Frequency Response of Amplifiers Questions and Answers

Answer: D

The order is 1, 2, 3, 4: a few hertz, a few hundred hertz, a few hundred kilohertz, and a few hundred megahertz. The gap between the third and the fourth is the Miller penalty, and it is usually two or three orders of magnitude - which is what makes the cascode worth its extra device. Laying the four out in order shows immediately where a design's effort should be spent.

Answer: A

Bandwidth is the difference between the two breaks:

\[ B = 100\mathrm{k} - 100 \approx 99.9 \ \mathrm{kHz} \]

which is about 99.9 kHz, and for practical purposes the lower break is negligible. Ten megahertz would be their product, which is not a bandwidth. When the two breaks differ by three orders of magnitude, the bandwidth is essentially the upper break alone, which is why it is usually the only figure quoted.

Answer: B

Dividing the product by the gain:

\[ B = \frac{4 \times 10^{6}}{20} = 200 \ \mathrm{kHz} \]

giving 200 kHz. Multiplying instead gives 80 MHz, which would be more bandwidth than the amplifier possesses at any gain. This is the calculation behind every operational amplifier data sheet, and it is why a unity-gain-stable device's full bandwidth is available only when no gain is being taken.

Answer: C

Feedback reduces the closed-loop gain, and since the gain-bandwidth product is roughly fixed, the bandwidth rises in the same proportion the gain falls. It cannot change the device capacitances or remove the Miller effect, though it does reduce the effective source impedance seen by the input. It also extends the low end, but through a different mechanism. Trading a surplus of gain for something scarcer is what feedback does in every respect, and bandwidth is the clearest case.

Answer: D

Dominant-pole compensation puts one break well below the others, so the gain has fallen to unity before the second pole adds its phase and the loop stays stable. Pole-zero cancellation is a different and more delicate technique, coincident poles would be the worst case for stability, and poles cannot simply be removed. Making one effect deliberately dominant, so that the others need not be controlled precisely, is a robust design strategy well beyond amplifiers.

Answer: A

Making one pole dominant means moving it downward, so the open-loop response begins falling earlier than it otherwise would and the closed-loop bandwidth at a given gain is reduced. No second pole is added, the low-frequency gain is untouched, and the low end is unaffected. Buying stability with bandwidth is the standard exchange in feedback design, and it is why an uncompensated amplifier is faster but harder to use.

Answer: B

A capacitor across part of the emitter resistor reduces the degeneration as frequency rises, so the gain climbs to offset the falling high-frequency response. It is the emitter-side counterpart of shunt peaking on the collector side. The other options describe shunt peaking, a compensation capacitor and output damping. Compensating a falling response by arranging for the gain to rise is a general technique, and it can be applied at either end of the device.

Answer: C

Because gain and bandwidth trade at a roughly constant product, a stage taking little gain is wide, and several of them in series give a large total gain with a bandwidth that shrinks only modestly. Roll-offs compound rather than cancelling, low-gain stages still have Miller capacitance though multiplied less, and the capacitor count rises rather than falling. Distributing a requirement across several stages, each operating where it is efficient, beats demanding everything of one.

Answer: D

The shrinkage factor worsens with each stage - modest for two, severe for six - so beyond some number the compounding costs more bandwidth than the extra stage's own width provides. The gain is not bounded by a frequency, the low-frequency breaks are a real but separate cost, and supply current is an economic rather than a bandwidth limit. An approach that improves a figure per stage while degrading it per cascade has an optimum number of stages, and finding it is part of the design.

Answer: A

A distributed amplifier sums its stages' currents into a common output line rather than passing the signal through each in turn, so the gains add while the roll-offs do not compound. Direct coupling, unity gain and a shared load do not describe it. Changing a cascade into a parallel summation is what escapes the compounding, and it is the standard arrangement wherever very wide bandwidths are needed at the cost of considerable complexity.