Final answer:
To plot a frequency response with unity gain bandwidth and DC gain for an RLC AC circuit, consider the resonant frequency, quality factor (Q), and bandwidth. The resonant frequency is where the circuit oscillates with the greatest amplitude, Q reflects the sharpness of the resonance peak, and the unity gain bandwidth surrounds the resonance where the gain is 1 or more.
Step-by-step explanation:
To plot the frequency response for an AC circuit, especially one involving a resonance phenomenon such as an RLC series circuit, you need to understand a few key concepts. The resonant frequency is where the inductive and capacitive reactances balance each other out, and the system naturally oscillates with the greatest amplitude. In such a system, the unity gain bandwidth is a range of frequencies around the resonant frequency where the circuit maintains a gain of 1 (or 0 dB) or more.
The DC gain refers to the gain of the circuit at zero frequency, which generally applies to systems including operational amplifiers. For an RLC circuit, the DC gain isn't usually defined, as these circuits don't pass DC signals (0 Hz) due to the capacitor being an open circuit at this frequency.
The quality factor (Q) is a measure of how 'sharp' the resonance peak is. The Q factor and bandwidth (Δω) are inversely related; a higher Q implies a narrower bandwidth. The plot of current versus frequency or power versus frequency will show a peak at the resonant frequency, and the width of this peak is the bandwidth. A high Q factor would indicate a very sharp and tall peak, whereas a lower Q factor would mean a wider and flatter peak.