In a not so distant issue, the mention of emf and reverse emf (electro motive force) reared its ugly head. These mathematical terms can be monstrously confusing, yet there’s no other way to expand our understanding of the various physical properties haunting the make-up of this highly complex device, the tattoo machine.

In order to really explain these terms and their designated roles I must insist that your tray table is stored, your seat is in the upright position and your seatbelt is securely fastened. Prepare yourself for the jump to hyperspace…

The flow of electricity through any conductor, in our case copper wire, has the effect of generating a magnetic field. This creation of magnetic energy represents a measurable power loss during the time that that field is being created, which is measurable as a voltage drop or back emf. This is quite different (and additional) to the voltage drop produced by the resistance of the copper wire and disappears once stable conditions have been reached. Therefore in a standard DC circuit (e.g. flashlight) the back emf tends to prevent the current rising rapidly when the circuit is switched on. Once a constant magnetic field has been established, the back emf disappears since no further energy is being extracted from the circuit and transferred to the magnetic field.

Would it surprise you to realize that our tattoo machine creates an AC circuit? It does, the voltage alternates between zero volts and +10 volts (give or take a few). In the case of our AC circuit, the current is constantly changing, creating a back emf, which is also changing at a similar rate. The value of the back emf is dependent on both the rate of change of current (frequency, or how fast the contact screw and front spring meet) and to a factor dependent on the form of the conductor (our coils), which governs its impedance. Inductance is thus another form of resistance to AC, generated in addition to pure resistance.

Every conductor has inductance when carrying AC, although in the case of straight wire this is usually negligible (except at very high frequencies). If the wire is wound in the form of a coil however, its inductance is greatly increased. If the coil is fitted with an iron core, as in our machines coils, then its inductance is even higher for the same number of turns and coil size.

With the AC flowing through our machine coil, the “resistive” condition established is not as drastic as may appear at first sight. The polarity of the back emf is always such as to oppose any change in current. Thus while the current is increasing, work is being done against the back emf by storing energy in the magnetic field. On the next part of the current cycle when the current is falling (no contact between front spring and contact screw), the stored energy in the magnetic field returns to the circuit, thus tending to keep the current flowing. An inductance, in fact, may be a very good conductor of AC, especially when combined with a capacitor in a tuned circuit in our tattoo machine. On the other hand, it may be designed to work as a resistive component or choke. If your machine manufacturer has not calculated these numbers, “choking your machine” is the mo’ likely scenario.

For simplicity I’ve reduced our machine coils to a single layer, so we can calculate the inductance of our coil as

L = R2N 2
9R+10l

where:
L , inductance in microhenrys
R , radius of the coil in inches
N , the number of turns
l , the length of the coil in inches.

This number is needed for two distinct purposes: First, to minimize ohmic resistance, thereby improving the efficiency or Q-factor of our machine’s coils. Secondly, we need this value to determine the “tuned circuit” we discussed earlier.

Keep in mind, the combination of resistance, capacitance and inductance determines how the machine will respond to changes in line current (poor power supply) or changes in load (differences in skin toughness). Therefore it is critical to have calculated values.

Theoretical values can be determined and give us an indication of the values required for maximum efficiency. However, just like all things in real life, field-testing is still required.

At this time I would like to make it clear that this flight is going to be a long one and we’ll be discussing the role of the capacitor in detail on the next leg of our journey.

By the way, the in-flight movie has been cancelled due to low visibility.