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Chapter 12: Problem 7

Calculate the transformer turns ratio required to connect four parallel \(16-\Omega\) speakers so that they appear as an \(8-\mathrm{k} \Omega\) effective load.

Short Answer

Expert verified
Substitute values for \(R_T\) and \(R_L\) in the formula for \(n\) to get the transformer turns ratio required to make the \(16-\Omega\) speakers appear as \(8-k\Omega\) effective load to the amplifier.

Step by step solution

01

Calculation of total resistance for parallel circuit.

Firstly, we need to calculate the total resistance of the four \(16-\Omega\) speakers wired in parallel. The formula to calculate total resistance (Rt) for parallel resistors is: \[\frac{1}{{R_T}} = \frac{1}{{R_1}} + \frac{1}{{R_2}} + \frac{1}{{R_3}} + \frac{1}{{R_4}}\]Substitute the given resistance values into the equation to calculate the total resistance.
02

Calculate the effective load resistance and transform to ohms

Given that the effective load to the amplifier should appear as \(8-k\Omega\), convert this to ohms for easier comparison with the total resistance calculated earlier. The conversion is done by multiplying by \(10^3\).
03

Calculate the transformer turns ratio

The transformer turns ratio can be calculated from the formula:\[n = \sqrt{\frac{R_L}{{R_T}}}\]where, \(n\) is the transformer turns ratio, \(R_L\) is the load resistance and \(R_T\) is the source resistance. As calculated earlier, you can now substitute \(R_L\) and \(R_T\) into the formula to get the transformer turns ratio.

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Most popular questions from this chapter

Draw the circuit diagram of a class B npn push-pull power amplifier using transformercoupled input.

Sketch the circuit diagram of a quasi-complementary amplifier, showing voltage waveforms in the circuit.

A transformer-coupled class A amplifier drives a \(16-\Omega\) speaker through a \(3.87: 1\) transformer. Using a power supply of \(V_{C C}=36 \mathrm{~V}\), the circuit delivers \(2 \mathrm{~W}\) to the load. Calculate: a. \(P(\) ac \()\) across transformer primary. b. \(V_{L}(\mathrm{ac})\). c. \(V(\mathrm{ac})\) at transformer primary. d. The rms values of load and primary current.

A \(160-\mathrm{W}\) silicon power transistor operated with a heat sink \(\left(\theta_{S A}=1.5^{\circ} \mathrm{C} / \mathrm{W}\right)\) has \(\theta_{J C}=0.5^{\circ} \mathrm{C} / \mathrm{W}\) and a mounting insulation of \(\theta_{C S}=0.8^{\circ} \mathrm{C} / \mathrm{W}\). What maximum power can be handled by the transistor at an ambient temperature of \(80^{\circ} \mathrm{C}\) ? (The junction temperature should not exceed \(200^{\circ} \mathrm{C}\).)

Draw the circuit diagram of a class A transformer-coupled amplifier using an \(n p n\) transistor.
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