Low gain amp that I can build that would output cleanest signal possible - Page 3  

But, there is something that is taught to every power electronics student or was briefly gone over in physics  is how transformer works.

I have mentioned above that transformer changes the output impedance.  How?  Impedance is the ratio of V/I because V=IZ.  Impedance is is a complex quantity. Z=R + JX  R is called a resistance where real power is lost.  X is what you call reactance, which causes a phase shift.  For DC circuits, Impedance is purely real or resistive, since is there is no time varying signal.  Impedance can be thought of as a either decreasing the rate of current and delaying the current from voltage.  Hence phase, voltage is not in phase with current.  Impedance, it impedes so therefore, it is laggings behind because of an impeding element(headphones).  

Now transformer changes the output impedance.  How?  We know transformers are coupled inductors.  Inductors are copper wound on different types of core.  If you put two of then next to each other have different winding on them.  One having 10 windings the other 5.  Connect a AC source to the the inductor with 10 winding, and there will be current flowing through the copper.  The flowing copper creates a magnetic field around it, and the inducter of 5 winding next to it will be induced to have current flow as a result of the magnetic field.  Lets say the AC source had 10 volts.  If that was the case, the voltage induced to the 10 winding inductor to the 5 winding inductor will step it down to 5 volts because of the winding ratio.  But we can't defy the laws of physics, ideally all power should transfer.  If voltage is stepped down, how do you keep power constant?  P=IV  Step the current up.  Therefore current is twice as much on the side the voltage is stepped down.  Now what happed to the impedance?  As I have stated impedance is the ratio V/I.  If the source side the V=10 and I = 2, then the induced side, V=5 stepped down, and I=4.  P=20 for both cases.  So V/I on the source side is 10/2 =5ohms.  on the induced side it is 5/4.  Wow, the impedance has lowered as expected!!  

As I have stated, do not equate volume with voltage.  Volume is power applied to the load.  Notice power stays constant with the transformer?  Impedance changes, but not power.  

Ideal power equation

The ideal transformer as a circuit element

If the secondary coil is attached to a load that allows current to flow, electrical power is transmitted from the primary circuit to the secondary circuit. Ideally, the transformer is perfectly efficient; all the incoming energy is transformed from the primary circuit to themagnetic field and into the secondary circuit. If this condition is met, the incoming electric power must equal the outgoing power:

giving the ideal transformer equation

Transformers normally have high efficiency, so this formula is a reasonable approximation.

If the voltage is increased, then the current is decreased by the same factor. The impedance in one circuit is transformed by the square of the turns ratio.^[29] For example, if an impedanceZ_s is attached across the terminals of the secondary coil, it appears to the primary circuit to have an impedance of (N_p/N_s)²Z_s. This relationship is reciprocal, so that the impedance Z_p of the primary circuit appears to the secondary to be (N_s/N_p)²Z_p.

[edit]Detailed operation

The simplified description above neglects several practical factors, in particular the primary current required to establish a magnetic field in the core, and the contribution to the field due to current in the secondary circuit.

Models of an ideal transformer typically assume a core of negligible reluctance with two windings of zero resistance.^[31] When a voltage is applied to the primary winding, a small current flows, driving flux around the magnetic circuit of the core.^[31] The current required to create the flux is termed the magnetizing current; since the ideal core has been assumed to have near-zero reluctance, the magnetizing current is negligible, although still required to create the magnetic field.

The changing magnetic field induces an electromotive force (EMF) across each winding.^[32] Since the ideal windings have no impedance, they have no associated voltage drop, and so the voltages V_P and V_S measured at the terminals of the transformer, are equal to the corresponding EMFs. The primary EMF, acting as it does in opposition to the primary voltage, is sometimes termed the "back EMF".^[33] This is due to Lenz's law which states that the induction of EMF would always be such that it will oppose development of any such change in magnetic field.

[edit]

So therefore, it is not an amp in the sense that it has gain, or is it an attenuator.  I would say adding a transformer will create power loss, I would not recommend it especially for low power circuits.  It is used for tube circuits I know because of the low output impedance it creates.

Look, the output impedance has lowered.  Current is upped?  That doesn't make sense?  If output impedance has lowered, than that means overall impedance has lowered.  What happend then?  Current is raised.