Amplifier of Hi-Fi channel
Take 15 minutes to prepare this exercise.
Then, if you lack ideas to begin, look at the given clue and start searching for the solution.
A detailed solution is then proposed to you.
If you have more questions, feel free to ask them on the forum.
A stereo amplifier can be modeled by the following circuit diagram in which the input resistance will be considered infinite :
It performs the following two tests :
Test n°1 :
, , RMS , .
Is measured with a digital oscilloscope effective (RMS) output value equals to .
Test n°2 :
, , RMS , .
We then measure the effective (RMS) output value equals to .
Moreover, we find that during each test, the two output signals keep, regardless of the frequency, the same effective (RMS) value and are in phase with .
Determine the gain and the complex output impedance .
We denote, in complex notation and noting and effective (RMS) values of the input and output voltages and the phase shift of with respect to :
The voltage divider rule gives :
By denoting :
Where the real and imaginary parts and a priori depend on the frequency, the effective value of the output voltage can be written :
With, in addition :
The phase shift between and is zero being regardless of the frequency, and deduce and :
As the effective (RMS) value does not depend on the frequency, the output of the stereo impedance is finally real and equivalent to a single resistor of constant value , independent of frequency.
Tests with two resistance values then lead to the system of two following equations :
With in .
The resolution leads to :
The amplifier being supplied with a voltage :
What should be the load resistor so that it provides the maximum average power at the constant amplitude input voltage ?
The average electrical power received by the load resistance is equal to :
It will be extremal, at given , and (amplifier characteristics) when :
The power is then effectively maximum and is equal to :
The load resistance is called adapted to the output resistance of the stereo and we talk about adaptation of resistors.