Frequency Response of Amplifiers Questions and Answers

Answer: D

Midband is the flat region between the two roll-offs, where the coupling capacitors are effectively short circuits and the shunt capacitances effectively open ones. The geometric mean happens to lie in that region but does not define it, one kilohertz is a common measurement frequency rather than a definition, and no averaging is involved. The whole value of the midband idea is that both sets of capacitances can be ignored there, which is exactly the assumption every small-signal gain calculation makes.

Answer: A

Well above their break frequencies the reactance has fallen far below the resistance in series with it, so the capacitor drops a negligible fraction of the signal. Charging, leakage and amplitude are all beside the point. It is the same argument that lets shunt capacitances be treated as open circuits in the same region, from the other direction - and together those two approximations are what make midband analysis a matter of resistors alone.

Answer: B

The construction draws flat and sloping straight lines meeting at the breaks, and the true curve departs from it by at most three decibels at each break. Zeros are handled just as easily, with an upward slope, and no equal spacing is required. Phase is not proportional to frequency. An approximation whose maximum error is known and small is far more useful than an exact method that cannot be done by hand, which is why the construction endures.

Answer: C

At the break the asymptotes meet at the passband level while the true response is three decibels below, which is the largest error the construction makes. Six decibels is the slope per octave, and the asymptotes certainly do not coincide with the curve there. Knowing the worst-case error of a graphical method is what tells you when it is good enough, and three decibels is usually well inside the tolerance of everything else in the circuit.

Answer: D

A zero contributes an upward six decibels per octave and ninety degrees of lead, exactly the mirror of a pole. It does not shift the response bodily, and it adds lead rather than lag. Because a zero can cancel a pole's slope and phase, zeros are what compensation networks are built from - and recognising that they are simply poles with the sign reversed halves the work of learning them.

Answer: A

A zero placed near a troublesome pole returns the slope to its previous value and the phase towards zero, recovering the margin the pole had cost. It does not raise the passband gain, cannot substitute for dominant-pole compensation in general, and has nothing to do with input capacitance. Cancelling an unwanted effect with an equal and opposite one is delicate, since the two must track, but it costs far less bandwidth than making one pole dominant.

Answer: B

Both poles lie below thirty megahertz, so both contribute:

\[ 6 + 6 = 12 \ \mathrm{dB/octave} \]

giving twelve decibels per octave, and a phase approaching one hundred and eighty degrees. Counting how many breaks lie below the frequency of interest gives the slope and the phase together, which is what makes the Bode construction a stability tool rather than merely a description.

Answer: C

Only the one-megahertz pole lies below three megahertz:

\[ 6 \ \mathrm{dB/octave} \]

so six decibels per octave, with a phase of somewhat more than forty-five degrees. The second pole has not yet taken effect. That the slope steepens in steps as each break is passed is the whole shape of an asymptotic plot, and reading it off is a matter of counting rather than calculating.

Answer: D

Stability requires the loop gain to have fallen below one while the phase shift is still short of one hundred and eighty degrees, since at that phase the feedback has become positive. Falling to unity before the first pole would waste all the available gain, and waiting until after the second pole is exactly the unstable case. The margin between where the gain reaches unity and where the phase reaches one hundred and eighty degrees is what the phase margin measures.

Answer: A

Phase margin is the number of degrees short of one hundred and eighty that the phase has reached at the frequency where the loop gain is unity, and forty-five degrees or more is usually specified. The second option describes gain margin, measured at the frequency of inversion instead. Two margins measured at two different frequencies, each reporting how far the loop is from oscillating, and quoting one where the other is meant makes a stability claim meaningless.