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When sinusoidal input is applied to a linear circuit, after a while all signals in the circuit are also sinusoidal and have the same frequency. Magnitudes and phases can differ. Bode plot shows magnitude (left axis) and phase (right axis) of an output voltage for a range of frequencies. As you can see, both magnitude and phase can change with frequency.
This circuit is a Low Pass Filter (fifth order Chebyshev LPF). It lets low frequency sine waves propagate from the input to the output with almost no change. At higher frequencies the signal is attenuated (rejected) and starts lagging behind the input. You can pinch-zoom and pan in oscilloscope to specify the frequency range for AC analysis.
Vertical trace in Bode plot lets you measure magnitude and phase at a certain frequency. EveryCircuit schematic displays mini-plots with a vector that describes a sine waves at that frequency. Size of the vector (radius of the circle) depicts magnitude, and angle of the vector depicts phase. As you move the trace or adjust source frequency, the mini-plots are updated in real time.
Given a sine wave at the input, non-linear circuits can produce signals that consist of many additional frequency components. However if the input signal is small enough, the additional frequencies can be neglected. AC analysis of a non-linear circuit produces results that are accurate for small input signals. Hence, "Small-signal AC analysis".
Time-domain transient analysis is key in understanding of frequency-domain AC analysis, one frequency at a time. In transient analysis input source generates a sine wave at a certain frequency. If the circuit is linear or the input signal is small enough, transient waveforms are also sine waves, with magnitudes and phases that match AC analysis results at that frequency of interest. This experiment can be repeated for various frequencies.
Typically, Bode plot displays magnitude in decibels (dB) computed as 20 log10(Vout/Vin). It represents a transfer function from input to output Vout/Vin in logarithmic scale. Transfer function magnitudes of 0 dB, -20 dB, and -40 dB correspond to decrease in sine wave amplitude of 1x, 10x, and 100x. In EveryCircuit, to provide better intuition, Bode plot displays output voltage as 20 log10(Vout) rather than transfer function. If you are looking for a transfer function, set the input to 1 volt, such that Vout is Vout/Vin. In most cases you don't have to do anything as the sine source has a magnitude of 1 volt by default.
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