On Christmas Eve itself, there is a crisis in the Lie family. They
have a tradition of singing karaoke, but now it turns out that the
facility does not work. Men Laura knows advice. She finds an old
CD player, a microphone and an amplifier in the attic. But the
amplifier has only one input. How should they be able to play
the audio track and the microphone signal at the same time?
“We connect them in parallel,” says Ms. Lie, who in her youth
had taken the low-voltage line in vocational school. Mrs Lie’s
solution is shown in Figure 1.
Now assume that the microphone, when not connected to anything, produces a voltage
signal vM (t) and has a Thévenin resistor RM. Similarly, the CD player produces an audio track
vL (t) through a Thévenin resistor RL. The amplifier can be assumed to have an input resistor
a) Create a circuit diagram showing a circuit model for the system.
b) Show that the voltage at the amplifier input is given by
c) The trip has come to Laura to sing karaoke, and she wants the genre of disco music. Laurentius
Lie protests, and demands that in that case the volume of the soundtrack must be halved. The
volume control does not work (this is probably why the equipment is located in the attic), and
more improvisation is needed.
Mrs. Lie suggests adding an extra resistor RS in series with the signal from the CD player. Find
an expression for RS to halve the contribution on the amplifier input from the CD player.