Analog Engineering

Analog Design, once the art of an electrical engineer was pushed out of the limelight by digital technologies. But it is not dead. For one, the real world is analog and when someone wants to measure something digitally it has to be converted. And in front of the analog-to-digital converter analog circuitry is needed. But this article does not focus on the mixed-signal design, because this is discussed in another.

This short article is about pure analog design issues. It is not for seasoned analog gurus - they already know everything in here - but for someone who does not know about some stumbling blocks in the "analog world". Here some rules that were true all the time become invalid. Let us take a normal wire as our example and see:

Mistake 1: A wire connected between two points makes them to be on identical potential.

Truth 1: A wire is an almost undamped resonator waiting to be excited.

Proof 1: A wire of 25mm (1") length will resonate at about 7GHz, one with 100mm at about 1.8GHz and so forth. Too high frequencies for the average device? Not at all! A circuit with an active device in it that has a slew rate in the order of 1000V/µs will be able to bring the 100mm wire into resonation and to act as an antenna. And 1000V/µs are pretty common today for devices in switching power supplies with fast MOS-FETs or IGBTs.

When not operating in parallel resonant mode a wire runs in series resonant mode biasing both of it's ends with the high frequency signal.

Mistake 2: When I stay well below these high frequencies (I use LF only) mistake 1 is no mistake.

Double fault!

Truth 2: A wire is some mixture of a battery, a capacitor, an inductor and a variable resistor.

Proof 2: The variable series resitance is there because metals have a positive coefficent of their specific resistance. Higher temperature means higher resistance. This coefficient can be rather high, like that of platinium or moderate like that of copper, but it is always there.

The capacitor is formed by the wire with it's surroundings. Any two conductive bodies make up a capacitor. The universum therefor contains more capacitors than suns, planets and all the other stuff combined. The good side of capacitors is that they can store charge. The bad side is that any change of charge on one "plate" or any change in distance between the two "plates" will definetly alter the potential of the other and in a real life circuit this will cause a current to flow. This current is proportional to the rate of change in either of the parameters.

The inductor is formed by the ability of the wire to carry current. It increases with the length and decreases with the thickness, but it never becomes zero (unless the wire has zero length, that is it is not there at all). And inductors have a temptation to form transformers with other inductors. The locations of the participating inductors are usually not strictly fixed in relation to each other. So these transformers like to couple any change in distance (or orientation) and any change in current flowing to the other side.

The battery is formed by the junctions of the wire to rest of the circuit. Actually there are a couple of batteries involved, but for DC with voltage levels in the 10V range the combination looks like one with a voltage protortional to absolute temperature multiplied by the difference of the thermo-electric coefficents of the two metals contacting each other.

Mistake 3: When I shield my wire, fix it tightly and do not run high currents (only micro-amperes) over them then I can safely assume that my wire and it's junctions are harmless.

Truth 3: By these means you have eliminated the capacitive coupling, minimized the inductive one and the series resitance is probably of no concern any more. But when you think you can safely use it now for high precision measurements in the nano-volt range you are completely wrong. Even if you keep all your junctions between different metals on the same temperature. Yes, the net DC voltage of the thermo-electric voltage will be zero then. But the noise will be still there. Not the Johnson noise alone (this is very small for a low-ohm resistor like a wire anyway), but the noise generated by the metal-metal junctions. This noise is the result of the statistical nature of the generation of thermo-electric electrons. When the junctions are all on the same temperature no DC current flows, but smaller AC currents still flow between the different junctions.

There are thermometers around that exploit this thermal noise to measure the time constant of a thermocouple under the actual process conditions. This time constant varies by two to three orders of magnitude, depending on the medium (e.g. still air, moving air, still liquid or moving liquid).

© Paul Elektronik, 1998-2002