Changing circuitry of analog computer *During* simulations?

[Kirana Kumara P]

I am wondering whether it would be possible for the analog circuitry itself to change DURING the time an analog computer does computations.

Over and above the above mentioned question, is it possible that the circuitry itself can change DURING simulations, while this change in the circuitry is decided by the result of the calculations during the previous step (while solving a problem).

I am asking the above question because I have not come across any example where an analog computer changes its circuitry (connections) DURING simulations. Or, the circuitry (connections) is constructed (wired) before the computations (simulations) start, and once a computation starts, the circuitry cannot change during that particular run.

Of course, I know that a circuitry can be re-wired to carry out some other computation.

And of course, the terms "circuitry", "connections", and "analogue computer" above may be interpreted in very general sense. I am aware that "re-wiring" need not necessarily involve manually re-wiring the circuitry ("re-wiring" may be accomplished using software tools).

I believe that if at all it is possible for the circuitry itself to change DURING simulations, it may be advantages to use analog computers instead of digital computers while solving certain problems.

Hope I am clear and looking for an answer.

Thanks and best regards,
Kirana Kumara P

 

[LvW]

Of course, you can modify any component value (amplifier, integrator,..) DURING a simulation with an ANALOG computer. This is not a problem because an anlaog computer is nothing else than an electronic analog circuitry consisting of amplifiers, analog summing circuits, integrators, voltage dividers,..).
Furthermore, there are block-based DIGITAL simulation packages (e.g. VISSIM) which also allow parameter changes during simulations in the time domain.

 

[anorlunda]

I agreed with @LvW , of course they can.

Even ancient analog computers from the 50s and 60s (programmed with plug cords) could have switches and relays that switch the equations being solved.

 

[Kirana Kumara P]

Of course, you can modify any component value (amplifier, integrator,..) DURING a simulation with an ANALOG computer. This is not a problem because an anlaog computer is nothing else than an electronic analog circuitry consisting of amplifiers, analog summing circuits, integrators, voltage dividers,..).
Furthermore, there are block-based DIGITAL simulation packages (e.g. VISSIM) which also allow parameter changes during simulations in the time domain.

Thank you for your reply. I wish to know answers to two more points: 1) Whether the "connections" can also change DURING a simulation 2) Whether the change in the component value and the change in the "connections" could be automatically calculated (decided) depending on a result that is already computed (but this result computed DURING the SAME simulation).

 

[LvW]

(1) Yes - why not? However, in the time slot between both connection states you have undefined conditions, of course. More than that, this seems meaningful only in case you have a continuous input signal (and not a step).
(2) This means that you will have an additional control loop which connects the output (decision maker) with one part of the circuit. In such a case, you must be careful in order to avoid self-excitement (stability problems).

 

[jim hardy]

In the early sixties i was a wireman on an assembly line building hybrid computers, analog computer controlled by a programmed digital one. They were destined for Cape Canaveral .
One of the assemblies i made was an array of multiturn potentiometers with little servomotors to turn the knobs. Of course today you'd use digital potentiometers.. That'd do part of what you propose.

Digital computers soon afterward got fast enough to replace most analog .

Doesn't a simple diode or analog comparator do what you suggest ?
What's your application ?

 

[Kirana Kumara P]

In the early sixties i was a wireman on an assembly line building hybrid computers, analog computer controlled by a programmed digital one. They were destined for Cape Canaveral .
One of the assemblies i made was an array of multiturn potentiometers with little servomotors to turn the knobs. Of course today you'd use digital potentiometers.. That'd do part of what you propose.

Digital computers soon afterward got fast enough to replace most analog .

Doesn't a simple diode or analog comparator do what you suggest ?
What's your application ?

Thank you for your reply. In fact I am a mechanical engineer and do not know much about electrical circuits. I knew that an analog computer can be programmed using a digital computer (thus making it a hybrid computer in fact). But I was under the impression that this "programming/"building" the circuitry" is possible only before a simulation starts; I thought that once a simulation starts (in other words, once an analog computer starts solving one particular problem), neither the analog "circuitry" (by "circuitry" I mean "connections") nor any of the parameters of the components in the circuitry can be changed. But as per the above replies from LuW, one can change the connections as well as parameters DURING a particular simulation.

My (speculative) application is in the area of the real-time simulation of biological organs (here very complicated calculations need to be completed within a very small fraction of a second). As of now, digital computers are incapable of meeting the requirement of real-time performance.

 

[Kirana Kumara P]

(1) Yes - why not? However, in the time slot between both connection states you have undefined conditions, of course. More than that, this seems meaningful only in case you have a continuous input signal (and not a step).
(2) This means that you will have an additional control loop which connects the output (decision maker) with one part of the circuit. In such a case, you must be careful in order to avoid self-excitement (stability problems).

Thank you once again for your replies. It would be helpful if you could answer the following questions also:

1) Why do we need to have a continuous input signal (why not a step)?
2) Is the self-excitation problem avoidable by a good design (at least to some extent so that it would not pose practical difficulties)?

(Just for information, I am a mechanical engineer and do not know much about electrical circuits.)

 

[Kirana Kumara P]

(1) Yes - why not? However, in the time slot between both connection states you have undefined conditions, of course. More than that, this seems meaningful only in case you have a continuous input signal (and not a step).
(2) This means that you will have an additional control loop which connects the output (decision maker) with one part of the circuit. In such a case, you must be careful in order to avoid self-excitement (stability problems).

Could you provide some quantitative idea about the time needed to change the connections and/or parameters when compared to the time required for the "simulations" (Of course, in an analog computer the time required for the "simulations" is negligibly small).

This is because I am thinking on the possibility of achieving real-time simulation of biological organs by building a suitable analog computer. I am thinking about analog computers because it is incredibly fast. I should be able to change the connections/parameters DURING the simulations because the geometry of biological organs can change DURING the simulations. Of course, for the time being I am not bothered about what would happen during the time the connections/parameters are changed. Hence I would get the solution using an analog computer for a particular set of connections/parameters; the solution can be obtained in real-time since I am using an analog computer. Next, if there is a change in the geometry of biological organs (because of a surgical cut, say), I would change the connections and parameters, and then I would again get the solution in real-time. But since I am interested to simulate the surgical cut in real-time (which means that I should be able to complete the solution within a very small fraction of a second), using analog computer will not solve my problem if changing the connections/parameters several times (which corresponds to cutting incrementally) cannot be completed within a very small fraction of a second.

Hence I wish to know whether the whole simulation (including the task of changing the connections/parameters) can be completed within a very small fraction of a second if one can build a suitable analog computer. (Of course, individual simulations can be completed within a very small fraction of a second if one goes for an analog computer. The term "individual simulations" here means solving for a particular set of connections and parameters.)

 

[LvW]

But as per the above replies from LuW, one can change the connections as well as parameters DURING a particular simulation.

Please note that this option is not available (as far as I know) for SPICE-based circuit simulation programs.
In this context, I have mentioned BLOCK-oriented programs only (like VISSIM).

Thank you once again for your replies. It would be helpful if you could answer the following questions also:
1) Why do we need to have a continuous input signal (why not a step)?
2) Is the self-excitation problem avoidable by a good design (at least to some extent so that it would not pose practical difficulties)?

1) The step response consists of a transient starting at t=0. If - during the response time - the system is changed by switchung between two states the transient (which you are interested in) is destroyed because intial conditions are altered.
2.) Yes - of course. However, you need to be familiar with feedback theory and stability criteria.

 

[f95toli]

This is because I am thinking on the possibility of achieving real-time simulation of biological organs by building a suitable analog computer. I am thinking about analog computers because it is incredibly fast.

But not as fast as a digital computer. The Strong Church Thesis tells us that any analog computer can be efficiently simulated using a digital computer. Since digital circuits are much, much faster than analog circuits it follows that there is nothing to be gained by this method in terms of speed.

Note that the speed of analog computers is limited by the same factors that limits the speed of any other analog circuits; there will always be some time associated with transferring information around a circuit and we do not have efficient memories or buffers to make this process easier.

 

[Baluncore]

This topic is all a bit hypothetical. Maybe you could give us some idea of the form of the equations that need to be solved. Many of us have years of electronic computation experience and know ways of doing quite complex things very simply and quickly.

It would be a pity to attach your project to analogue computing if there was a more flexible digital solution available. I would be quite surprised if we could not digitally out-compute an analogue computer with an array of digital RISC or signal processors.

On the other hand, if there were simple analogue solutions, we would probably recognise them quite quickly.

 

[Kirana Kumara P]

This topic is all a bit hypothetical. Maybe you could give us some idea of the form of the equations that need to be solved. Many of us have years of electronic computation experience and know ways of doing quite complex things very simply and quickly.

It would be a pity to attach your project to analogue computing if there was a more flexible digital solution available. I would be quite surprised if we could not digitally out-compute an analogue computer with an array of digital RISC or signal processors.

On the other hand, if there were simple analogue solutions, we would probably recognise them quite quickly.

My problem is to solve a set of coupled nonlinear partial differential equations over an arbitrary region (solution region). I may also use numerical techniques like the finite difference method or the finite element method to get the solutions. Do you think it is impossible to obtain faster solutions using analog computers when compared to digital computers, when the set of equations, boundary conditions, and the solution region are specified?

 

[anorlunda]

My problem is to solve a set of coupled nonlinear partial differential equations over an arbitrary region (solution region). I may also use numerical techniques like the finite difference method or the finite element method to get the solutions. Do you think it is impossible to obtain faster solutions using analog computers when compared to digital computers, when the set of equations, boundary conditions, and the solution region are specified?

You must put numbers on it before we can answer. We have no idea what you mean by fast.

 

[Baluncore]

Do you think it is impossible to obtain faster solutions using analog computers when compared to digital computers, when the set of equations, boundary conditions, and the solution region are specified?

It might be that your non-linear equations perfectly fit some electronic analogue. Without seeing the form of the equations, and the non-linearity, it is impossible to tell.

An analogue computer can get trapped in a dead end as easily as a digital computer. With the digital computer you can repeat the failure exactly and analyse the problem. Because of analogue noise, an analogue computer will not always take the same path to a destination so it is difficult to repeat a failure for analysis.

I believe the digital simulation of an analogue computer has for some time now been faster and more accurate than the analogue computer itself.

 

[jim hardy]

it is incredibly fast. I should be able to change the connections/parameters DURING the simulations because the geometry of biological organs can change DURING the simulations.

The idea that animal tissue can outrun a computer just doesn't ring true for me.
Nerve impulses move only around 400 ft/sec i was taught. A physical cut proceeds only as fast as a scalpel can move . Or are you simulating something more kinematic like a high power laser ?


As fascinating as it'd be to do this analog
i recommend you write a program with one of your finite element solutions , have it access a timer and report how many microseconds elapsed during execution.

I did something similar on an embedded microcontroller running interpreted Basic which is really slow . It was for a crane weigh cell that put out an ASCII string every 0.3 second representing the weight on the hook, some tens of tons. That ASCII number had to be converted to analog voltage with a DAC and handed to a monitor that compared tension to strain gages looking for unexpected deformation..
I had it set one output line high at routine start and set it back low at when finished. Watching that line with a 'scope i could see how long it took.
Wow did i learn about streamlining a program with that one ! Cut my execution time by 75% with common sense things like eliminating loops and unnecessary calculations..

So my point is
If your criterion for "Extremely Fast" is what you can perceive with your senses, i think you need to familiarize yourself with just what the digital guys can do nowadays.
Search on DSP IC" .

old jim

 

[Kirana Kumara P]

You must put numbers on it before we can answer. We have no idea what you mean by fast.

By "fast" I mean that I should be able to complete the calculation within 30 milliseconds. It would be even better if I could complete the calculations within 1 millisecond.

 

[anorlunda]

But not as fast as a digital computer. The Strong Church Thesis tells us that any analog computer can be efficiently simulated using a digital computer. Since digital circuits are much, much faster than analog circuits it follows that there is nothing to be gained by this method in terms of speed.

Huh? Your definitions must not match mine. Two electrons experiencing Coulomb force are an analog computer that runs instantaneously. A resistor with voltage applied instantaneously solves Ohm's Law (or Maxwell's Equations if you prefer.). How could digital be faster than that?

 

[anorlunda]

By "fast" I mean that I should be able to complete the calculation within 30 milliseconds. It would be even better if I could complete the calculations within 1 millisecond.

Do you mean that to simulate the process in real time, you would like to calculate 1 ms of elapsed time in 1 ms of computer time?

Most of today's CPUs can accomplish very complicated things in 1ms.

 

[f95toli]

Huh? Your definitions must not match mine. Two electrons experiencing Coulomb force are an analog computer that runs instantaneously. A resistor with voltage applied instantaneously solves Ohm's Law (or Maxwell's Equations if you prefer.). How could digital be faster than that?

I guess it depends on what you mean by a computer. This is far outside my expertise, all I know about this comes from reading about e.g. adiabatic quantum computing and whether the D-Wave computer (which if it is classical is analog) is faster than a digital computer.
However, I think the point is that the time required for a digital computer to solve a given problem is bounded by a polynomial function of the resources used by the analog computer.
According to one of my review articles one standard reference where my statement is discussed in more details (although it mainly deals with the NP completeness etc)

Vergis, Anastasios, Kenneth Steiglitz, and Bradley Dickinson. "The complexity of analog computation." Mathematics and computers in simulation 28.2 (1986): 91-113.

You can find a PDF of the article online.

Also, the following is somewhat more readable
https://www.cs.princeton.edu/courses/archive/fall06/cos576/papers/yao_acm03.pdf

(see the bit about the ECT)

One interesting consequence of this is that physical systems of any kind can not solve NP complete problems.

Also, on somewhat related note, I recently saw a talk about work on using superconducting electronics to simulate neurons; although the circuit was still digital.

 

[Kirana Kumara P]

I believe the digital simulation of an analogue computer has for some time now been faster and more accurate than the analogue computer itself.

I can interpret the term "digital simulation of analog computer" these ways:

1) There are software packages for normal digital computers which can "build" the circuits virtually, and then simulate on the digital computers how the circuit behaves when subjected to a given input. The software packages can even predict the time required to solve a problem on the analog computer/circuit, without really building a prototype of the analog computer.

2) Manually writing the code for the normal digital computers, where the code delivers the same results (or almost the same results) when compared to the results that would have been obtained if an analog computer was used for the calculations (instead of the digital computer). Here, the code for the normal dital computer should describe/model the analog computer in mind.

3) Hybrid computer, where the coding is done on the normal digital computer, and then transferred to a processor which is a sufficiently general-purpose circuit/processor.

Right now I have assumed that you mean point number 2) while saying "digital simulation of analog computer". I request you to please correct me if my interpretation of the phrase is wrong.

 

[Baluncore]

Right now I have assumed that you mean point number 2) while saying "digital simulation of analog computer". I request you to please correct me if my interpretation of the phrase is wrong.

 

[Kirana Kumara P]

I am grateful to everyone who has replied to my thread. I have got answers from this forum to many of my questions.

Apart from thinking about a project, the reason I picked up the topic is because I thought it would be great if it is possible for analog computers to change the connections and parameters DURING simulations. It is really a great news that during a simulation, the connections and parameters can change depending on the result from the previous computation that is carried out during the same simulation. This may be a step towards a "general purpose analog computer".

I wish to know how fast or how slow it would be to change the connections and parameters DURING a simulation, i.e., is there anything like "the time required to change the connections and parameters is much more than the time required for the true simulation part" or "the time required to change the connections and parameters is negligible" or "the ratio of the time required to change the connections and parameters to the time required for the true simulation part is problem/circuit/parameters dependent" etc. If it happens to be the case that "the time required to change the connections and parameters is negligible", it would be a great news for those who would like to see analog computers competing with digital computers (at least while solving certain specific problems).

We may see that in a normal digital computer, transistors can change their states several times a second. This is nothing but changing the "connections", and this happens very fast. Same way, is it possible for analog computers to change their "connections" very fast, that too DURING simulations?

The true reason that I started this thread is that I believed that it would be really great if analog computers possesses the following three properties: 1) they can change their connections and/or parameters DURING a simulation 2) it takes extremely small amount of time to change the connections and/or parameters 3) the connections and parameters can change automatically DURING a simulation, depending on the result from the previous computation that is carried out during the same simulation. I believed that if all of the above three points happen to be true, that can result in an analog computer that can outsmart digital computers (at least while solving certain specific problems which have important applications, e.g., surgery/surgical simulation). I wanted to know whether what I believed is true and whether the three points mentioned above are true.

 

[Kirana Kumara P]

As fascinating as it'd be to do this analog
i recommend you write a program with one of your finite element solutions , have it access a timer and report how many microseconds elapsed during execution.
old jim

Several researchers have tried to get nonlinear finite element solutions using digital computers. They tried to obtain the solutions within 30 milliseconds but without success. Even employing clusters or supercomputers has not been successful since that involves inefficient data transfers between processors. Hence the thoughts about going for analog computing.

Nonlinear finite elements invariably require the solution of a set of nonlinear simultaneous algebraic equations. Would it be possible to obtain this solution within 30 milliseconds if one goes for analog computing?

 

[Baluncore]

Would it be possible to obtain this solution within 30 milliseconds if one goes for analog computing?

It depends on the equations being solved.

 

[jim hardy]

Are you up to something like this ?
https://blogs.scientificamerican.co...groundbreaking-simulation-of-the-human-heart/

Nonlinear finite elements invariably require the solution of a set of nonlinear simultaneous algebraic equations.

hmmm how many equations in that set? You might need one analog computer per equation.
I'm assuming these equations are f(time) ?
The little bit of analog computing I've done gives continuous solution as time rolls by.
One can scale it to run faster or slower than real time.

With what will you monitor its output(s) ?

 

[Baluncore]

The problem with FE methods is that all elements communicate with their immediate neighbours. That must be true for both analogue and digitally implemented arrays of processors. The problem with an analogue array is that each must be built and connected, initialised and then started. If you have 10,000 nodes you will need 10,000 analogue processors. A digital processor on the other hand can quickly switch algorithm or be reloaded with the next problem. It has more flexibility. It takes time to read an analogue voltage maybe 1usec, or to charge a capacitor to a specified voltage, say 10usec. Loading a digital register now takes only a few nanoseconds.

There are digital arrays like these now beginning to appear that will make a big difference to FEM.
https://www.parallella.org/2016/10/05/epiphany-v-a-1024-core-64-bit-risc-processor/

http://www.hotchips.org/wp-content/uploads/hc_archives/hc28/HC28.23-Tuesday-Epub/HC28.23.70-Many-Core-Epub/HC28.23.720-KiloCore-BrentBohnenstiehl-v06-41.pdf

 

[Kirana Kumara P]

Are you up to something like this ?
https://blogs.scientificamerican.co...groundbreaking-simulation-of-the-human-heart/



hmmm how many equations in that set? You might need one analog computer per equation.
I'm assuming these equations are f(time) ?
The little bit of analog computing I've done gives continuous solution as time rolls by.
One can scale it to run faster or slower than real time.

With what will you monitor its output(s) ?

My project is something similar. But the differences are:
1) I am happy with just the macroscopic level (no multiscale modelling)
2) I am happy with just solid mechanics (multiphysics is not a necessity)
3) But in my case one should be able to obtain one complete solution within 30 milliseconds

I may need around five thousand equations in the set for the modelling to be reasonably accurate. More the equations, more accurate the modelling is going to be. However, slightly lesser number of equations (say three thousand equations, or one thousand equations in the worst case) are also okay (here I am ready to sacrifice some amount of accuracy as a trade off for speed).

Equations (i.e., a particular set of equations) are not time dependent.

However, the set of equations can change over the time. This may need change in the connections and parameters of the analog circuit. Changing the connections and/or parameters should not take too much time.

Ideally, I should be able to solve 30 different sets of equations in one second (the number 30 assumes significance because, for visual continuity, one needs about 30 frames per second, like for a reasonably good video, one needs to have 30 still photos per second). In the worst case, I should be able to solve 10 different sets of equations (each set having about 5000 equations) in one second. Of course, the time required to change the connections and/or parameters should also be included in this one second time interval.

 

[Kirana Kumara P]

The problem with FE methods is that all elements communicate with their immediate neighbours. That must be true for both analogue and digitally implemented arrays of processors. The problem with an analogue array is that each must be built and connected, initialised and then started. If you have 10,000 nodes you will need 10,000 analogue processors. A digital processor on the other hand can quickly switch algorithm or be reloaded with the next problem. It has more flexibility. It takes time to read an analogue voltage maybe 1usec, or to charge a capacitor to a specified voltage, say 10usec. Loading a digital register now takes only a few nanoseconds.

There are digital arrays like these now beginning to appear that will make a big difference to FEM.
https://www.parallella.org/2016/10/05/epiphany-v-a-1024-core-64-bit-risc-processor/

http://www.hotchips.org/wp-content/uploads/hc_archives/hc28/HC28.23-Tuesday-Epub/HC28.23.70-Many-Core-Epub/HC28.23.720-KiloCore-BrentBohnenstiehl-v06-41.pdf

Let us assume that we can find a good electrical analogy for our problem in hand. Then it may be possible to get faster solutions using an analog computer (when compared to digital computers) if building, connecting, initialising, and starting does not take too much time (10 microsecond delay is okay for me since I have 30 milliseconds to complete "one simulation"; here "one simulation" includes the time required to change the connections and parameters, initialize, start etc. once). Of course, I have made use of some of the replies in this thread to arrive at this conclusion. Please correct me if I am wrong.

Regarding the links, many a times lesser general-purpose processors are not as useful as they appear to be, while solving complicated problems. For example one may follow this link on GPUs:
http://dl.acm.org/citation.cfm?id=1816021

 

[Baluncore]

Let us assume that we can find a good electrical analogy for our problem in hand.

There is no problem in hand, because you have not yet presented a single example equation, let alone a set of equations for any processor. It is time to stop hypothesising and get real.

Let's instead make the safe assumption that there is a digital algorithm that runs at 100 times the speed of an analogue computer and can be reprogrammed on the fly. Indeed, nine of those kilo-processor arrays would give you a 96 x 96 processor array with 9216 elements. There is no way an analogue computer could be built and calibrated before a digital processor array finished that and many other jobs.

Intel manufactures CPUs. I do not trust a committee of twelve Intel employees when they set out to denigrate multiple GPUs, claiming that Intel CPUs are better. It suggests Intel have stagnated and are now being threatened by multiple GPUs.

 

[analogdesign]

But not as fast as a digital computer. The Strong Church Thesis tells us that any analog computer can be efficiently simulated using a digital computer. Since digital circuits are much, much faster than analog circuits it follows that there is nothing to be gained by this method in terms of speed.

Note that the speed of analog computers is limited by the same factors that limits the speed of any other analog circuits; there will always be some time associated with transferring information around a circuit and we do not have efficient memories or buffers to make this process easier.

I'm not familiar with the Strong Church Thesis but I can tell you that the fastest signal processing systems have always been analog systems. Most communications technologies (voiceband, RF, hard-disk read channel, fiber optics, etc) start out as analog because digital isn't fast enough and eventually turn digital once the technology catches up.

For a current example, the highest rate communications channels (for example, DDR4 and 40G+ ethernet) use primarily analog signal paths. An analog equalizer and decision circuit is much, much faster than an ADC followed by a DSP. 40G systems are moving to ADC-based architectures now but analog signal processing is still competitive. A digital computer could in principle "simulate" an analog equalizer, but I assure you it wouldn't be faster or more efficient.

I would say general purpose analog computing is done because digital computers are so good at "simulating the simulations". However, analog signal processing is still alive and well and mostly working in the communications and imaging spaces.

 

[Baluncore]

A digital computer could in principle "simulate" an analog equalizer, but I assure you it wouldn't be faster or more efficient.

In that example the analogue signal is real time, so both the digital processor and analogue systems are operating in real time, both waiting for the next data. But since the continuously changing state variables in an analogue equaliser can only be stored in analogue components, usually capacitors, the analogue system can only ever equalise one channel, while a digital signal processor could equalise a great many channels in parallel, all at the same time. That is where the efficiency of digital systems arises. The digital system never needs to be calibrated as unstable components drift off value with to heat and time.

I would say general purpose analog computing is done because digital computers are so good at "simulating the simulations". However, analog signal processing is still alive and well and mostly working in the communications and imaging spaces.

What do you mean by "is done"? Do you mean "is now dead and gone", or "is still used today"?

There is a big difference between building parallel arrays of analogue computers to solve non-linear differential equations, and using RF technology to receive and demodulate one signal channel. Signal processing using algorithms like digital IQ mixing, the DFT and digital filtering is rapidly replacing analogue signal processing. Look at the world of SDR where only the front-end down-converter is still analogue.

Analogue computing was replaced by digital processors many decades ago.

 

[analogdesign]

In that example the analogue signal is real time, so both the digital processor and analogue systems are operating in real time, both waiting for the next data. But since the continuously changing state variables in an analogue equaliser can only be stored in analogue components, usually capacitors, the analogue system can only ever equalise one channel, while a digital signal processor could equalise a great many channels in parallel, all at the same time. That is where the efficiency of digital systems arises. The digital system never needs to be calibrated as unstable components drift off value with to heat and time.

I do not agree with this. Typically a communication system migrates to digital implementation for functionality and cost reasons, not efficiency. The capacitor here is analogous to a register. Just as you can have multiple registers (in memory or physically) you can have arrays of capacitors to do multiple channels in parallel. I worked on an integrated analog signal processor (in this century) that had 10s of thousands of physical equalizer channels. It would have been impossible to process this volume of data digitally using FPGAs or even custom digital ASICs because of power and area constraints. Remember the power of an ADC goes up about 4X per bit (if it is noise limited), so keeping the data in the analog domain when feasible is an excellent power-saving technique (it creates its own problems, of course). In my experience, an analog solution is almost always lower power than a competing digital solution, but it loses out in development cost, design time, functionality, and ease of use and integration in a larger system. But it wins on power, and that is why analog solutions still find use in practice.

I completely agree that as time goes on applications that were once served by analog signal processing (out of necessity) migrate to digital processing for various reasons. However, analog techniques are continuously applied to new, faster, or more power-sensitive applications. For the foreseeable future I believe analog signal processing will still be of interest.

What do you mean by "is done"? Do you mean "is now dead and gone", or "is still used today"?

I wasn't clear enough here. I meant "dead and gone". As you said, general purpose analog computers (and hybrid computers) were for the most part gone by the early 1980s and by then only used in very specialized applications (such as aerodynamics simulation).

There is a big difference between building parallel arrays of analogue computers to solve non-linear differential equations, and using RF technology to receive and demodulate one signal channel. Signal processing using algorithms like digital IQ mixing, the DFT and digital filtering is rapidly replacing analogue signal processing. Look at the world of SDR where only the front-end down-converter is still analogue.

Analogue computing was replaced by digital processors many decades ago.

Indeed, although be sure you define what you mean by "one channel". Typically in a celluar basestation (where I have some design experience, and these days are implemented as SDRs) the intermediate frequency (or the baseband if a ZIF architecture is used) is sampled and an entire band of channels is digitized at once. So, the analog front end processes a great many (100s) of channels simultaneously. Lastly, I would submit that the front end of any DSP, namely the ADC, is itself a sophisticated analog signal processor, although how much analog processing it does depends strongly on the architecture (SAR vs Pipelined vs Sigma-Delta).

I guess my point in all of this was to show that rather sophisticated analog signal processing is still used in practical systems, although it is "under the hood". Certainly no one these days would use a general-purpose analog computer. It would make no sense except I suppose as a hobby project.

 

[Kirana Kumara P]

I am very much grateful to all those who have replied to my questions.

I am still not very clear whether the time required to change the connections is significant when compared to the time required for the simulation.

Of course, the answer to the above question may be problem dependent. However, let us for now assume that I can come up with a good electrical analogy for a problem in my mind. I think how I can come up with a suitable electrical analogy could itself be a research problem. And I may try to find a solution to the research problem only if there is a possibility of finding a solution to the research problem. Hence the above question.

To be clearer, I may define my research problem as a set of coupled nonlinear partial differential equations involving three variables (that correspond to three dimensions). The equations have to be solved over a 3D region of arbitrary shape (the solution domain is a specified 3D region). Now approximating the equations together with the geometry to an analog computer itself could be a serious research problem.

One of the methods of solving the above problem could be to make use of the finite element method (although it may be possible to solve the differential equations directly by building a suitable analog computer, without making use of the finite element method). The finite element method enables one to approximate the set of differential equations by a set of nonlinear simultaneous algebraic equations (but here each of the equations in the set of algebraic equations can contain hundreds of terms). Again, building an analog computer that can carry out this simulation could itself be a research problem.

Now coming to the details of the simulation, there can be change in the geometry (or solution domain or solution region) during simulations. But let us assume that this change in geometry can be properly addressed by substituting the whole simulation by a set of simulations; for each of the individual simulations within the set, there is no change in the geometry during the (individual) simulations. Now each of the individual simulations correspond to a particular network of connections, and when one switches from one individual simulation to the next individual simulation, network of connections would change. I am worried whether this switching would take significant amount of time. For now let us assume that I would come up with a really good electrical analogy so that the time required for the individual simulations is negligibly small (of course, this is the idea behind choosing an analog computer over a digital computer). Still, we can expect the analog computer to be faster than a digital computer only if changing the connections (or switching) does not take significant amount of time.

My goal is not to prove that an analog computer is faster than a digital computer or vice versa. I want to complete a whole simulation within one second. The whole simulation consists of a set of thirty individual simulations. Each of the individual simulations require a particular configuration of connections, while the configuration of connections is different for each of the individual simulations. It is a well known fact that present day digital computers (even clusters or supercomputers) are not capable of providing the correct solution (they cannot complete the thirty individual simulations within one second). Hence I am curious whether one could be able to address the problem by building a suitable analog computer. I can see that building an analog computer would solve the problem if both of these hold good 1) one should be able to find a very good electrical analogy 2) the time required to change the connections (or the network of connections) should be sufficiently small. Assuming that it is possible to find a very good electrical analogy, the success of the analog computer to be built depends on whether one can change the network of connections within a sufficiently small time interval. Since finding a suitable electrical analogy would require significant amount of work, I would involve myself in that task only if there is a possibility that it is possible to change the network of connections within a sufficiently small time interval.

 

[anorlunda]

I am worried whether this switching would take significant amount of time.

We can not possibly answer that without knowing how long you define significant. Let's say that a relay switches in 10 milliseconds. Is that significant?

Your description of the problem does not describe any dynamics at all. It is the dynamics (i.e. range of interest in the frequency domain) that determine the needs of switching. Indeed, your description sounds like the problem may be static, with no dynamics at all.

If you have a nonlinear 3D problem, the required granularity is also a critical parameter. If you represented it with finite elements, how many elements would you need?

The quality of answers you receive here depends strongly on the quality of the question description. You are asking for design advice. In engineering, requirements specifications always precede design.