1.

Fig. 2. Circuit level schematic

Assume that the audio amplifier is a linear-time invariant system. What is the output Vour(t) of the

audio amplifier in response to the input signal Vin(t)=Acos(wot)? Write your answer in terms of the

magnitude |H(jw) and the phase ZH(jw) of the frequency response H(jw) of the audio amplifier./n2. Consider the periodic square wave signal shown in Fig. 3, where wo-2n fo, fo-50 KHz, and A₁-10 mV,

as the input signal Vin(t).

-2π

wo

-TT

Л

400

Fig. 3. Periodic square wave

Assume that the audio amplifier system has a frequency response of the form

H(jw) =

2π

wo

α

1 + ß jw

with a > 0 and 3 > 0

Write an expression for the output signal Vou(t) in terms of the Fourier series coefficients at of Vin(t)

(for all k) and the frequency response H(jw)./n3.

Focus on the speaker in the amplifier-speaker circuit shown in Fig. 1. Explain, in detail, how the

speaker works, i.e., how it generates sound from the electric signal it receives. Sketch a figure showing

the construction with all the essential parts of a speaker. Identify a magnetic circuit within the speaker

and explain the purpose of this circuit. What kind of relationship exists between the sound intensity and

different parameters of the magnetic circuit, such as the number of wire turns, the dimensions of the

circuit, the type of magnetic material for the core (e.g., a neodymium magnet vs. a ceramic magnet,

etc.), the magnetization curve of the core, and so on. Observe the hysteresis loops shown in Figure 5.23

in the Electromagnetics textbook. Which of the two materials should be used for making the coils

("magnetic winding") and the permanent magnet, respectively, in the speaker? Justify your answer.

What would happen if we swap the materials?