an additional capacitor for better frequency stability) >> are also significant, the Colpitts design is often praised for its >> balance of simplicity, efficiency, and versatility. >> >> >> In conclusion, the Colpitts oscillator stands out for its impressive >> combination of simplicity, effectiveness, and adaptability, making it >> one of the most ingenious classic oscillator designs from a technical >> perspective. >> >> ************************************************************************** >> >> Any observations? > > Yeah. The resonant frequency formula is wrong. To first approximation, > it's f=1/(2π sqrt(L C1 C2 / (C1+C2))). (Inline algebraic notation is a > dog...) > > It looks like Grok has trouble reading formulae. > > Of course, it doesn't really know what it's talking about. > It just ladles out some phrases it gathered from various web sites on > the subject. > > Jeroen Belleman The formula error is not Grok's mistake. The sqrt didn't survive the cut'n'paste I'm afraid. I didn't reckon on someone spotting that so didn't mention it in the OP.