So, since all the commentary above is

__factually correct__, here's the redux:

*Transformers *__transform__ the primary __to__ the secondary, __and__ the secondary __to__ the primary. Got that? Transformers are

*necessarily *__bidirectional__.

To understand

**why** a 5.1 to 1 ratio of primary-to-secondary has a 5.1² or 26×

*transformation of impedance*, consider the lowly resistor as a power eating device.

If we have a 100 Ω resistor, and put 10 volts across it, due to Ohm's Law (E = IR), we see that

E = IR … rearranged to

I = E/R … and with E = 10 V, R = 100 Ω

I = 10 ÷ 100 amps

I = 0.10 A

Now, using the resistive power formula

P = IE

P = 0.10 A × 10 V

P = 1 W

Our lil' power eater will be heating up with 1 watt of power dissipated thru it. To carry this further, with 20 volts:

I = E/R

I = 20 V ÷ 100 Ω

I = 0.20 A

And thru the power formula

P = IE

P = 0.20 A × 20 V

P = 4 W

You can see that as far as power goes, doubling the voltage

__quadruples__ the power generated thru the resistor, all other things being equal. Perhaps this will make it more clear then, how a transformer might have a 5.1 : 1 ratio between windings (note that I'm specifically

__not__ saying 'primary' and 'secondary'), given that a transformer's unique ability is to

*transform* power

V_{IN} • A_{IN} = kV_{OUT} • A_{OUT}/k … where

k = turns ratio of (IN over OUT) windings

shows that the

*voltage change* and the

*current change* are

*inversely in proportion* to each other, yet the net is still 'VA'

**because the 'k' cancels**. Transformers transform power.

But what about the Z² (impedance squared) idea? That turns up in

__this__ way. Lets use our resistor again, the 100 Ω job. Setting the power at 1 W (the first example), we had:

P = IE … and

E = IR … so substitute in

P = E²/R or

P = I²R

They're both equivalent. So, using the idea that a transformer's

*transformation* of

__power__ is nearly ideal to pass-thru, we get

P = E²/R … is

PR = E²

R = E²/P

Right? Working

__just__ with the transformer's E

_{IN} I

_{IN} = kE

_{OUT} • I

_{OUT}/k identity above, we get

R_{IN} = E_{IN} / I_{IN}

on one side, and

R_{OUT} = E_{OUT} / I_{OUT}

which now substitutes

E_{OUT} = 1/k E_{IN} … and

I_{OUT} = k I_{IN} … so

R_{OUT} = 1/k E_{IN} / k I_{IN}

R_{OUT} = 1/k² E_{IN} / I_{IN}, and substituting Z for the EI business:

**R**_{OUT} = 1/k² Z_{IN} ... __And __**vice-versa!**

There's your k² or ratio² relationship. Mathematically shown.

Hope that helps, and if not, I apologize for taking all y'all's time.

⋅-⋅-⋅ Just saying, ⋅-⋅-⋅

⋅-=≡

**Goat**Guy ✓ ≡=-⋅