Frequency Response of Amplifiers Questions and Answers

Answer: D

Well below the frequency where its length matters, a cable looks like a lumped capacitance of perhaps a hundred picofarads per metre, and that is what loads the stage. Its inductance and characteristic impedance become relevant only when the length approaches a wavelength, and dielectric loss is a second-order effect. Knowing which model applies at which frequency prevents both over-complicating a low-frequency problem and under-modelling a high-frequency one.

Answer: A

The output impedance works into the cable capacitance:

\[ \begin{aligned} f &= \frac{1}{2\pi (2000)(100 \times 10^{-12})} \\ &\approx 800 \ \mathrm{kHz} \end{aligned} \]

so about 800 kHz. Driving the same cable from sixty ohms would move the break to twenty-six megahertz, which is why a follower or a line driver is fitted whenever a cable has to be driven. The cable is the same; the difference is entirely in what drives it.

Answer: B

The gain-bandwidth product states what is available to trade, so the bandwidth at any chosen gain follows from one division. Midband gain alone says nothing about speed, the lower break concerns the other end entirely, and the phase at the break is fixed at forty-five degrees for a single pole and so carries no information. A figure of merit that combines two specifications into a conserved quantity is worth more than either alone, and it is why data sheets lead with it.

Answer: C

Increasing the collector load raises the gain and lowers the break in the same proportion, so the bandwidth falls. The other three all attack a factor in one of the limiting time constants without raising the gain. Because gain and bandwidth trade at a roughly constant product, any change that raises the gain has to be checked for what it costs at the band edge, and this one costs exactly what it gains.

Answer: D

This is the midband region, and its usefulness is precisely that both sets of capacitances can be ignored there, leaving a calculation in resistors alone. Transition refers to the device's unity-gain frequency, and saturation and the ohmic region are operating regions rather than parts of a response. Every small-signal gain figure quoted for a stage is implicitly a midband figure, which is worth remembering when a measurement at the band edge fails to match.

Answer: A

The circuit is (A): a series 0.1 μF capacitor with a shunt 0.5 kΩ resistor, a differentiator with a short time constant.

The output is a sharp spike at each edge of the square wave that dies away to zero long before the next edge. That is the response of a high-pass RC circuit (capacitor in series, output across the resistor) whose time constant is much shorter than the half period.

\[ \begin{aligned} \tau_{A} &= 0.5\ \text{k}\Omega \times 0.1\ \mu\text{F} = 50\ \mu\text{s} \\ T/2 &= 0.5\ \text{ms} \end{aligned} \]

With \(\tau \ll T/2\) each spike decays fully, as drawn. Circuit (B) has the same layout but \(\tau = 5\) ms, ten times the half period, so its output would barely decay and look like a slightly tilted square wave. Circuits (C) and (D) take the output across the capacitor; these low-pass integrators give smoothed or ramp-like versions of the square wave, not spikes.

Answer: A

The steady state response is tested with a sinusoidal input.

A linear circuit driven by a sinusoid settles, after the transients die out, into a sinusoid of the same frequency, changed only in amplitude and phase. Measuring that change over a range of frequencies gives the circuit's steady state (frequency) response, and any other periodic input can be built from sinusoids by Fourier analysis.

Square, triangular and sawtooth waves contain many harmonics at once. A square wave is the usual test for the transient response, such as rise time and overshoot, rather than for the steady state, and the others are used mainly for sweep and ramp testing.

Answer: A

The ascending order is dc amplifier, audio amplifier, radio amplifier, video amplifier.

Bandwidths grow in this order. A dc amplifier is usually meant for slowly varying signals, with a bandwidth from 0 Hz up to a few hundred hertz or kilohertz. An audio amplifier covers about 20 Hz to 20 kHz. A radio-frequency (tuned) amplifier passes a band of the order of tens to hundreds of kilohertz around its carrier. A video amplifier must pass about 0 Hz to several megahertz.

The other options put the video amplifier first or in the middle, or the dc amplifier after the radio amplifier, which does not match these bandwidths.