A signal generator produces a carrier of peak amplitude and frequency

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Communication systems and RF engineering · Communication systems and RF engineering

Electronics for Measurement, Ch Modulation, receivers and the link that carries the measurement

Problem

A signal generator produces a carrier of peak amplitude A=10 VA = 10\,\mathrm{V} and frequency fcar=500 kHzf_{\rm car} = 500\,\mathrm{kHz}. It is amplitude-modulated by two tones together, so the transmitted voltage is v(t)=A[1+m1cos⁡(2πf1t)+m2cos⁡(2πf2t)]cos⁡(2πfcart)v(t) = A\left[1 + m_1\cos(2\pi f_1 t) + m_2\cos(2\pi f_2 t)\right]\cos(2\pi f_{\rm car}t) with f1=2 kHzf_1 = 2\,\mathrm{kHz}, m1=0.60m_1 = 0.60, f2=6 kHzf_2 = 6\,\mathrm{kHz}, m2=0.30m_2 = 0.30. ((a)) Using the product-to-sum identity, expand v(t)v(t) as a sum of cosines each at a single frequency. State the frequency and peak amplitude of every line present. ((b)) Give the transmitted bandwidth BB this signal occupies, and the range of frequencies it spans.

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