Impedance matching

The maximum power transfomer theorem is:


"Maximum energy is transferred when impedances are matched."


The output impedance of the generator is equal to the input impedance of the load.


Otherwise energy is reflected back.


Some examples of mismatch:


Standing waves by acoustic waves, (sound) bouncing of walls due to impedance mismatch.


A tennis ball bouncing of the wall due to impedance mismatch.


Trying to harm a mosquito with a 10Kg mass in our hand. It is much more likely we will do damage to ourselves or the surroundings.


Some example of matching:


Phil Collins placing his hands in front of mouth and microphone at 6:20 on:
https://m.youtube.com/watch?v=pbSDcan7WWE
Or he might be making an acoustic reasonant filter.


But definitely horn loaded speakers and horns from ancient times are used to impedance match the acoustic wave from a heavier vibrating source to the light air.


The gearbox of an automobile. We impedance match for different conditions so that we can optimize the energy transfer from engine to kinetic energy of the car. Note when speed increases torque decreases by the diameter ratio or angular velocity of gears. This is a mechanical transformer.


A bit on transformers:


Power equals voltage time current on electrical systems. On mechanical systems it equals torque times velocity. It is by the conservation of energy principle that when voltage is stepped up by a transformer that current must go down. So impedance is changed. And transformers can help to impedance match. In electrical transformers, the step up voltage ratio is equal to the insulated wire turns ratio. Impedance change is found by the square of this. So a 1:10 transformer will make voltage ten times more, current ten times less therefore the impedance will become 100 times more.



Matching impedance can sound good too.


An example is a good quality transistor or electron tube amplifier that has an output impedance that is not much different than the speaker impedance.


An interesting article is this:
http://www.audioxpress.com/article/Current-Source-Amps-and-Sensitive-Full-Range-Drivers


The Pleiades Electra III is an example towards a current source with an EF183 electron tube triode connected, operated at just 12V, with anode connected to the Sennheiser HD580. A high (typically 1-2MΩ resistor from anode to grid makes operation possible, cathode is grounded. The output impedance of the electron type at these conditions (5ΚΩ?) is way higher than 300Ω yet the sound is exceptionally good and extended in both extremes of the frequency spectrum. Some mid bass accent may be observed. Also a series resistor can be seen in the speaker output of the B&O Beocenter 2600 to the headphone output. It sounds great.


It seems logical to play the game neither towards ideal voltage source (0 output impedance) neither towards ideal current source (infinite output impedance) but somewhere in between ie impedance matching? So that there is both a healthy current and voltage.


Just a 2N3053 transistor connected to a 800ohm PHILIPS AD5046N speaker can sound phenomenally good and unbelievably loud for just being driven by 30mW. Example is the Pleiades 2N3053 power amplifier operated with 12V. Power can be increased or decreased by changing the supply voltage and adjusting the collector to base bias resistor. Especialy at higher powers a heat sink should be used to avoid thermal runaway, or snowball like increase of current. The 800Ω speaker is directly connected to the collector. It operates in class A (electrons flowing all the time). The electrons are also continuously flowing through the voice coil. Extremely low noise, and superb sound quality.


Also the Pleiades Elctra II headphone amplifier with just one deliberately cathode underheated 12K5 electron tube per channel driving the 300Ω voice coil of the Sennheiser HD580 headphones. Again the impedances are fairly nearly matched and the sound is fabulous.


Transformers are not used in the above examples as the output impedance of the active device is very near to the voice coil load impedance.


References:


Introduction to System Dynamics - Shearer, Murphy, Richardson - MIT - Addison Wesley


Electromagnetism - Grant, Phillips


Pleiades Electra II schematic - euroelectron


Pleiades 2N3053 schematic
http://euroelectron.blogspot.gr/2018/03/madonnas-voice-coming-from-point-source.html


Musical Acoustics - Donald Hall


Electronics, a systems approach - Neil Storey