Digital, or analog?

It seems to me important to agree on criteria for deciding whether a 
particular circuit or signal is digital or analog

One criterion is intended use; there seems to be general agreement about 
that, so I don't address it here. Another criterion is the nature if the 
signal or circuit itself, without reference to intentions. That is the 
topic of this short essay.

*SIGNALS*
A digital signal consists of a sequence of a fixed number of discrete 
states, with no intermediate states are allowed. Outside the realm of 
quantum mechanics, a continuous signal is not digital. It can be made 
digital by quantizing it, and different quantizers will convert the same 
analog signal into different quantized signals. As far as I know, 
digital signals exist only as abstractions and in computer circuits. I 
would be delighted to learn of exceptions.

*CIRCUITS*
A circuit intended for a digital application has a fixed number of 
discrete input and output states. The useful states are limited to those 
common to both input and output. For simplicity of design, the number of 
states is usually chosen to be 2, although other arrangements are 
possible and some have been utilized. States are represented at outputs 
as voltage or current ranges, and recognized at inputs in the same way. 
The thresholds need not be the same at input or output. For example, the 
specification for the 74LS logic family requires a high-level (1) to 
equal or exceed 2 volts and a low level (0) to be no more than .8 volts 
at the input, and guarantees that a 1 will be at least 2.4 volts and a 0 
no more than .5 volts at the output. That specification makes the 
devices well suited for digital use, but it defines them as analog 
devices by defining voltages which are, as far as states go, ambiguous.

A CMOS CD4011B makes that point better. It is a quad 2-input NAND gate. 
With a 15-volt supply, a 1 is 11 volts or greater, and a 0 is 4 volts or 
less. The output swings between .05 and 14.95 volts when lightly loaded, 
and can sink or source more than 5 ma at 4 and 11 volts. The /intended/ 
use of a NAND gate makes it digital devices, but these are inherently 
analog by construction. Their inherent analog nature seen by connecting 
a 1 megohm resistor from output to the inputs tied together.  You will 
have an analog amplifier with 23dB voltage gain and much higher power 
gain. With capacitive coupling, the four gates can be connected as two H 
bridges that will deliver 18 milliwatts per channel into 1500 ohms. To 
be truly digital, a device must have discrete states, and be incapable 
of exhibiting any other state.

That situation is approximated by cross coupling a pair of the gates to 
make a set-reset flip-flop. Now there are only two stable states, but 
the in-between states still exist as transient states passed through 
when the device is in transition. Rise and fall times greater than zero, 
and the well known but often ignored metastable state attest to that. 
http://www.interfacebus.com/Design_MetaStable.html As far as I know, 
digital circuits exist only as abstractions and on schematics. I would 
be delighted to learn of exceptions.

Jerry
-- 
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
���������������������������������������������������������������������

On Wed, 01 Nov 2006 15:40:51 -0500, Jerry Avins <jya@ieee.org> wrote:

>It seems to me important to agree on criteria for deciding whether a 
>particular circuit or signal is digital or analog
>
>One criterion is intended use; there seems to be general agreement about 
>that, so I don't address it here. Another criterion is the nature if the 
>signal or circuit itself, without reference to intentions. That is the 
>topic of this short essay.
>
>*SIGNALS*
>A digital signal consists of a sequence of a fixed number of discrete 
>states, with no intermediate states are allowed. Outside the realm of 
>quantum mechanics, a continuous signal is not digital. It can be made 
>digital by quantizing it, and different quantizers will convert the same 
>analog signal into different quantized signals. As far as I know, 
>digital signals exist only as abstractions and in computer circuits. I 
>would be delighted to learn of exceptions.
>
>*CIRCUITS*
>A circuit intended for a digital application has a fixed number of 
>discrete input and output states. The useful states are limited to those 
>common to both input and output. For simplicity of design, the number of 
>states is usually chosen to be 2, although other arrangements are 
>possible and some have been utilized. States are represented at outputs 
>as voltage or current ranges, and recognized at inputs in the same way. 
>The thresholds need not be the same at input or output. For example, the 
>specification for the 74LS logic family requires a high-level (1) to 
>equal or exceed 2 volts and a low level (0) to be no more than .8 volts 
>at the input, and guarantees that a 1 will be at least 2.4 volts and a 0 
>no more than .5 volts at the output. That specification makes the 
>devices well suited for digital use, but it defines them as analog 
>devices by defining voltages which are, as far as states go, ambiguous.
>
>A CMOS CD4011B makes that point better. It is a quad 2-input NAND gate. 
>With a 15-volt supply, a 1 is 11 volts or greater, and a 0 is 4 volts or 
>less. The output swings between .05 and 14.95 volts when lightly loaded, 
>and can sink or source more than 5 ma at 4 and 11 volts. The /intended/ 
>use of a NAND gate makes it digital devices, but these are inherently 
>analog by construction. Their inherent analog nature seen by connecting 
>a 1 megohm resistor from output to the inputs tied together.  You will 
>have an analog amplifier with 23dB voltage gain and much higher power 
>gain. With capacitive coupling, the four gates can be connected as two H 
>bridges that will deliver 18 milliwatts per channel into 1500 ohms. To 
>be truly digital, a device must have discrete states, and be incapable 
>of exhibiting any other state.
>
>That situation is approximated by cross coupling a pair of the gates to 
>make a set-reset flip-flop. Now there are only two stable states, but 
>the in-between states still exist as transient states passed through 
>when the device is in transition. Rise and fall times greater than zero, 
>and the well known but often ignored metastable state attest to that. 
>http://www.interfacebus.com/Design_MetaStable.html As far as I know, 
>digital circuits exist only as abstractions and on schematics. I would 
>be delighted to learn of exceptions.
>
>Jerry

Jerry, that's good work on a rational foundation for the terms.

I think, however, that the significant quibbling comes in only on
boundary cases where the distinction gets blurred, and it's just
always going to be tough to avoid semantic arguments popping up there.
For example, even with "digital" devices, by your definitions, at both
ends of a circuit board trace, the trace may still need carefully
designed termination and interference isolation which are often best
treated as "analog" phenomena.

Although your definitions generally hold, there's still plenty of room
for argument and confusion at the boundaries.  Because of that, I
don't think the problem of whether certain things are really "digital"
or "analog" is going to be solved with world-class
unanimously-approved definitions.

Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org

Jerry Avins wrote:
> It seems to me important to agree on criteria for deciding whether a
> particular circuit or signal is digital or analog
...
> As far as I know, digital circuits exist only as abstractions ...

I remember an old-time engineer once telling me "There
is no such thing as digital".  We merely interpret certain
behaviors of analog circuits as transitions, noise, or
metastability, etc. and then attempt to ignore those for
our convenience, or at our own peril.

Of course, he was talking about the real world.  We are
free to make abstract models, but should not confuse
a model with some engineering reality, especially if
a circuit is working near its limits of behaving similar
to our first-order models.

So I would agree with you that digital circuits exist only
as abstractions.

However, there is also no such thing as analog.  It is
merely a model where we assume that some continuous
curve or function is associated with our measurements
of what are actually numbers discrete quantum events
(the measurements are usually far too course to
notice the error).

If the quantum events are below some noise floor and
you are already ignoring this noise floor, then a continuous
model might be the computationally or cognitively more
efficient tool of abstraction.

So, as to the question about whether some circuit or
signal is digital or analog, I would say the answer
depends on which model best serves your specific
purpose or question regarding the given circuit or signal.

For some things DSP engineers do, the answer might
well be both.


IMHO. YMMV.
-- 
rhn A.T nicholson d.0.t C-o-M

Jerry Avins wrote:
> [snip much]
 > As far as I know,
> digital circuits exist only as abstractions and on schematics. I would 
> be delighted to learn of exceptions.
> 

electo-mechanical relays

'nuff said ;)

Jerry Avins wrote:

> It seems to me important to agree on criteria for deciding whether a
> particular circuit or signal is digital or analog
> 
> One criterion is intended use; there seems to be general agreement about
> that, so I don't address it here. Another criterion is the nature if the
> signal or circuit itself, without reference to intentions. That is the
> topic of this short essay.
> 
> *SIGNALS*
> A digital signal consists of a sequence of a fixed number of discrete
> states, with no intermediate states are allowed. Outside the realm of
> quantum mechanics, a continuous signal is not digital. It can be made
> digital by quantizing it, and different quantizers will convert the same
> analog signal into different quantized signals. As far as I know,
> digital signals exist only as abstractions and in computer circuits. I
> would be delighted to learn of exceptions.
> 
> *CIRCUITS*
> A circuit intended for a digital application has a fixed number of
> discrete input and output states. The useful states are limited to those
> common to both input and output. For simplicity of design, the number of
> states is usually chosen to be 2, although other arrangements are
> possible and some have been utilized. States are represented at outputs
> as voltage or current ranges, and recognized at inputs in the same way.
> The thresholds need not be the same at input or output. For example, the
> specification for the 74LS logic family requires a high-level (1) to
> equal or exceed 2 volts and a low level (0) to be no more than .8 volts
> at the input, and guarantees that a 1 will be at least 2.4 volts and a 0
> no more than .5 volts at the output. That specification makes the
> devices well suited for digital use, but it defines them as analog
> devices by defining voltages which are, as far as states go, ambiguous.
> 
> A CMOS CD4011B makes that point better. It is a quad 2-input NAND gate.
> With a 15-volt supply, a 1 is 11 volts or greater, and a 0 is 4 volts or
> less. The output swings between .05 and 14.95 volts when lightly loaded,
> and can sink or source more than 5 ma at 4 and 11 volts. The /intended/
> use of a NAND gate makes it digital devices, but these are inherently
> analog by construction. Their inherent analog nature seen by connecting
> a 1 megohm resistor from output to the inputs tied together.  You will
> have an analog amplifier with 23dB voltage gain and much higher power
> gain. With capacitive coupling, the four gates can be connected as two H
> bridges that will deliver 18 milliwatts per channel into 1500 ohms. To
> be truly digital, a device must have discrete states, and be incapable
> of exhibiting any other state.
> 
> That situation is approximated by cross coupling a pair of the gates to
> make a set-reset flip-flop. Now there are only two stable states, but
> the in-between states still exist as transient states passed through
> when the device is in transition. Rise and fall times greater than zero,
> and the well known but often ignored metastable state attest to that.
> http://www.interfacebus.com/Design_MetaStable.html As far as I know,
> digital circuits exist only as abstractions and on schematics. I would
> be delighted to learn of exceptions.
> 
> Jerry

Yes, our world is analog, isn't it?
I agree that the digital world is an abstraction, therefore not real.

But what is our world or what is real? (keeping the technological
perspective rather than philosophical). Isn't it because our sensors
integrate incoming signals so that they appear continuous? (I prefer
continuous rather than analog, as opposed to digital). Because our world,
the real world, is what we perceive using our natural sensors. But this is
the macroscopic world, in the microscopic one (as you mentioned quantum
mechanics) it could be the other way around. The continuous signals might
be the abstraction.

Adrian

Richard Owlett wrote:
> Jerry Avins wrote:
>> [snip much]
>  > As far as I know,
>> digital circuits exist only as abstractions and on schematics. I would 
>> be delighted to learn of exceptions.
>>
> 
> electo-mechanical relays
> 
> 'nuff said ;)

Better say more. Make before break, or break before make? We're looking 
at transitions here. Even with SPST, contacts bounce

Jerry
-- 
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
���������������������������������������������������������������������

Richard Owlett wrote:
> Jerry Avins wrote:
> > [snip much]
>  > As far as I know,
> > digital circuits exist only as abstractions and on schematics. I would
> > be delighted to learn of exceptions.
> >
>
> electo-mechanical relays
>
> 'nuff said ;)

The first time I tried to make a toggle flip flop out of
relays (in junior high, I think), it went into metastable
oscillation, dependent on the power supply voltage.

Another DPDT relay (there were scavenged discards)
had one bad (randomly high resistance) contact.

Try again.  :-)


IMHO. YMMV.
-- 
rhn A.T nicholson d.0.t C-o-M

Jerry Avins wrote:

> Richard Owlett wrote:
> 
>> Jerry Avins wrote:
>>
>>> [snip much]
>>
>>  > As far as I know,
>>
>>> digital circuits exist only as abstractions and on schematics. I 
>>> would be delighted to learn of exceptions.
>>>
>>
>> electo-mechanical relays
>>
>> 'nuff said ;)
> 
> 
> Better say more. Make before break, or break before make? We're looking 
> at transitions here. Even with SPST, contacts bounce
> 
> Jerry


The contacts have *ONLY* 2 states.

No matter how much bounce, the contacts are *EITHER* "open" or "closed"

ain't no other option!


Now as to a "system", can you make it emulate 'analog'? YEPP.

Does that make relay analog? NOPE.

Disagree? well, zip is now 658xx so "SHOW ME" ;)

Richard Owlett wrote:
> The contacts have *ONLY* 2 states.
>
> No matter how much bounce, the contacts are *EITHER* "open" or "closed"

Said by somebody who's never put a VOM across a batch
of old rusted relays (scavenged from dead pinball machine
parts found in a outdoor scrap heap I think).

Your abstraction does work a bit better with new ones.


IMHO. YMMV.
-- 
rhn A.T nicholson d.0.t C-o-M

Richard Owlett wrote:
> Jerry Avins wrote:
> 
>> Richard Owlett wrote:
>>
>>> Jerry Avins wrote:
>>>
>>>> [snip much]
>>>
>>>  > As far as I know,
>>>
>>>> digital circuits exist only as abstractions and on schematics. I 
>>>> would be delighted to learn of exceptions.
>>>>
>>>
>>> electo-mechanical relays
>>>
>>> 'nuff said ;)
>>
>>
>> Better say more. Make before break, or break before make? We're 
>> looking at transitions here. Even with SPST, contacts bounce
>>
>> Jerry
> 
> 
> The contacts have *ONLY* 2 states.
> 
> No matter how much bounce, the contacts are *EITHER* "open" or "closed"
> 
> ain't no other option!

Arcing contacts? Zero risetime?

Jerry
-- 
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
���������������������������������������������������������������������