A certain op-amp has three internal amplifier stages with the following gains and critical frequencies:

Stage 1: $A_{v 1}^{\prime}=40 \mathrm{~dB}, f_{c 1}=2000 \mathrm{~Hz}$

Stage 2: $A_{v 2}^{\prime}=32 \mathrm{~dB}, f_{c 2}=40 ~\mathrm{kHz}$

Stage 3: $A_{v 3}^{\prime}=20 \mathrm{~dB}, f_{c 3}=150 ~\mathrm{kHz}$

Determine the open-loop midrange dB gain and the total phase lag when $f=f_{c 1}$ .

Question

A certain op-amp has three internal amplifier stages with the following gains and critical frequencies:

Stage 1: [latex]A_{v 1}^{\prime}=40 \mathrm{~dB}, f_{c 1}=2000 \mathrm{~Hz}[/latex]

Stage 2: [latex]A_{v 2}^{\prime}=32 \mathrm{~dB}, f_{c 2}=40 ~\mathrm{kHz}[/latex]

Stage 3: [latex]A_{v 3}^{\prime}=20 \mathrm{~dB}, f_{c 3}=150 ~\mathrm{kHz}[/latex]

Determine the open-loop midrange dB gain and the total phase lag when [latex]f=f_{c 1}[/latex].

Accepted Answer

[latex]A_{o l(m i d)}^{\prime}=A_{v 1}^{\prime}+A_{v 2}^{\prime}+A_{v 3}^{\prime}=40 \mathrm{~dB}+32 \mathrm{~dB}+20 \mathrm{~dB}=92 \mathrm{~dB}[/latex]

[latex]\phi_{t o t}=- an ^{-1}\left(\frac{f}{f_{c 1}} ight)- an ^{-1}\left(\frac{f}{f_{c 2}} ight)- an ^{-1}\left(\frac{f}{f_{c 3}} ight)[/latex]

[latex]=- an ^{-1}(1)- an ^{-1}\left(\frac{2}{40} ight)- an ^{-1}\left(\frac{2}{150} ight)[/latex]

[latex]=-45^{\circ}-2.86^{\circ}-0.76^{\circ}=-48.6^{\circ}[/latex]

P R A C T I C E EXERCISE

The internal stages of a two-stage amplifier have the following characteristics: [latex]A_{v 1}^{\prime}=50 \mathrm{~dB}, A_{v 2}^{\prime}=25 \mathrm{~dB}, f_{c 1}=1500 \mathrm{~Hz}, ext { and } f_{c 2}=3000 \mathrm{~Hz}[/latex]. Determine the open-loop midrange gain in dB and the total phase lag when [latex]f=f_{c 1}[/latex].

Question 7.3: A certain op-amp has three internal amplifier stages with th...

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