Electronic – Inductance of planar (spiral) coil near solid copper surface

Long ago before diodes, DC was made from AC by synchronous commutation. This usually meant a motor spinning at the AC frequency with contacts driven by the motor shaft so that connections from the input AC to the output DC were effectively flipped twice per line cycle so that the output was always presented with a positive or zero voltage.

You could possibly do something similar with relays switching on and off at the right times to capture only the positive spikes of your pulses.

However, why not use diodes? That is the obvious and simple way to fulfill your other requirements.

When modeling an ideal transformer, why do we not consider the inductance of the primary and secondary winding of the transformer.

For an ideal transformer, the primary and secondary inductances are arbitrarily large ('infinite'). This must be so since, for an ideal transformer, there is no frequency dependence.

To see this, consider the equations (in the phasor domain) for ideally coupled ideal inductors:

$$V_1 = j\omega L_1I_1 - j\omega M I_2$$

$$V_2 = j \omega M I_1 - j \omega L_2 I_2$$

where

$$M = \sqrt{L_1L_2}$$

Solving for \$V_2\$ yields

$$V_2 = \left(\sqrt{\frac{L_2}{L_1}}\right)V_1 = \frac{N_2}{N_1}V_1$$

Now, assume the primary is driven by a voltage source and that there is an impedance \$Z_2\$ connected to the secondary such that

$$V_2 = I_2 Z_2$$

It follows that

$$I_2 = \frac{j \omega M}{Z_2 + j \omega L_2}I_1 = \left(\sqrt{\frac{L_1}{L_2}}\cdot\frac{1}{1 + \frac{Z_2}{j\omega L_2}}\right)I_1 = \left(\frac{N_1}{N_2}\cdot\frac{1}{1 + \frac{Z_2}{j\omega L_2}}\right)I_1$$

This is certainly not the behaviour of an ideal transformer where we expect

$$I_2 = \frac{N_1}{N_2}I_1$$

But notice that in the case that \$j\omega L_2 \gg Z_2\$ we have

$$I_2 \approx \frac{N_1}{N_2}I_1$$

which is exact in the limit that \$\frac{Z_2}{j \omega L_2} \rightarrow 0\$

Thus, we recover the ideal transformer equations from the ideally coupled ideal inductors in the limit that \$L_1, L_2\$ go to infinity (keeping their ratio constant).

In summary, we don't consider the inductances for the ideal transformer since, as shown above, the ideal transformer equations hold only in the limit of arbitrarily large primary and secondary inductances.