# Can an electrical signal be truly analog?

I once heard a professor say no electrical signal according to present knowledge is truly analog in amplitude. I find it amazing considering how most schools go with the "world is analog" statement.. any views on this? BTW, the inherent discrete nature of the electric charge is the principle that leads to the amplitude being discrete.

I think the question really is "Can an electrical signal be truly digital?". The world is pretty much analog by its nature, but digital signals are really only 'digital' because we've defined a certain signal level as 'on', and a different level as 'off'. It's only be convention. Something made up. So yeah, analog exists, but digital only exists as an invention.

when an electron moves through space, does it advance in discrete steps?

I don't think you quite understood it. Let me put it this way,

Consider a capacitor, the voltage across the capacitor is a function of the charge stored. So to increase the voltage one has to add more charge. The least charge that can be added is 1.602*10^-19... This inherent discrete nature of the electric charge causes the voltage too to be discrete, albeit in very small steps.

yes, that's all fine. i realize that charge comes in discrete packages. but not all of electromagnetism consists of charged plates at a fixed distance. (and i would debate the idea that the distance is truly fixed, fwiw). when you say "electrical signal", that opens up a whole world of electromagnetic fields. and the only way for these fields to be "truly digital" is if the discrete charge carriers move in discrete steps through space.

let's say i use an electron gun to fire an electron at you. does the electrical field change discretely as the electron approaches you? it can only do so if space-time is discrete. which is maybe a question for the physics guys. i think i've seen the idea proposed before, but i'm not sure there's any evidence of it.

There is noise in circuits called shot noise or schottky noise. The basis for this noise is that all currents are made up of discrete charges. Consider a 1 microamp signal. It is equivalent to 6.25 x 1012 electrons per second. If you had a signal aperture bandwidth of 1 GHz (w = 6.3 x 109 radians per sec), the equivalent dt (aperture windown seconds) is 1.6 x 10-10 sec (because dw dt =1). So using 6.25 x 1012 electrons per sec and a dt of 1.6 x 10-10 sec gives 1000 electrons in the aperture. These electrons in this time window have a typical Gaussian distribution of +/- sqrt(1000) = 32 = 3% of signal. So the shot noise on the 1 microamp current is +/- 3%. There is also a thermal bandwidth noise called kTB noise, where k is Boltzmanns constant, T is temperature in kelvin, and B is bandwidth.

f95toli
Gold Member
The least charge that can be added is 1.602*10^-19... This inherent discrete nature of the electric charge causes the voltage too to be discrete, albeit in very small steps.

No, that is not correct. We quite often measure effective charges smaller than e. This is essentially due to screening effects which "hides" part of the charge.
There are also other effects that come into play that "smears" the charge.
Note that this is true EVEN when we are really dealing with single electrons, e.g. in single electrons transistors.
Hence, there is no such thing as the "smallest possible" charge.

Also, I am not sure how you came to the conclusion that this would also lead to quantization of voltage, but this would be wrong even if charge really was discrete.

This becomes quite obvious if you know how the Volt (the unit) is defined. The definition (and also the realization, i.e. the real experiment) is based upon the Josephson effect which relates voltage and frequency via the Josephson constant (483 GHz/mV). V=Kj*f.
Hence, the fact that frequency is not quantized means that neither is voltage.

i wonder what would happen when you add one electron, do you get the new 'mean' voltage inside the 'possible voltage strip' or a mean outside of it? if it lies within, then you couldn't tell how many electrons are inside the thing.. the quantum world is a ***** :rofl:

I think the question really is "Can an electrical signal be truly digital?". The world is pretty much analog by its nature, but digital signals are really only 'digital' because we've defined a certain signal level as 'on', and a different level as 'off'. It's only be convention. Something made up. So yeah, analog exists, but digital only exists as an invention.

I was going to say that exactly. Maybe the prof was talking about Planck-level features but that's close to the reality where the dichotomy is likely to be experienced. The world is only analog and digital is the approximation.

Yes Virginia, signals are analog!

While a DC value may be quantized to the resolution of a single electron, signals are, by definition, functions of time and are NOT DC values! For example; I = C dv/dt can have any value. I hope that we can all agree that time is continuous, and not discrete?

By the way, I found this becuase my blog is titled "http://the-world-is-analog.blogspot.com/" [Broken]", and I have a google search widget that alerts me of uses of that phrase.

Mike Demler
http://the-world-is-analog.blogspot.com/

Last edited by a moderator:
P.S. to J Roshan: I'd love to know the name of that professor! I turly hope he is not an electrical engineering professor.

MATLABdude
Maybe a little late into the fray, but when the smallest unit of current that we deal with is a milliamp (10^16 electrons) the contribution of any individual electron is negligible--not to mention that the thermal noise vastly outstrips this contribution (as others have mentioned in this thread). However, there are Coulomb blockade devices (most notably, the single electron transistor) in which the accumulation / removal of individual electrons isn't negligible (these are mostly research-type devices and IIRC, the warmest ones operate at liquid nitrogen temperatures):
http://physicsworld.com/cws/article/print/1420

I had an analog prof ask the converse: is there really such a thing as a purely digital circuit? Anyways, these are rather philosophical questions, though it's important to take away the 'big picture': when do digital / analog circuits stop acting as such, and start acting like analog / digital ones instead?

Last edited by a moderator:
"Analog" is the root for "analogy" or "analgous". It means "similar to". Take an analog transducer, like a microphone for example. When the speaker outputs an acoustic waveform, the mic translates it into a similar or "analagous" electrical waveform. Of course the quantum nature of the current and voltage is indeed discrete. But the word "analog" does not literally mean infinitely continuous, but "similar" as in "analogy".

The electric waveform amplitude, phase, and frquency are truly indeed "analagous" to those of the acoustic signal. Hence the term "analog".

That is all that "analog" means.

Claude

The only part of the signal that is not truly analog is the discrete nature of charge- i.e., electrons. I have had to deal with shot (Schottky) noise in very low noise electrical signals. If your signal is say 1 nanoamp (6.25E9 electrons/sec), and your bandwidth is 1 MHz, then you have roughly 6,000 electrons per sample in your signal, and your shot noise is roughly +/- sqrt(6,000) = +/- 75 electrons per sample, or +/- 1.25%. If your analog design is good, the only source of "non-analog" signal will be your input signal.

There are a lot of interesting points here, but most of you are making it a lot more complicated than it really is. KISS philosophy I say.. Keep It Simple...

1. BY definition, signals are time-varying voltages or currents; i.e. we measure signal FLOW.
2. Therefore, the discrete nature of an electron is irrelevant!
3. Signals flow through conductors that have real impedances, with finite capacitance and inductance.
4. An idealized (non-real) discrete signal assumes a change of amplitude in zero time
5. Since I = C dv/dt, and we can never have infinite current.. there is no such thing as a discrete signal!

There are a lot of interesting points here, but most of you are making it a lot more complicated than it really is. KISS philosophy I say.. Keep It Simple...

1. BY definition, signals are time-varying voltages or currents; i.e. we measure signal FLOW.
2. Therefore, the discrete nature of an electron is irrelevant!
3. Signals flow through conductors that have real impedances, with finite capacitance and inductance.
4. An idealized (non-real) discrete signal assumes a change of amplitude in zero time
5. Since I = C dv/dt, and we can never have infinite current.. there is no such thing as a discrete signal!

"KISS" philosophy is nonsense. Instead, we should employ "KIIRC" philosophy, or "keep it ir-reduceably complex". Simple does not mean correct. Sometimes we have to examine things at a deeper level.

But, you make some valid points. I can't argue about the finite time concept.

Claude

It's just a philosophical question as far as I am concerned. If it was the case that there were some extremely small quantum steps in voltage or current, our definition of analog would simply be "with resolution to the smallest discrete change". And bam!, it's analog again.

Our definitions are a product of our environment. Study an electrical charge and it's aspects without the influence of environmental factors and the true equation will be easy to discern. Our understanding is equivalent of defining water by sampling the ocean with all of it's environmental influences and assuming that to be the standard.

I would be interested in your interpetation of my posting. There is a gap there that most won't or can't understand.

I would be interested in your interpetation of my posting.

you think you're saying something deep and philosophical, but mostly have a deep need for validation.

you think you're saying something deep and philosophical, but mostly have a deep need for validation.