Calculate the phase shift for an RC lag network for each of the following frequencies, and then plot the curve of phase shift versus frequency. Assume $f_c=100$ Hz.

(a) f = 1 Hz (b) f = 10 Hz (c) f = 100 Hz (d) f = 1000 Hz (e) f = 10 kHz

Question

Calculate the phase shift for an RC lag network for each of the following frequencies, and then plot the curve of phase shift versus frequency. Assume [latex]f_c=100[/latex] Hz.

(a) f = 1 Hz (b) f = 10 Hz (c) f = 100 Hz (d) f = 1000 Hz (e) f = 10 kHz

Accepted Answer

(a) [latex]\phi=- an ^{-1}\left(\frac{f}{f_c} ight)=- an ^{-1}\left(\frac{1 \mathrm{~Hz}}{100 \mathrm{~Hz}} ight)=-\mathbf{0 . 6}{ }^{\circ}[/latex]

(b) [latex]\phi=- an ^{-1}\left(\frac{10 \mathrm{~Hz}}{100 \mathrm{~Hz}} ight)=-\mathbf{5 . 7 ^ { \circ }}[/latex]

(c) [latex]\phi=- an ^{-1}\left(\frac{100 \mathrm{~Hz}}{100 \mathrm{~Hz}} ight)=-\mathbf{4 5 . 0 ^ { \circ }}[/latex]

(d) [latex]\phi=- an ^{-1}\left(\frac{1000 \mathrm{~Hz}}{100 \mathrm{~Hz}} ight)=-\mathbf{8 4 . 3 ^ { \circ }}[/latex]

(e) [latex]\phi=- an ^{-1}\left(\frac{10 ~\mathrm{kHz}}{100 \mathrm{~Hz}} ight)=-\mathbf{8 9 . 4 ^ { \circ }}[/latex]

The phase shift versus frequency curve is plotted in Figure 7–6 . Note that the frequency axis is logarithmic.

P R A C T I C E EXERCISE

At what frequency, in this example, is the phase shift -60°?

Question 7.2: Calculate the phase shift for an RC lag network for each of ...

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