Solved: Resistor networks are sometimes used as volumecontrol circuits. In this

Chapter 3, Problem 3.66

(choose chapter or problem)

Resistor networks are sometimes used as volume control circuits. In this application, they are referred to as resistance attenuators or pads. A typical fixed-attenuator pad is shown in Fig. P3.66. In designing an attenuation pad, the circuit designer will select the values of \(R_{1}\) and \(R_{2}\) so that the ratio of \(v_{o} / v_{i}\) and the resistance seen by the input voltage source \(R_{\mathrm{ab}}\) both have a specified value.

a) Show that if \(R_{\mathrm{ab}}=R_{\mathrm{L}}\), then

\(R_{\mathrm{L}}^{2}=4 R_{1}\left(R_{1}+R_{2}\right)\),

\(\frac{v_{o}}{v_{i}}=\frac{R_{2}}{2 R_{1}+R_{2}+R_{\mathrm{L}}}\).

b) Select the values of \(R_{1}\) and \(R_{2}\) so that \(R_{\mathrm{ab}}=R_{\mathrm{L}}=300 \ \Omega\) and \(v_{o} / v_{i}=0.5\).

c) Choose values from Appendix H that are closest to \(R_{1}\) and \(R_{2}\) from part (b). Calculate the percent error in the resulting values for \(R_{\mathrm{ab}}\) and \(v_{0} / v_{1}\) if these new resistor values are used.