(a) Determine the frequency at which maximum power is transferred from the amplifier to the speaker in Figure 19-41(a).The amplifier and coupling capacitor are the source, and the speaker is the load, as shown in the equivalent circuit of Figure 19-41(b).
(b) How many watts of power are delivered to the speaker at this frequency if $V_{s}$ =3.8 V rms?

Question

(a) Determine the frequency at which maximum power is transferred from the amplifier to the speaker in Figure 19-41(a).The amplifier and coupling capacitor are the source, and the speaker is the load, as shown in the equivalent circuit of Figure 19-41(b).
(b) How many watts of power are delivered to the speaker at this frequency if [latex]V_{s}[/latex]=3.8 V rms?

Accepted Answer

(a) When the power to the speaker is maximum, the source impedance ([latex]R_{s}[/latex] - j[latex]X_{C}[/latex]) and the load impedance([latex]R_{W}[/latex] + j[latex] X_{L}[/latex]) are complex conjugates, so

[latex] X_{C}[/latex]= [latex] X_{L}[/latex]

[latex]\frac{1}{2\pi f C} = 2\pi f L[/latex]

Solving for f,

[latex]f^{2}= \frac{1}{4\pi^{2} LC}[/latex]

[latex]f= \frac{1}{2\pi\sqrt{LC} }= \frac{1}{2\pi \sqrt{(100 \ mH)(0.1 \ \mu F)} }= 1.59 \ kHz[/latex]

(b) Calculate the power to the speaker as follows:

[latex]Z_{tot}= R_{s}+ R_{W}= 8 \ \Omega + 8 \ \Omega = 16 \ \Omega [/latex]

[latex]I= \frac{V_{s}}{Z_{tot}}= \frac{3.8 \ V}{16 \ \Omega }= 238 \ mA[/latex]

[latex]P_{max}= I^{2}R_{W}= (238 \ mA)^{2}(8 \ \Omega )=453 \ mW[/latex]

Question 19.17: (a) Determine the frequency at which maximum power is transf...

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