Summary
Highlights
The video begins by introducing the task: constructing a Bode plot for a given circuit's transfer function. The transfer function U2/U1 is derived using voltage division, and the expression is then simplified by multiplying by jωC to remove a double denominator. Two corner frequencies, ωg1 and ωg2, are defined, with ωg1 being ten times larger than ωg2.
The amplitude response is constructed by analyzing the numerator and denominator separately. The numerator, 'jω/ωg1', has a linear increase of 20 dB per decade. The denominator '1 + jω/ωg2' is approximated. For ω << ωg2, the amplitude is 0 dB. For ω >> ωg2, it shows a decrease of -20 dB per decade. Combining these, the overall amplitude response starts with a 20 dB/decade slope, then flattens out to 0 dB after ωg2.
The phase response is also analyzed for the numerator and denominator. The numerator 'jω/ωg1' always contributes a +90-degree phase shift. The denominator '1 + jω/ωg2' contributes 0 degrees for ω << ωg2 and -90 degrees for ω >> ωg2, with a smooth transition over two decades around ωg2. The combined phase response starts at +90 degrees and then transitions down to 0 degrees as frequency increases past ωg2.
The video then calculates the actual corner frequencies (fg) from the given corner angular frequencies (ωg) by dividing by 2π. The calculated values are fg1 = 3183 Hz and fg2 = 318.3 Hz. Finally, the Bode phase plot is used to determine the frequency at which the phase shift is 60 degrees. By visually inspecting the plot, the frequency is found to be 0.058 times fg1, which equates to 184 Hz.